diff --git a/besseltransforms/2-1-0 b/besseltransforms/2-1-0 deleted file mode 100644 index e19fb5b..0000000 --- a/besseltransforms/2-1-0 +++ /dev/null @@ -1,2 +0,0 @@ -(-2/(Sqrt[1 + k^2/(c - I*k0)^2]*(c - I*k0)) + 1/(Sqrt[1 + k^2/(2*c - I*k0)^2]*(2*c - I*k0)) + (Sqrt[Pi]*(I*Piecewise[{{0, k0^2/k^2 <= 1}}, k/(Sqrt[-k^2 + k0^2]*Sqrt[Pi])] + Piecewise[{{k/(Sqrt[k^2 - k0^2]*Sqrt[Pi]), k0^2/k^2 < 1}}, 0]))/k)/k0 -SeriesData[k, Infinity, {-(c^2/(k^2*k0)), 0, (3*(7*c^4 - (12*I)*c^3*k0 - 6*c^2*k0^2))/(4*k^2*k0), 0, (-5*(31*c^6 - (90*I)*c^5*k0 - 105*c^4*k0^2 + (60*I)*c^3*k0^3 + 15*c^2*k0^4))/(8*k^2*k0), 0, (35*(127*c^8 - (504*I)*c^7*k0 - 868*c^6*k0^2 + (840*I)*c^5*k0^3 + 490*c^4*k0^4 - (168*I)*c^3*k0^5 - 28*c^2*k0^6))/(64*k^2*k0), 0, ((((c - I*k0)^3*(2*c - I*k0)^3)/(4*k^2) + ((-((c - I*k0)^3*(2*c - I*k0))/(2*k^2) - ((c - I*k0)*(2*c - I*k0)^3)/(2*k^2))*k0^2)/2 + (3*(c - I*k0)*(2*c - I*k0)*k0^4)/(8*k^2) + (3*(c - I*k0)^4*(2*c - I*k0)*(c/k - (I*k0)/k))/(8*k) + (3*(c - I*k0)*(2*c - I*k0)^4*((2*c)/k - (I*k0)/k))/(8*k))*(2*c^2*((c - I*k0)^5/(16*(2*c - I*k0)) - ((c - I*k0)^3*(2*c - I*k0))/16 - ((c - I*k0)*(2*c - I*k0)^3)/16 + (2*c - I*k0)^5/(16*(c - I*k0))) - (3*I)*c*((c - I*k0)^5/(16*(2*c - I*k0)) - ((c - I*k0)^3*(2*c - I*k0))/16 - ((c - I*k0)*(2*c - I*k0)^3)/16 + (2*c - I*k0)^5/(16*(c - I*k0)))*k0 + (-(c - I*k0)^5/(16*(2*c - I*k0)) + ((c - I*k0)^3*(2*c - I*k0))/16 + ((c - I*k0)*(2*c - I*k0)^3)/16 - (2*c - I*k0)^5/(16*(c - I*k0)))*k0^2 + c*((c - I*k0)^5/16 + ((c - I*k0)^3*k0^2)/16 - ((c - I*k0)*k0^4)/16 - k0^6/(16*(c - I*k0))) - I*k0*((c - I*k0)^5/16 + ((c - I*k0)^3*k0^2)/16 - ((c - I*k0)*k0^4)/16 - k0^6/(16*(c - I*k0))) - 4*c*((2*c - I*k0)^5/16 + ((2*c - I*k0)^3*k0^2)/16 - ((2*c - I*k0)*k0^4)/16 - k0^6/(16*(2*c - I*k0))) + (2*I)*k0*((2*c - I*k0)^5/16 + ((2*c - I*k0)^3*k0^2)/16 - ((2*c - I*k0)*k0^4)/16 - k0^6/(16*(2*c - I*k0)))) + (-((c - I*k0)^3*(2*c - I*k0))/(2*k^2) - ((c - I*k0)*(2*c - I*k0)^3)/(2*k^2) + ((c - I*k0)*(2*c - I*k0)*k0^2)/(2*k^2))*(2*c^2*((-5*(c - I*k0)^7)/(128*(2*c - I*k0)) + ((c - I*k0)^5*(2*c - I*k0))/32 + ((c - I*k0)^3*(2*c - I*k0)^3)/64 + ((c - I*k0)*(2*c - I*k0)^5)/32 - (5*(2*c - I*k0)^7)/(128*(c - I*k0))) - (3*I)*c*((-5*(c - I*k0)^7)/(128*(2*c - I*k0)) + ((c - I*k0)^5*(2*c - I*k0))/32 + ((c - I*k0)^3*(2*c - I*k0)^3)/64 + ((c - I*k0)*(2*c - I*k0)^5)/32 - (5*(2*c - I*k0)^7)/(128*(c - I*k0)))*k0 + ((5*(c - I*k0)^7)/(128*(2*c - I*k0)) - ((c - I*k0)^5*(2*c - I*k0))/32 - ((c - I*k0)^3*(2*c - I*k0)^3)/64 - ((c - I*k0)*(2*c - I*k0)^5)/32 + (5*(2*c - I*k0)^7)/(128*(c - I*k0)))*k0^2 + c*((-5*(c - I*k0)^7)/128 - ((c - I*k0)^5*k0^2)/32 + ((c - I*k0)^3*k0^4)/64 - ((c - I*k0)*k0^6)/32 - (5*k0^8)/(128*(c - I*k0))) - I*k0*((-5*(c - I*k0)^7)/128 - ((c - I*k0)^5*k0^2)/32 + ((c - I*k0)^3*k0^4)/64 - ((c - I*k0)*k0^6)/32 - (5*k0^8)/(128*(c - I*k0))) - 4*c*((-5*(2*c - I*k0)^7)/128 - ((2*c - I*k0)^5*k0^2)/32 + ((2*c - I*k0)^3*k0^4)/64 - ((2*c - I*k0)*k0^6)/32 - (5*k0^8)/(128*(2*c - I*k0))) + (2*I)*k0*((-5*(2*c - I*k0)^7)/128 - ((2*c - I*k0)^5*k0^2)/32 + ((2*c - I*k0)^3*k0^4)/64 - ((2*c - I*k0)*k0^6)/32 - (5*k0^8)/(128*(2*c - I*k0)))) + ((c - I*k0)*(2*c - I*k0)*(2*c^2*((7*(c - I*k0)^9)/(256*(2*c - I*k0)) - (5*(c - I*k0)^7*(2*c - I*k0))/256 - ((c - I*k0)^5*(2*c - I*k0)^3)/128 - ((c - I*k0)^3*(2*c - I*k0)^5)/128 - (5*(c - I*k0)*(2*c - I*k0)^7)/256 + (7*(2*c - I*k0)^9)/(256*(c - I*k0))) - (3*I)*c*((7*(c - I*k0)^9)/(256*(2*c - I*k0)) - (5*(c - I*k0)^7*(2*c - I*k0))/256 - ((c - I*k0)^5*(2*c - I*k0)^3)/128 - ((c - I*k0)^3*(2*c - I*k0)^5)/128 - (5*(c - I*k0)*(2*c - I*k0)^7)/256 + (7*(2*c - I*k0)^9)/(256*(c - I*k0)))*k0 + ((-7*(c - I*k0)^9)/(256*(2*c - I*k0)) + (5*(c - I*k0)^7*(2*c - I*k0))/256 + ((c - I*k0)^5*(2*c - I*k0)^3)/128 + ((c - I*k0)^3*(2*c - I*k0)^5)/128 + (5*(c - I*k0)*(2*c - I*k0)^7)/256 - (7*(2*c - I*k0)^9)/(256*(c - I*k0)))*k0^2 + c*((7*(c - I*k0)^9)/256 + (5*(c - I*k0)^7*k0^2)/256 - ((c - I*k0)^5*k0^4)/128 + ((c - I*k0)^3*k0^6)/128 - (5*(c - I*k0)*k0^8)/256 - (7*k0^10)/(256*(c - I*k0))) - I*k0*((7*(c - I*k0)^9)/256 + (5*(c - I*k0)^7*k0^2)/256 - ((c - I*k0)^5*k0^4)/128 + ((c - I*k0)^3*k0^6)/128 - (5*(c - I*k0)*k0^8)/256 - (7*k0^10)/(256*(c - I*k0))) - 4*c*((7*(2*c - I*k0)^9)/256 + (5*(2*c - I*k0)^7*k0^2)/256 - ((2*c - I*k0)^5*k0^4)/128 + ((2*c - I*k0)^3*k0^6)/128 - (5*(2*c - I*k0)*k0^8)/256 - (7*k0^10)/(256*(2*c - I*k0))) + (2*I)*k0*((7*(2*c - I*k0)^9)/256 + (5*(2*c - I*k0)^7*k0^2)/256 - ((2*c - I*k0)^5*k0^4)/128 + ((2*c - I*k0)^3*k0^6)/128 - (5*(2*c - I*k0)*k0^8)/256 - (7*k0^10)/(256*(2*c - I*k0)))))/k^2 + ((11*c^4 - (24*I)*c^3*k0 - 12*c^2*k0^2)*((3*(-((c - I*k0)^3*(2*c - I*k0))/(2*k^2) - ((c - I*k0)*(2*c - I*k0)^3)/(2*k^2))*k0^4)/8 + (5*(c - I*k0)*(2*c - I*k0)*k0^6)/(16*k^2) - (5*(c - I*k0)^6*(2*c - I*k0)*(c/k - (I*k0)/k))/(16*k) - (3*(c - I*k0)^4*(2*c - I*k0)^3*(c/k - (I*k0)/k))/(16*k) - (3*(c - I*k0)^3*(2*c - I*k0)^4*((2*c)/k - (I*k0)/k))/(16*k) - (5*(c - I*k0)*(2*c - I*k0)^6*((2*c)/k - (I*k0)/k))/(16*k) + (k0^2*(((c - I*k0)^3*(2*c - I*k0)^3)/(4*k^2) + (3*(c - I*k0)^4*(2*c - I*k0)*(c/k - (I*k0)/k))/(8*k) + (3*(c - I*k0)*(2*c - I*k0)^4*((2*c)/k - (I*k0)/k))/(8*k)))/2))/4 - c^2*((5*(-((c - I*k0)^3*(2*c - I*k0))/(2*k^2) - ((c - I*k0)*(2*c - I*k0)^3)/(2*k^2))*k0^6)/16 + (35*(c - I*k0)*(2*c - I*k0)*k0^8)/(128*k^2) + (35*(c - I*k0)^8*(2*c - I*k0)*(c/k - (I*k0)/k))/(128*k) + (5*(c - I*k0)^6*(2*c - I*k0)^3*(c/k - (I*k0)/k))/(32*k) + (5*(c - I*k0)^3*(2*c - I*k0)^6*((2*c)/k - (I*k0)/k))/(32*k) + (35*(c - I*k0)*(2*c - I*k0)^8*((2*c)/k - (I*k0)/k))/(128*k) + (9*(c - I*k0)^4*(2*c - I*k0)^4*(c/k - (I*k0)/k)*((2*c)/k - (I*k0)/k))/64 + (3*k0^4*(((c - I*k0)^3*(2*c - I*k0)^3)/(4*k^2) + (3*(c - I*k0)^4*(2*c - I*k0)*(c/k - (I*k0)/k))/(8*k) + (3*(c - I*k0)*(2*c - I*k0)^4*((2*c)/k - (I*k0)/k))/(8*k)))/8 + (k0^2*((-5*(c - I*k0)^6*(2*c - I*k0)*(c/k - (I*k0)/k))/(16*k) - (3*(c - I*k0)^4*(2*c - I*k0)^3*(c/k - (I*k0)/k))/(16*k) - (3*(c - I*k0)^3*(2*c - I*k0)^4*((2*c)/k - (I*k0)/k))/(16*k) - (5*(c - I*k0)*(2*c - I*k0)^6*((2*c)/k - (I*k0)/k))/(16*k)))/2))/((c - I*k0)*(2*c - I*k0)*k0)}, 1, 11, 1] diff --git a/besseltransforms/2-1-1 b/besseltransforms/2-1-1 deleted file mode 100644 index 346813f..0000000 --- a/besseltransforms/2-1-1 +++ /dev/null @@ -1,2 +0,0 @@ -(k^(-1) - (2*(1 - 1/Sqrt[1 + k^2/(c - I*k0)^2]))/k - 1/(k*Sqrt[1 + k^2/(2*c - I*k0)^2]) + Sqrt[Pi]*((I*Piecewise[{{k0/(Sqrt[k^2 - k0^2]*Sqrt[Pi]), k0^2/k^2 < 1}}, 0])/k + Piecewise[{{(k0*(1 - k0/Sqrt[-k^2 + k0^2]))/(k*Sqrt[Pi]), k^2/k0^2 < 1}, {k0/(k*Sqrt[Pi]), k^2/k0^2 > 1}}, 0]/k0))/k0 -Piecewise[{{SeriesData[k, Infinity, {(3*c^2*(c - I*k0))/(k^2*k0), 0, (15*(-3*c^5 + (7*I)*c^4*k0 + 6*c^3*k0^2 - (2*I)*c^2*k0^3))/(4*k^2*k0), 0, (35*(9*c^7 - (31*I)*c^6*k0 - 45*c^5*k0^2 + (35*I)*c^4*k0^3 + 15*c^3*k0^4 - (3*I)*c^2*k0^5))/(8*k^2*k0), 0, (105*(-85*c^9 + (381*I)*c^8*k0 + 756*c^7*k0^2 - (868*I)*c^6*k0^3 - 630*c^5*k0^4 + (294*I)*c^4*k0^5 + 84*c^3*k0^6 - (12*I)*c^2*k0^7))/(64*k^2*k0), 0, (693*(93*c^11 - (511*I)*c^10*k0 - 1275*c^9*k0^2 + (1905*I)*c^8*k0^3 + 1890*c^7*k0^4 - (1302*I)*c^6*k0^5 - 630*c^5*k0^6 + (210*I)*c^4*k0^7 + 45*c^3*k0^8 - (5*I)*c^2*k0^9))/(128*k^2*k0)}, 2, 11, 1], (k0 <= 0 && k^2/k0^2 > 1) || k0 > 0}}, SeriesData[k, Infinity, {I/k^2, 0, (I/2*((-6*I)*c^3 - 6*c^2*k0 + k0^3))/(k^2*k0), 0, ((I/2*(6*c^3 - I*c^2*k0 + 6*c*k0^2 - (3*I)*k0^3)*((-I/2*(c - I*k0)*(2*c - I*k0)*k0^2)/k^2 - I*(-((c - I*k0)^3*(2*c - I*k0))/(2*k^2) - ((c - I*k0)*(2*c - I*k0)^3)/(2*k^2) + ((c - I*k0)*(2*c - I*k0)*k0^2)/(2*k^2))))/((c - I*k0)*(2*c - I*k0)) - (k0*(((-3*I)/8*(c - I*k0)*(2*c - I*k0)*k0^4)/k^2 - I/2*k0^2*(-((c - I*k0)^3*(2*c - I*k0))/(2*k^2) - ((c - I*k0)*(2*c - I*k0)^3)/(2*k^2) + ((c - I*k0)*(2*c - I*k0)*k0^2)/(2*k^2)) - I*(((c - I*k0)^3*(2*c - I*k0)^3)/(4*k^2) + ((-((c - I*k0)^3*(2*c - I*k0))/(2*k^2) - ((c - I*k0)*(2*c - I*k0)^3)/(2*k^2))*k0^2)/2 + (3*(c - I*k0)*(2*c - I*k0)*k0^4)/(8*k^2) + (3*(c - I*k0)^4*(2*c - I*k0)*(c/k - (I*k0)/k))/(8*k) + (3*(c - I*k0)*(2*c - I*k0)^4*((2*c)/k - (I*k0)/k))/(8*k))))/((c - I*k0)*(2*c - I*k0)) + (I*(c - I*k0)*(2*c - I*k0)*((-I/8*k0^4)/(c - I*k0) - I/2*k0^2*((c - I*k0)/2 - k0^2/(2*(c - I*k0))) + I*(-(c - I*k0)^3/8 - ((c - I*k0)*k0^2)/4 - k0^4/(8*(c - I*k0))) + k0*(-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)) - (((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*k0^2)/2 - k0^4/(8*(c - I*k0)*(2*c - I*k0))) - I*k0*(I*(-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0))) - I/2*((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*k0^2 - (I/8*k0^4)/((c - I*k0)*(2*c - I*k0))) - 2*((-I/8*k0^4)/(2*c - I*k0) - I/2*k0^2*((2*c - I*k0)/2 - k0^2/(2*(2*c - I*k0))) + I*(-(2*c - I*k0)^3/8 - ((2*c - I*k0)*k0^2)/4 - k0^4/(8*(2*c - I*k0))))))/k^2)/k0, 0, ((I/2*(6*c^3 - I*c^2*k0 + 6*c*k0^2 - (3*I)*k0^3)*(((-3*I)/8*(c - I*k0)*(2*c - I*k0)*k0^4)/k^2 - I/2*k0^2*(-((c - I*k0)^3*(2*c - I*k0))/(2*k^2) - ((c - I*k0)*(2*c - I*k0)^3)/(2*k^2) + ((c - I*k0)*(2*c - I*k0)*k0^2)/(2*k^2)) - I*(((c - I*k0)^3*(2*c - I*k0)^3)/(4*k^2) + ((-((c - I*k0)^3*(2*c - I*k0))/(2*k^2) - ((c - I*k0)*(2*c - I*k0)^3)/(2*k^2))*k0^2)/2 + (3*(c - I*k0)*(2*c - I*k0)*k0^4)/(8*k^2) + (3*(c - I*k0)^4*(2*c - I*k0)*(c/k - (I*k0)/k))/(8*k) + (3*(c - I*k0)*(2*c - I*k0)^4*((2*c)/k - (I*k0)/k))/(8*k))))/((c - I*k0)*(2*c - I*k0)) - ((-I/2*(c - I*k0)*(2*c - I*k0)*k0^2)/k^2 - I*(-((c - I*k0)^3*(2*c - I*k0))/(2*k^2) - ((c - I*k0)*(2*c - I*k0)^3)/(2*k^2) + ((c - I*k0)*(2*c - I*k0)*k0^2)/(2*k^2)))*((-I/8*k0^4)/(c - I*k0) - I/2*k0^2*((c - I*k0)/2 - k0^2/(2*(c - I*k0))) + I*(-(c - I*k0)^3/8 - ((c - I*k0)*k0^2)/4 - k0^4/(8*(c - I*k0))) + k0*(-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)) - (((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*k0^2)/2 - k0^4/(8*(c - I*k0)*(2*c - I*k0))) - I*k0*(I*(-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0))) - I/2*((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*k0^2 - (I/8*k0^4)/((c - I*k0)*(2*c - I*k0))) - 2*((-I/8*k0^4)/(2*c - I*k0) - I/2*k0^2*((2*c - I*k0)/2 - k0^2/(2*(2*c - I*k0))) + I*(-(2*c - I*k0)^3/8 - ((2*c - I*k0)*k0^2)/4 - k0^4/(8*(2*c - I*k0))))) + (I*(c - I*k0)*(2*c - I*k0)*((-I/16*k0^6)/(c - I*k0) - I/8*k0^4*((c - I*k0)/2 - k0^2/(2*(c - I*k0))) - I/2*k0^2*(-(c - I*k0)^3/8 - ((c - I*k0)*k0^2)/4 - k0^4/(8*(c - I*k0))) + I*((c - I*k0)^5/16 + ((c - I*k0)^3*k0^2)/16 - ((c - I*k0)*k0^4)/16 - k0^6/(16*(c - I*k0))) + k0*((c - I*k0)^5/(16*(2*c - I*k0)) - ((c - I*k0)^3*(2*c - I*k0))/16 - ((c - I*k0)*(2*c - I*k0)^3)/16 + (2*c - I*k0)^5/(16*(c - I*k0)) - ((-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)))*k0^2)/2 - (((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*k0^4)/8 - k0^6/(16*(c - I*k0)*(2*c - I*k0))) - I*k0*(I*((c - I*k0)^5/(16*(2*c - I*k0)) - ((c - I*k0)^3*(2*c - I*k0))/16 - ((c - I*k0)*(2*c - I*k0)^3)/16 + (2*c - I*k0)^5/(16*(c - I*k0))) - I/2*(-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)))*k0^2 - I/8*((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*k0^4 - (I/16*k0^6)/((c - I*k0)*(2*c - I*k0))) - 2*((-I/16*k0^6)/(2*c - I*k0) - I/8*k0^4*((2*c - I*k0)/2 - k0^2/(2*(2*c - I*k0))) - I/2*k0^2*(-(2*c - I*k0)^3/8 - ((2*c - I*k0)*k0^2)/4 - k0^4/(8*(2*c - I*k0))) + I*((2*c - I*k0)^5/16 + ((2*c - I*k0)^3*k0^2)/16 - ((2*c - I*k0)*k0^4)/16 - k0^6/(16*(2*c - I*k0))))))/k^2 - (k0*(((-5*I)/16*(c - I*k0)*(2*c - I*k0)*k0^6)/k^2 - (3*I)/8*k0^4*(-((c - I*k0)^3*(2*c - I*k0))/(2*k^2) - ((c - I*k0)*(2*c - I*k0)^3)/(2*k^2) + ((c - I*k0)*(2*c - I*k0)*k0^2)/(2*k^2)) - I/2*k0^2*(((c - I*k0)^3*(2*c - I*k0)^3)/(4*k^2) + ((-((c - I*k0)^3*(2*c - I*k0))/(2*k^2) - ((c - I*k0)*(2*c - I*k0)^3)/(2*k^2))*k0^2)/2 + (3*(c - I*k0)*(2*c - I*k0)*k0^4)/(8*k^2) + (3*(c - I*k0)^4*(2*c - I*k0)*(c/k - (I*k0)/k))/(8*k) + (3*(c - I*k0)*(2*c - I*k0)^4*((2*c)/k - (I*k0)/k))/(8*k)) - I*((3*(-((c - I*k0)^3*(2*c - I*k0))/(2*k^2) - ((c - I*k0)*(2*c - I*k0)^3)/(2*k^2))*k0^4)/8 + (5*(c - I*k0)*(2*c - I*k0)*k0^6)/(16*k^2) - (5*(c - I*k0)^6*(2*c - I*k0)*(c/k - (I*k0)/k))/(16*k) - (3*(c - I*k0)^4*(2*c - I*k0)^3*(c/k - (I*k0)/k))/(16*k) - (3*(c - I*k0)^3*(2*c - I*k0)^4*((2*c)/k - (I*k0)/k))/(16*k) - (5*(c - I*k0)*(2*c - I*k0)^6*((2*c)/k - (I*k0)/k))/(16*k) + (k0^2*(((c - I*k0)^3*(2*c - I*k0)^3)/(4*k^2) + (3*(c - I*k0)^4*(2*c - I*k0)*(c/k - (I*k0)/k))/(8*k) + (3*(c - I*k0)*(2*c - I*k0)^4*((2*c)/k - (I*k0)/k))/(8*k)))/2)))/((c - I*k0)*(2*c - I*k0)))/k0, 0, (-((((-3*I)/8*(c - I*k0)*(2*c - I*k0)*k0^4)/k^2 - I/2*k0^2*(-((c - I*k0)^3*(2*c - I*k0))/(2*k^2) - ((c - I*k0)*(2*c - I*k0)^3)/(2*k^2) + ((c - I*k0)*(2*c - I*k0)*k0^2)/(2*k^2)) - I*(((c - I*k0)^3*(2*c - I*k0)^3)/(4*k^2) + ((-((c - I*k0)^3*(2*c - I*k0))/(2*k^2) - ((c - I*k0)*(2*c - I*k0)^3)/(2*k^2))*k0^2)/2 + (3*(c - I*k0)*(2*c - I*k0)*k0^4)/(8*k^2) + (3*(c - I*k0)^4*(2*c - I*k0)*(c/k - (I*k0)/k))/(8*k) + (3*(c - I*k0)*(2*c - I*k0)^4*((2*c)/k - (I*k0)/k))/(8*k)))*((-I/8*k0^4)/(c - I*k0) - I/2*k0^2*((c - I*k0)/2 - k0^2/(2*(c - I*k0))) + I*(-(c - I*k0)^3/8 - ((c - I*k0)*k0^2)/4 - k0^4/(8*(c - I*k0))) + k0*(-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)) - (((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*k0^2)/2 - k0^4/(8*(c - I*k0)*(2*c - I*k0))) - I*k0*(I*(-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0))) - I/2*((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*k0^2 - (I/8*k0^4)/((c - I*k0)*(2*c - I*k0))) - 2*((-I/8*k0^4)/(2*c - I*k0) - I/2*k0^2*((2*c - I*k0)/2 - k0^2/(2*(2*c - I*k0))) + I*(-(2*c - I*k0)^3/8 - ((2*c - I*k0)*k0^2)/4 - k0^4/(8*(2*c - I*k0)))))) - ((-I/2*(c - I*k0)*(2*c - I*k0)*k0^2)/k^2 - I*(-((c - I*k0)^3*(2*c - I*k0))/(2*k^2) - ((c - I*k0)*(2*c - I*k0)^3)/(2*k^2) + ((c - I*k0)*(2*c - I*k0)*k0^2)/(2*k^2)))*((-I/16*k0^6)/(c - I*k0) - I/8*k0^4*((c - I*k0)/2 - k0^2/(2*(c - I*k0))) - I/2*k0^2*(-(c - I*k0)^3/8 - ((c - I*k0)*k0^2)/4 - k0^4/(8*(c - I*k0))) + I*((c - I*k0)^5/16 + ((c - I*k0)^3*k0^2)/16 - ((c - I*k0)*k0^4)/16 - k0^6/(16*(c - I*k0))) + k0*((c - I*k0)^5/(16*(2*c - I*k0)) - ((c - I*k0)^3*(2*c - I*k0))/16 - ((c - I*k0)*(2*c - I*k0)^3)/16 + (2*c - I*k0)^5/(16*(c - I*k0)) - ((-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)))*k0^2)/2 - (((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*k0^4)/8 - k0^6/(16*(c - I*k0)*(2*c - I*k0))) - I*k0*(I*((c - I*k0)^5/(16*(2*c - I*k0)) - ((c - I*k0)^3*(2*c - I*k0))/16 - ((c - I*k0)*(2*c - I*k0)^3)/16 + (2*c - I*k0)^5/(16*(c - I*k0))) - I/2*(-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)))*k0^2 - I/8*((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*k0^4 - (I/16*k0^6)/((c - I*k0)*(2*c - I*k0))) - 2*((-I/16*k0^6)/(2*c - I*k0) - I/8*k0^4*((2*c - I*k0)/2 - k0^2/(2*(2*c - I*k0))) - I/2*k0^2*(-(2*c - I*k0)^3/8 - ((2*c - I*k0)*k0^2)/4 - k0^4/(8*(2*c - I*k0))) + I*((2*c - I*k0)^5/16 + ((2*c - I*k0)^3*k0^2)/16 - ((2*c - I*k0)*k0^4)/16 - k0^6/(16*(2*c - I*k0))))) + (I*(c - I*k0)*(2*c - I*k0)*(((-5*I)/128*k0^8)/(c - I*k0) - I/16*k0^6*((c - I*k0)/2 - k0^2/(2*(c - I*k0))) - I/8*k0^4*(-(c - I*k0)^3/8 - ((c - I*k0)*k0^2)/4 - k0^4/(8*(c - I*k0))) - I/2*k0^2*((c - I*k0)^5/16 + ((c - I*k0)^3*k0^2)/16 - ((c - I*k0)*k0^4)/16 - k0^6/(16*(c - I*k0))) + I*((-5*(c - I*k0)^7)/128 - ((c - I*k0)^5*k0^2)/32 + ((c - I*k0)^3*k0^4)/64 - ((c - I*k0)*k0^6)/32 - (5*k0^8)/(128*(c - I*k0))) + k0*((-5*(c - I*k0)^7)/(128*(2*c - I*k0)) + ((c - I*k0)^5*(2*c - I*k0))/32 + ((c - I*k0)^3*(2*c - I*k0)^3)/64 + ((c - I*k0)*(2*c - I*k0)^5)/32 - (5*(2*c - I*k0)^7)/(128*(c - I*k0)) - (((c - I*k0)^5/(16*(2*c - I*k0)) - ((c - I*k0)^3*(2*c - I*k0))/16 - ((c - I*k0)*(2*c - I*k0)^3)/16 + (2*c - I*k0)^5/(16*(c - I*k0)))*k0^2)/2 - ((-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)))*k0^4)/8 - (((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*k0^6)/16 - (5*k0^8)/(128*(c - I*k0)*(2*c - I*k0))) - I*k0*(I*((-5*(c - I*k0)^7)/(128*(2*c - I*k0)) + ((c - I*k0)^5*(2*c - I*k0))/32 + ((c - I*k0)^3*(2*c - I*k0)^3)/64 + ((c - I*k0)*(2*c - I*k0)^5)/32 - (5*(2*c - I*k0)^7)/(128*(c - I*k0))) - I/2*((c - I*k0)^5/(16*(2*c - I*k0)) - ((c - I*k0)^3*(2*c - I*k0))/16 - ((c - I*k0)*(2*c - I*k0)^3)/16 + (2*c - I*k0)^5/(16*(c - I*k0)))*k0^2 - I/8*(-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)))*k0^4 - I/16*((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*k0^6 - ((5*I)/128*k0^8)/((c - I*k0)*(2*c - I*k0))) - 2*(((-5*I)/128*k0^8)/(2*c - I*k0) - I/16*k0^6*((2*c - I*k0)/2 - k0^2/(2*(2*c - I*k0))) - I/8*k0^4*(-(2*c - I*k0)^3/8 - ((2*c - I*k0)*k0^2)/4 - k0^4/(8*(2*c - I*k0))) - I/2*k0^2*((2*c - I*k0)^5/16 + ((2*c - I*k0)^3*k0^2)/16 - ((2*c - I*k0)*k0^4)/16 - k0^6/(16*(2*c - I*k0))) + I*((-5*(2*c - I*k0)^7)/128 - ((2*c - I*k0)^5*k0^2)/32 + ((2*c - I*k0)^3*k0^4)/64 - ((2*c - I*k0)*k0^6)/32 - (5*k0^8)/(128*(2*c - I*k0))))))/k^2 + (I/2*(6*c^3 - I*c^2*k0 + 6*c*k0^2 - (3*I)*k0^3)*(((-5*I)/16*(c - I*k0)*(2*c - I*k0)*k0^6)/k^2 - (3*I)/8*k0^4*(-((c - I*k0)^3*(2*c - I*k0))/(2*k^2) - ((c - I*k0)*(2*c - I*k0)^3)/(2*k^2) + ((c - I*k0)*(2*c - I*k0)*k0^2)/(2*k^2)) - I/2*k0^2*(((c - I*k0)^3*(2*c - I*k0)^3)/(4*k^2) + ((-((c - I*k0)^3*(2*c - I*k0))/(2*k^2) - ((c - I*k0)*(2*c - I*k0)^3)/(2*k^2))*k0^2)/2 + (3*(c - I*k0)*(2*c - I*k0)*k0^4)/(8*k^2) + (3*(c - I*k0)^4*(2*c - I*k0)*(c/k - (I*k0)/k))/(8*k) + (3*(c - I*k0)*(2*c - I*k0)^4*((2*c)/k - (I*k0)/k))/(8*k)) - I*((3*(-((c - I*k0)^3*(2*c - I*k0))/(2*k^2) - ((c - I*k0)*(2*c - I*k0)^3)/(2*k^2))*k0^4)/8 + (5*(c - I*k0)*(2*c - I*k0)*k0^6)/(16*k^2) - (5*(c - I*k0)^6*(2*c - I*k0)*(c/k - (I*k0)/k))/(16*k) - (3*(c - I*k0)^4*(2*c - I*k0)^3*(c/k - (I*k0)/k))/(16*k) - (3*(c - I*k0)^3*(2*c - I*k0)^4*((2*c)/k - (I*k0)/k))/(16*k) - (5*(c - I*k0)*(2*c - I*k0)^6*((2*c)/k - (I*k0)/k))/(16*k) + (k0^2*(((c - I*k0)^3*(2*c - I*k0)^3)/(4*k^2) + (3*(c - I*k0)^4*(2*c - I*k0)*(c/k - (I*k0)/k))/(8*k) + (3*(c - I*k0)*(2*c - I*k0)^4*((2*c)/k - (I*k0)/k))/(8*k)))/2)))/((c - I*k0)*(2*c - I*k0)) - (k0*(((-35*I)/128*(c - I*k0)*(2*c - I*k0)*k0^8)/k^2 - (5*I)/16*k0^6*(-((c - I*k0)^3*(2*c - I*k0))/(2*k^2) - ((c - I*k0)*(2*c - I*k0)^3)/(2*k^2) + ((c - I*k0)*(2*c - I*k0)*k0^2)/(2*k^2)) - (3*I)/8*k0^4*(((c - I*k0)^3*(2*c - I*k0)^3)/(4*k^2) + ((-((c - I*k0)^3*(2*c - I*k0))/(2*k^2) - ((c - I*k0)*(2*c - I*k0)^3)/(2*k^2))*k0^2)/2 + (3*(c - I*k0)*(2*c - I*k0)*k0^4)/(8*k^2) + (3*(c - I*k0)^4*(2*c - I*k0)*(c/k - (I*k0)/k))/(8*k) + (3*(c - I*k0)*(2*c - I*k0)^4*((2*c)/k - (I*k0)/k))/(8*k)) - I/2*k0^2*((3*(-((c - I*k0)^3*(2*c - I*k0))/(2*k^2) - ((c - I*k0)*(2*c - I*k0)^3)/(2*k^2))*k0^4)/8 + (5*(c - I*k0)*(2*c - I*k0)*k0^6)/(16*k^2) - (5*(c - I*k0)^6*(2*c - I*k0)*(c/k - (I*k0)/k))/(16*k) - (3*(c - I*k0)^4*(2*c - I*k0)^3*(c/k - (I*k0)/k))/(16*k) - (3*(c - I*k0)^3*(2*c - I*k0)^4*((2*c)/k - (I*k0)/k))/(16*k) - (5*(c - I*k0)*(2*c - I*k0)^6*((2*c)/k - (I*k0)/k))/(16*k) + (k0^2*(((c - I*k0)^3*(2*c - I*k0)^3)/(4*k^2) + (3*(c - I*k0)^4*(2*c - I*k0)*(c/k - (I*k0)/k))/(8*k) + (3*(c - I*k0)*(2*c - I*k0)^4*((2*c)/k - (I*k0)/k))/(8*k)))/2) - I*((5*(-((c - I*k0)^3*(2*c - I*k0))/(2*k^2) - ((c - I*k0)*(2*c - I*k0)^3)/(2*k^2))*k0^6)/16 + (35*(c - I*k0)*(2*c - I*k0)*k0^8)/(128*k^2) + (35*(c - I*k0)^8*(2*c - I*k0)*(c/k - (I*k0)/k))/(128*k) + (5*(c - I*k0)^6*(2*c - I*k0)^3*(c/k - (I*k0)/k))/(32*k) + (5*(c - I*k0)^3*(2*c - I*k0)^6*((2*c)/k - (I*k0)/k))/(32*k) + (35*(c - I*k0)*(2*c - I*k0)^8*((2*c)/k - (I*k0)/k))/(128*k) + (9*(c - I*k0)^4*(2*c - I*k0)^4*(c/k - (I*k0)/k)*((2*c)/k - (I*k0)/k))/64 + (3*k0^4*(((c - I*k0)^3*(2*c - I*k0)^3)/(4*k^2) + (3*(c - I*k0)^4*(2*c - I*k0)*(c/k - (I*k0)/k))/(8*k) + (3*(c - I*k0)*(2*c - I*k0)^4*((2*c)/k - (I*k0)/k))/(8*k)))/8 + (k0^2*((-5*(c - I*k0)^6*(2*c - I*k0)*(c/k - (I*k0)/k))/(16*k) - (3*(c - I*k0)^4*(2*c - I*k0)^3*(c/k - (I*k0)/k))/(16*k) - (3*(c - I*k0)^3*(2*c - I*k0)^4*((2*c)/k - (I*k0)/k))/(16*k) - (5*(c - I*k0)*(2*c - I*k0)^6*((2*c)/k - (I*k0)/k))/(16*k)))/2)))/((c - I*k0)*(2*c - I*k0)))/k0, 0, (-((((-3*I)/8*(c - I*k0)*(2*c - I*k0)*k0^4)/k^2 - I/2*k0^2*(-((c - I*k0)^3*(2*c - I*k0))/(2*k^2) - ((c - I*k0)*(2*c - I*k0)^3)/(2*k^2) + ((c - I*k0)*(2*c - I*k0)*k0^2)/(2*k^2)) - I*(((c - I*k0)^3*(2*c - I*k0)^3)/(4*k^2) + ((-((c - I*k0)^3*(2*c - I*k0))/(2*k^2) - ((c - I*k0)*(2*c - I*k0)^3)/(2*k^2))*k0^2)/2 + (3*(c - I*k0)*(2*c - I*k0)*k0^4)/(8*k^2) + (3*(c - I*k0)^4*(2*c - I*k0)*(c/k - (I*k0)/k))/(8*k) + (3*(c - I*k0)*(2*c - I*k0)^4*((2*c)/k - (I*k0)/k))/(8*k)))*((-I/16*k0^6)/(c - I*k0) - I/8*k0^4*((c - I*k0)/2 - k0^2/(2*(c - I*k0))) - I/2*k0^2*(-(c - I*k0)^3/8 - ((c - I*k0)*k0^2)/4 - k0^4/(8*(c - I*k0))) + I*((c - I*k0)^5/16 + ((c - I*k0)^3*k0^2)/16 - ((c - I*k0)*k0^4)/16 - k0^6/(16*(c - I*k0))) + k0*((c - I*k0)^5/(16*(2*c - I*k0)) - ((c - I*k0)^3*(2*c - I*k0))/16 - ((c - I*k0)*(2*c - I*k0)^3)/16 + (2*c - I*k0)^5/(16*(c - I*k0)) - ((-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)))*k0^2)/2 - (((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*k0^4)/8 - k0^6/(16*(c - I*k0)*(2*c - I*k0))) - I*k0*(I*((c - I*k0)^5/(16*(2*c - I*k0)) - ((c - I*k0)^3*(2*c - I*k0))/16 - ((c - I*k0)*(2*c - I*k0)^3)/16 + (2*c - I*k0)^5/(16*(c - I*k0))) - I/2*(-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)))*k0^2 - I/8*((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*k0^4 - (I/16*k0^6)/((c - I*k0)*(2*c - I*k0))) - 2*((-I/16*k0^6)/(2*c - I*k0) - I/8*k0^4*((2*c - I*k0)/2 - k0^2/(2*(2*c - I*k0))) - I/2*k0^2*(-(2*c - I*k0)^3/8 - ((2*c - I*k0)*k0^2)/4 - k0^4/(8*(2*c - I*k0))) + I*((2*c - I*k0)^5/16 + ((2*c - I*k0)^3*k0^2)/16 - ((2*c - I*k0)*k0^4)/16 - k0^6/(16*(2*c - I*k0)))))) - ((-I/2*(c - I*k0)*(2*c - I*k0)*k0^2)/k^2 - I*(-((c - I*k0)^3*(2*c - I*k0))/(2*k^2) - ((c - I*k0)*(2*c - I*k0)^3)/(2*k^2) + ((c - I*k0)*(2*c - I*k0)*k0^2)/(2*k^2)))*(((-5*I)/128*k0^8)/(c - I*k0) - I/16*k0^6*((c - I*k0)/2 - k0^2/(2*(c - I*k0))) - I/8*k0^4*(-(c - I*k0)^3/8 - ((c - I*k0)*k0^2)/4 - k0^4/(8*(c - I*k0))) - I/2*k0^2*((c - I*k0)^5/16 + ((c - I*k0)^3*k0^2)/16 - ((c - I*k0)*k0^4)/16 - k0^6/(16*(c - I*k0))) + I*((-5*(c - I*k0)^7)/128 - ((c - I*k0)^5*k0^2)/32 + ((c - I*k0)^3*k0^4)/64 - ((c - I*k0)*k0^6)/32 - (5*k0^8)/(128*(c - I*k0))) + k0*((-5*(c - I*k0)^7)/(128*(2*c - I*k0)) + ((c - I*k0)^5*(2*c - I*k0))/32 + ((c - I*k0)^3*(2*c - I*k0)^3)/64 + ((c - I*k0)*(2*c - I*k0)^5)/32 - (5*(2*c - I*k0)^7)/(128*(c - I*k0)) - (((c - I*k0)^5/(16*(2*c - I*k0)) - ((c - I*k0)^3*(2*c - I*k0))/16 - ((c - I*k0)*(2*c - I*k0)^3)/16 + (2*c - I*k0)^5/(16*(c - I*k0)))*k0^2)/2 - ((-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)))*k0^4)/8 - (((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*k0^6)/16 - (5*k0^8)/(128*(c - I*k0)*(2*c - I*k0))) - I*k0*(I*((-5*(c - I*k0)^7)/(128*(2*c - I*k0)) + ((c - I*k0)^5*(2*c - I*k0))/32 + ((c - I*k0)^3*(2*c - I*k0)^3)/64 + ((c - I*k0)*(2*c - I*k0)^5)/32 - (5*(2*c - I*k0)^7)/(128*(c - I*k0))) - I/2*((c - I*k0)^5/(16*(2*c - I*k0)) - ((c - I*k0)^3*(2*c - I*k0))/16 - ((c - I*k0)*(2*c - I*k0)^3)/16 + (2*c - I*k0)^5/(16*(c - I*k0)))*k0^2 - I/8*(-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)))*k0^4 - I/16*((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*k0^6 - ((5*I)/128*k0^8)/((c - I*k0)*(2*c - I*k0))) - 2*(((-5*I)/128*k0^8)/(2*c - I*k0) - I/16*k0^6*((2*c - I*k0)/2 - k0^2/(2*(2*c - I*k0))) - I/8*k0^4*(-(2*c - I*k0)^3/8 - ((2*c - I*k0)*k0^2)/4 - k0^4/(8*(2*c - I*k0))) - I/2*k0^2*((2*c - I*k0)^5/16 + ((2*c - I*k0)^3*k0^2)/16 - ((2*c - I*k0)*k0^4)/16 - k0^6/(16*(2*c - I*k0))) + I*((-5*(2*c - I*k0)^7)/128 - ((2*c - I*k0)^5*k0^2)/32 + ((2*c - I*k0)^3*k0^4)/64 - ((2*c - I*k0)*k0^6)/32 - (5*k0^8)/(128*(2*c - I*k0))))) + (I*(c - I*k0)*(2*c - I*k0)*(((-7*I)/256*k0^10)/(c - I*k0) - (5*I)/128*k0^8*((c - I*k0)/2 - k0^2/(2*(c - I*k0))) - I/16*k0^6*(-(c - I*k0)^3/8 - ((c - I*k0)*k0^2)/4 - k0^4/(8*(c - I*k0))) - I/8*k0^4*((c - I*k0)^5/16 + ((c - I*k0)^3*k0^2)/16 - ((c - I*k0)*k0^4)/16 - k0^6/(16*(c - I*k0))) - I/2*k0^2*((-5*(c - I*k0)^7)/128 - ((c - I*k0)^5*k0^2)/32 + ((c - I*k0)^3*k0^4)/64 - ((c - I*k0)*k0^6)/32 - (5*k0^8)/(128*(c - I*k0))) + I*((7*(c - I*k0)^9)/256 + (5*(c - I*k0)^7*k0^2)/256 - ((c - I*k0)^5*k0^4)/128 + ((c - I*k0)^3*k0^6)/128 - (5*(c - I*k0)*k0^8)/256 - (7*k0^10)/(256*(c - I*k0))) + k0*((7*(c - I*k0)^9)/(256*(2*c - I*k0)) - (5*(c - I*k0)^7*(2*c - I*k0))/256 - ((c - I*k0)^5*(2*c - I*k0)^3)/128 - ((c - I*k0)^3*(2*c - I*k0)^5)/128 - (5*(c - I*k0)*(2*c - I*k0)^7)/256 + (7*(2*c - I*k0)^9)/(256*(c - I*k0)) - (((-5*(c - I*k0)^7)/(128*(2*c - I*k0)) + ((c - I*k0)^5*(2*c - I*k0))/32 + ((c - I*k0)^3*(2*c - I*k0)^3)/64 + ((c - I*k0)*(2*c - I*k0)^5)/32 - (5*(2*c - I*k0)^7)/(128*(c - I*k0)))*k0^2)/2 - (((c - I*k0)^5/(16*(2*c - I*k0)) - ((c - I*k0)^3*(2*c - I*k0))/16 - ((c - I*k0)*(2*c - I*k0)^3)/16 + (2*c - I*k0)^5/(16*(c - I*k0)))*k0^4)/8 - ((-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)))*k0^6)/16 - (5*((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*k0^8)/128 - (7*k0^10)/(256*(c - I*k0)*(2*c - I*k0))) - I*k0*(I*((7*(c - I*k0)^9)/(256*(2*c - I*k0)) - (5*(c - I*k0)^7*(2*c - I*k0))/256 - ((c - I*k0)^5*(2*c - I*k0)^3)/128 - ((c - I*k0)^3*(2*c - I*k0)^5)/128 - (5*(c - I*k0)*(2*c - I*k0)^7)/256 + (7*(2*c - I*k0)^9)/(256*(c - I*k0))) - I/2*((-5*(c - I*k0)^7)/(128*(2*c - I*k0)) + ((c - I*k0)^5*(2*c - I*k0))/32 + ((c - I*k0)^3*(2*c - I*k0)^3)/64 + ((c - I*k0)*(2*c - I*k0)^5)/32 - (5*(2*c - I*k0)^7)/(128*(c - I*k0)))*k0^2 - I/8*((c - I*k0)^5/(16*(2*c - I*k0)) - ((c - I*k0)^3*(2*c - I*k0))/16 - ((c - I*k0)*(2*c - I*k0)^3)/16 + (2*c - I*k0)^5/(16*(c - I*k0)))*k0^4 - I/16*(-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)))*k0^6 - (5*I)/128*((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*k0^8 - ((7*I)/256*k0^10)/((c - I*k0)*(2*c - I*k0))) - 2*(((-7*I)/256*k0^10)/(2*c - I*k0) - (5*I)/128*k0^8*((2*c - I*k0)/2 - k0^2/(2*(2*c - I*k0))) - I/16*k0^6*(-(2*c - I*k0)^3/8 - ((2*c - I*k0)*k0^2)/4 - k0^4/(8*(2*c - I*k0))) - I/8*k0^4*((2*c - I*k0)^5/16 + ((2*c - I*k0)^3*k0^2)/16 - ((2*c - I*k0)*k0^4)/16 - k0^6/(16*(2*c - I*k0))) - I/2*k0^2*((-5*(2*c - I*k0)^7)/128 - ((2*c - I*k0)^5*k0^2)/32 + ((2*c - I*k0)^3*k0^4)/64 - ((2*c - I*k0)*k0^6)/32 - (5*k0^8)/(128*(2*c - I*k0))) + I*((7*(2*c - I*k0)^9)/256 + (5*(2*c - I*k0)^7*k0^2)/256 - ((2*c - I*k0)^5*k0^4)/128 + ((2*c - I*k0)^3*k0^6)/128 - (5*(2*c - I*k0)*k0^8)/256 - (7*k0^10)/(256*(2*c - I*k0))))))/k^2 - ((-I/8*k0^4)/(c - I*k0) - I/2*k0^2*((c - I*k0)/2 - k0^2/(2*(c - I*k0))) + I*(-(c - I*k0)^3/8 - ((c - I*k0)*k0^2)/4 - k0^4/(8*(c - I*k0))) + k0*(-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)) - (((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*k0^2)/2 - k0^4/(8*(c - I*k0)*(2*c - I*k0))) - I*k0*(I*(-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0))) - I/2*((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*k0^2 - (I/8*k0^4)/((c - I*k0)*(2*c - I*k0))) - 2*((-I/8*k0^4)/(2*c - I*k0) - I/2*k0^2*((2*c - I*k0)/2 - k0^2/(2*(2*c - I*k0))) + I*(-(2*c - I*k0)^3/8 - ((2*c - I*k0)*k0^2)/4 - k0^4/(8*(2*c - I*k0)))))*(((-5*I)/16*(c - I*k0)*(2*c - I*k0)*k0^6)/k^2 - (3*I)/8*k0^4*(-((c - I*k0)^3*(2*c - I*k0))/(2*k^2) - ((c - I*k0)*(2*c - I*k0)^3)/(2*k^2) + ((c - I*k0)*(2*c - I*k0)*k0^2)/(2*k^2)) - I/2*k0^2*(((c - I*k0)^3*(2*c - I*k0)^3)/(4*k^2) + ((-((c - I*k0)^3*(2*c - I*k0))/(2*k^2) - ((c - I*k0)*(2*c - I*k0)^3)/(2*k^2))*k0^2)/2 + (3*(c - I*k0)*(2*c - I*k0)*k0^4)/(8*k^2) + (3*(c - I*k0)^4*(2*c - I*k0)*(c/k - (I*k0)/k))/(8*k) + (3*(c - I*k0)*(2*c - I*k0)^4*((2*c)/k - (I*k0)/k))/(8*k)) - I*((3*(-((c - I*k0)^3*(2*c - I*k0))/(2*k^2) - ((c - I*k0)*(2*c - I*k0)^3)/(2*k^2))*k0^4)/8 + (5*(c - I*k0)*(2*c - I*k0)*k0^6)/(16*k^2) - (5*(c - I*k0)^6*(2*c - I*k0)*(c/k - (I*k0)/k))/(16*k) - (3*(c - I*k0)^4*(2*c - I*k0)^3*(c/k - (I*k0)/k))/(16*k) - (3*(c - I*k0)^3*(2*c - I*k0)^4*((2*c)/k - (I*k0)/k))/(16*k) - (5*(c - I*k0)*(2*c - I*k0)^6*((2*c)/k - (I*k0)/k))/(16*k) + (k0^2*(((c - I*k0)^3*(2*c - I*k0)^3)/(4*k^2) + (3*(c - I*k0)^4*(2*c - I*k0)*(c/k - (I*k0)/k))/(8*k) + (3*(c - I*k0)*(2*c - I*k0)^4*((2*c)/k - (I*k0)/k))/(8*k)))/2)) + (I/2*(6*c^3 - I*c^2*k0 + 6*c*k0^2 - (3*I)*k0^3)*(((-35*I)/128*(c - I*k0)*(2*c - I*k0)*k0^8)/k^2 - (5*I)/16*k0^6*(-((c - I*k0)^3*(2*c - I*k0))/(2*k^2) - ((c - I*k0)*(2*c - I*k0)^3)/(2*k^2) + ((c - I*k0)*(2*c - I*k0)*k0^2)/(2*k^2)) - (3*I)/8*k0^4*(((c - I*k0)^3*(2*c - I*k0)^3)/(4*k^2) + ((-((c - I*k0)^3*(2*c - I*k0))/(2*k^2) - ((c - I*k0)*(2*c - I*k0)^3)/(2*k^2))*k0^2)/2 + (3*(c - I*k0)*(2*c - I*k0)*k0^4)/(8*k^2) + (3*(c - I*k0)^4*(2*c - I*k0)*(c/k - (I*k0)/k))/(8*k) + (3*(c - I*k0)*(2*c - I*k0)^4*((2*c)/k - (I*k0)/k))/(8*k)) - I/2*k0^2*((3*(-((c - I*k0)^3*(2*c - I*k0))/(2*k^2) - ((c - I*k0)*(2*c - I*k0)^3)/(2*k^2))*k0^4)/8 + (5*(c - I*k0)*(2*c - I*k0)*k0^6)/(16*k^2) - (5*(c - I*k0)^6*(2*c - I*k0)*(c/k - (I*k0)/k))/(16*k) - (3*(c - I*k0)^4*(2*c - I*k0)^3*(c/k - (I*k0)/k))/(16*k) - (3*(c - I*k0)^3*(2*c - I*k0)^4*((2*c)/k - (I*k0)/k))/(16*k) - (5*(c - I*k0)*(2*c - I*k0)^6*((2*c)/k - (I*k0)/k))/(16*k) + (k0^2*(((c - I*k0)^3*(2*c - I*k0)^3)/(4*k^2) + (3*(c - I*k0)^4*(2*c - I*k0)*(c/k - (I*k0)/k))/(8*k) + (3*(c - I*k0)*(2*c - I*k0)^4*((2*c)/k - (I*k0)/k))/(8*k)))/2) - I*((5*(-((c - I*k0)^3*(2*c - I*k0))/(2*k^2) - ((c - I*k0)*(2*c - I*k0)^3)/(2*k^2))*k0^6)/16 + (35*(c - I*k0)*(2*c - I*k0)*k0^8)/(128*k^2) + (35*(c - I*k0)^8*(2*c - I*k0)*(c/k - (I*k0)/k))/(128*k) + (5*(c - I*k0)^6*(2*c - I*k0)^3*(c/k - (I*k0)/k))/(32*k) + (5*(c - I*k0)^3*(2*c - I*k0)^6*((2*c)/k - (I*k0)/k))/(32*k) + (35*(c - I*k0)*(2*c - I*k0)^8*((2*c)/k - (I*k0)/k))/(128*k) + (9*(c - I*k0)^4*(2*c - I*k0)^4*(c/k - (I*k0)/k)*((2*c)/k - (I*k0)/k))/64 + (3*k0^4*(((c - I*k0)^3*(2*c - I*k0)^3)/(4*k^2) + (3*(c - I*k0)^4*(2*c - I*k0)*(c/k - (I*k0)/k))/(8*k) + (3*(c - I*k0)*(2*c - I*k0)^4*((2*c)/k - (I*k0)/k))/(8*k)))/8 + (k0^2*((-5*(c - I*k0)^6*(2*c - I*k0)*(c/k - (I*k0)/k))/(16*k) - (3*(c - I*k0)^4*(2*c - I*k0)^3*(c/k - (I*k0)/k))/(16*k) - (3*(c - I*k0)^3*(2*c - I*k0)^4*((2*c)/k - (I*k0)/k))/(16*k) - (5*(c - I*k0)*(2*c - I*k0)^6*((2*c)/k - (I*k0)/k))/(16*k)))/2)))/((c - I*k0)*(2*c - I*k0)) - (k0*(((-63*I)/256*(c - I*k0)*(2*c - I*k0)*k0^10)/k^2 - (35*I)/128*k0^8*(-((c - I*k0)^3*(2*c - I*k0))/(2*k^2) - ((c - I*k0)*(2*c - I*k0)^3)/(2*k^2) + ((c - I*k0)*(2*c - I*k0)*k0^2)/(2*k^2)) - (5*I)/16*k0^6*(((c - I*k0)^3*(2*c - I*k0)^3)/(4*k^2) + ((-((c - I*k0)^3*(2*c - I*k0))/(2*k^2) - ((c - I*k0)*(2*c - I*k0)^3)/(2*k^2))*k0^2)/2 + (3*(c - I*k0)*(2*c - I*k0)*k0^4)/(8*k^2) + (3*(c - I*k0)^4*(2*c - I*k0)*(c/k - (I*k0)/k))/(8*k) + (3*(c - I*k0)*(2*c - I*k0)^4*((2*c)/k - (I*k0)/k))/(8*k)) - (3*I)/8*k0^4*((3*(-((c - I*k0)^3*(2*c - I*k0))/(2*k^2) - ((c - I*k0)*(2*c - I*k0)^3)/(2*k^2))*k0^4)/8 + (5*(c - I*k0)*(2*c - I*k0)*k0^6)/(16*k^2) - (5*(c - I*k0)^6*(2*c - I*k0)*(c/k - (I*k0)/k))/(16*k) - (3*(c - I*k0)^4*(2*c - I*k0)^3*(c/k - (I*k0)/k))/(16*k) - (3*(c - I*k0)^3*(2*c - I*k0)^4*((2*c)/k - (I*k0)/k))/(16*k) - (5*(c - I*k0)*(2*c - I*k0)^6*((2*c)/k - (I*k0)/k))/(16*k) + (k0^2*(((c - I*k0)^3*(2*c - I*k0)^3)/(4*k^2) + (3*(c - I*k0)^4*(2*c - I*k0)*(c/k - (I*k0)/k))/(8*k) + (3*(c - I*k0)*(2*c - I*k0)^4*((2*c)/k - (I*k0)/k))/(8*k)))/2) - I/2*k0^2*((5*(-((c - I*k0)^3*(2*c - I*k0))/(2*k^2) - ((c - I*k0)*(2*c - I*k0)^3)/(2*k^2))*k0^6)/16 + (35*(c - I*k0)*(2*c - I*k0)*k0^8)/(128*k^2) + (35*(c - I*k0)^8*(2*c - I*k0)*(c/k - (I*k0)/k))/(128*k) + (5*(c - I*k0)^6*(2*c - I*k0)^3*(c/k - (I*k0)/k))/(32*k) + (5*(c - I*k0)^3*(2*c - I*k0)^6*((2*c)/k - (I*k0)/k))/(32*k) + (35*(c - I*k0)*(2*c - I*k0)^8*((2*c)/k - (I*k0)/k))/(128*k) + (9*(c - I*k0)^4*(2*c - I*k0)^4*(c/k - (I*k0)/k)*((2*c)/k - (I*k0)/k))/64 + (3*k0^4*(((c - I*k0)^3*(2*c - I*k0)^3)/(4*k^2) + (3*(c - I*k0)^4*(2*c - I*k0)*(c/k - (I*k0)/k))/(8*k) + (3*(c - I*k0)*(2*c - I*k0)^4*((2*c)/k - (I*k0)/k))/(8*k)))/8 + (k0^2*((-5*(c - I*k0)^6*(2*c - I*k0)*(c/k - (I*k0)/k))/(16*k) - (3*(c - I*k0)^4*(2*c - I*k0)^3*(c/k - (I*k0)/k))/(16*k) - (3*(c - I*k0)^3*(2*c - I*k0)^4*((2*c)/k - (I*k0)/k))/(16*k) - (5*(c - I*k0)*(2*c - I*k0)^6*((2*c)/k - (I*k0)/k))/(16*k)))/2) - I*((35*(-((c - I*k0)^3*(2*c - I*k0))/(2*k^2) - ((c - I*k0)*(2*c - I*k0)^3)/(2*k^2))*k0^8)/128 + (63*(c - I*k0)*(2*c - I*k0)*k0^10)/(256*k^2) - (63*(c - I*k0)^10*(2*c - I*k0)*(c/k - (I*k0)/k))/(256*k) - (35*(c - I*k0)^8*(2*c - I*k0)^3*(c/k - (I*k0)/k))/(256*k) - (35*(c - I*k0)^3*(2*c - I*k0)^8*((2*c)/k - (I*k0)/k))/(256*k) - (63*(c - I*k0)*(2*c - I*k0)^10*((2*c)/k - (I*k0)/k))/(256*k) - (15*(c - I*k0)^6*(2*c - I*k0)^4*(c/k - (I*k0)/k)*((2*c)/k - (I*k0)/k))/128 - (15*(c - I*k0)^4*(2*c - I*k0)^6*(c/k - (I*k0)/k)*((2*c)/k - (I*k0)/k))/128 + (5*k0^6*(((c - I*k0)^3*(2*c - I*k0)^3)/(4*k^2) + (3*(c - I*k0)^4*(2*c - I*k0)*(c/k - (I*k0)/k))/(8*k) + (3*(c - I*k0)*(2*c - I*k0)^4*((2*c)/k - (I*k0)/k))/(8*k)))/16 + (3*k0^4*((-5*(c - I*k0)^6*(2*c - I*k0)*(c/k - (I*k0)/k))/(16*k) - (3*(c - I*k0)^4*(2*c - I*k0)^3*(c/k - (I*k0)/k))/(16*k) - (3*(c - I*k0)^3*(2*c - I*k0)^4*((2*c)/k - (I*k0)/k))/(16*k) - (5*(c - I*k0)*(2*c - I*k0)^6*((2*c)/k - (I*k0)/k))/(16*k)))/8 + (k0^2*((35*(c - I*k0)^8*(2*c - I*k0)*(c/k - (I*k0)/k))/(128*k) + (5*(c - I*k0)^6*(2*c - I*k0)^3*(c/k - (I*k0)/k))/(32*k) + (5*(c - I*k0)^3*(2*c - I*k0)^6*((2*c)/k - (I*k0)/k))/(32*k) + (35*(c - I*k0)*(2*c - I*k0)^8*((2*c)/k - (I*k0)/k))/(128*k) + (9*(c - I*k0)^4*(2*c - I*k0)^4*(c/k - (I*k0)/k)*((2*c)/k - (I*k0)/k))/64))/2)))/((c - I*k0)*(2*c - I*k0)))/k0}, 0, 11, 1]] diff --git a/besseltransforms/2-1-2 b/besseltransforms/2-1-2 deleted file mode 100644 index 38fc03e..0000000 --- a/besseltransforms/2-1-2 +++ /dev/null @@ -1,2 +0,0 @@ -(-2/(Sqrt[1 + k^2/(c - I*k0)^2]*(c - I*k0)) + (4*(c - I*k0))/k^2 - (4*(c - I*k0))/(k^2*Sqrt[1 + k^2/(c - I*k0)^2]) + 1/(Sqrt[1 + k^2/(2*c - I*k0)^2]*(2*c - I*k0)) + (4*c - (2*I)*k0)/(k^2*Sqrt[1 + k^2/(2*c - I*k0)^2]) + (-4*c + (2*I)*k0)/k^2 + (Sqrt[Pi]*(Piecewise[{{0, k^2/k0^2 <= 1}}, (k0*(k^2 - 2*k0^2))/(k^3*Sqrt[Pi - (k0^2*Pi)/k^2])] + I*Piecewise[{{(k0*(k^2 + 2*k0*(-k0 + Sqrt[-k^2 + k0^2])))/(k^2*Sqrt[-k^2 + k0^2]*Sqrt[Pi]), k^2/k0^2 < 1}, {(2*k0^2)/(k^2*Sqrt[Pi]), k^2/k0^2 > 1}}, 0]))/k0)/k0 -Piecewise[{{SeriesData[k, Infinity, {(3*c^2)/(k^2*k0), 0, (-5*(7*c^4 - (12*I)*c^3*k0 - 6*c^2*k0^2))/(4*k^2*k0), 0, (7*(31*c^6 - (90*I)*c^5*k0 - 105*c^4*k0^2 + (60*I)*c^3*k0^3 + 15*c^2*k0^4))/(8*k^2*k0), 0, (-45*(127*c^8 - (504*I)*c^7*k0 - 868*c^6*k0^2 + (840*I)*c^5*k0^3 + 490*c^4*k0^4 - (168*I)*c^3*k0^5 - 28*c^2*k0^6))/(64*k^2*k0), 0, (77*(511*c^10 - (2550*I)*c^9*k0 - 5715*c^8*k0^2 + (7560*I)*c^7*k0^3 + 6510*c^6*k0^4 - (3780*I)*c^5*k0^5 - 1470*c^4*k0^6 + (360*I)*c^3*k0^7 + 45*c^2*k0^8))/(128*k^2*k0)}, 1, 11, 1], (k0 <= 0 && k^2/k0^2 > 1) || k0 > 0}}, SeriesData[k, Infinity, {(3*c^2)/(k^2*k0), 0, (-5*(7*c^4 - (12*I)*c^3*k0 - 6*c^2*k0^2))/(4*k^2*k0), 0, (7*(31*c^6 - (90*I)*c^5*k0 - 105*c^4*k0^2 + (60*I)*c^3*k0^3 + 15*c^2*k0^4))/(8*k^2*k0), 0, ((-I*(-((c - I*k0)^3*(2*c - I*k0))/(2*k^2) - ((c - I*k0)*(2*c - I*k0)^3)/(2*k^2)) - (I/2*(c - I*k0)*(2*c - I*k0)*k0^2)/k^2)*((2*I)*c^2*((c - I*k0)^5/(16*(2*c - I*k0)) - ((c - I*k0)^3*(2*c - I*k0))/16 - ((c - I*k0)*(2*c - I*k0)^3)/16 + (2*c - I*k0)^5/(16*(c - I*k0))) + 3*c*((c - I*k0)^5/(16*(2*c - I*k0)) - ((c - I*k0)^3*(2*c - I*k0))/16 - ((c - I*k0)*(2*c - I*k0)^3)/16 + (2*c - I*k0)^5/(16*(c - I*k0)))*k0 - (4*I)*c^2*(-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)))*k0^2 - I*((c - I*k0)^5/(16*(2*c - I*k0)) - ((c - I*k0)^3*(2*c - I*k0))/16 - ((c - I*k0)*(2*c - I*k0)^3)/16 + (2*c - I*k0)^5/(16*(c - I*k0)))*k0^2 - 6*c*(-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)))*k0^3 + (2*I)*(-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)))*k0^4 + 8*c^3*(-I/8*(c - I*k0)^3 - I/4*(c - I*k0)*k0^2 - (I/8*k0^4)/(c - I*k0)) - (16*I)*c^2*k0*(-I/8*(c - I*k0)^3 - I/4*(c - I*k0)*k0^2 - (I/8*k0^4)/(c - I*k0)) - 10*c*k0^2*(-I/8*(c - I*k0)^3 - I/4*(c - I*k0)*k0^2 - (I/8*k0^4)/(c - I*k0)) + (2*I)*k0^3*(-I/8*(c - I*k0)^3 - I/4*(c - I*k0)*k0^2 - (I/8*k0^4)/(c - I*k0)) - 8*c^3*(-I/8*(2*c - I*k0)^3 - I/4*(2*c - I*k0)*k0^2 - (I/8*k0^4)/(2*c - I*k0)) + (20*I)*c^2*k0*(-I/8*(2*c - I*k0)^3 - I/4*(2*c - I*k0)*k0^2 - (I/8*k0^4)/(2*c - I*k0)) + 16*c*k0^2*(-I/8*(2*c - I*k0)^3 - I/4*(2*c - I*k0)*k0^2 - (I/8*k0^4)/(2*c - I*k0)) - (4*I)*k0^3*(-I/8*(2*c - I*k0)^3 - I/4*(2*c - I*k0)*k0^2 - (I/8*k0^4)/(2*c - I*k0)) + c*(I/16*(c - I*k0)^5 + I/16*(c - I*k0)^3*k0^2 - I/16*(c - I*k0)*k0^4 - (I/16*k0^6)/(c - I*k0)) - I*k0*(I/16*(c - I*k0)^5 + I/16*(c - I*k0)^3*k0^2 - I/16*(c - I*k0)*k0^4 - (I/16*k0^6)/(c - I*k0)) - 4*c*(I/16*(2*c - I*k0)^5 + I/16*(2*c - I*k0)^3*k0^2 - I/16*(2*c - I*k0)*k0^4 - (I/16*k0^6)/(2*c - I*k0)) + (2*I)*k0*(I/16*(2*c - I*k0)^5 + I/16*(2*c - I*k0)^3*k0^2 - I/16*(2*c - I*k0)*k0^4 - (I/16*k0^6)/(2*c - I*k0))) - (I*(c - I*k0)*(2*c - I*k0)*((2*I)*c^2*((-5*(c - I*k0)^7)/(128*(2*c - I*k0)) + ((c - I*k0)^5*(2*c - I*k0))/32 + ((c - I*k0)^3*(2*c - I*k0)^3)/64 + ((c - I*k0)*(2*c - I*k0)^5)/32 - (5*(2*c - I*k0)^7)/(128*(c - I*k0))) + 3*c*((-5*(c - I*k0)^7)/(128*(2*c - I*k0)) + ((c - I*k0)^5*(2*c - I*k0))/32 + ((c - I*k0)^3*(2*c - I*k0)^3)/64 + ((c - I*k0)*(2*c - I*k0)^5)/32 - (5*(2*c - I*k0)^7)/(128*(c - I*k0)))*k0 - (4*I)*c^2*((c - I*k0)^5/(16*(2*c - I*k0)) - ((c - I*k0)^3*(2*c - I*k0))/16 - ((c - I*k0)*(2*c - I*k0)^3)/16 + (2*c - I*k0)^5/(16*(c - I*k0)))*k0^2 - I*((-5*(c - I*k0)^7)/(128*(2*c - I*k0)) + ((c - I*k0)^5*(2*c - I*k0))/32 + ((c - I*k0)^3*(2*c - I*k0)^3)/64 + ((c - I*k0)*(2*c - I*k0)^5)/32 - (5*(2*c - I*k0)^7)/(128*(c - I*k0)))*k0^2 - 6*c*((c - I*k0)^5/(16*(2*c - I*k0)) - ((c - I*k0)^3*(2*c - I*k0))/16 - ((c - I*k0)*(2*c - I*k0)^3)/16 + (2*c - I*k0)^5/(16*(c - I*k0)))*k0^3 + (2*I)*((c - I*k0)^5/(16*(2*c - I*k0)) - ((c - I*k0)^3*(2*c - I*k0))/16 - ((c - I*k0)*(2*c - I*k0)^3)/16 + (2*c - I*k0)^5/(16*(c - I*k0)))*k0^4 + 8*c^3*(I/16*(c - I*k0)^5 + I/16*(c - I*k0)^3*k0^2 - I/16*(c - I*k0)*k0^4 - (I/16*k0^6)/(c - I*k0)) - (16*I)*c^2*k0*(I/16*(c - I*k0)^5 + I/16*(c - I*k0)^3*k0^2 - I/16*(c - I*k0)*k0^4 - (I/16*k0^6)/(c - I*k0)) - 10*c*k0^2*(I/16*(c - I*k0)^5 + I/16*(c - I*k0)^3*k0^2 - I/16*(c - I*k0)*k0^4 - (I/16*k0^6)/(c - I*k0)) + (2*I)*k0^3*(I/16*(c - I*k0)^5 + I/16*(c - I*k0)^3*k0^2 - I/16*(c - I*k0)*k0^4 - (I/16*k0^6)/(c - I*k0)) - 8*c^3*(I/16*(2*c - I*k0)^5 + I/16*(2*c - I*k0)^3*k0^2 - I/16*(2*c - I*k0)*k0^4 - (I/16*k0^6)/(2*c - I*k0)) + (20*I)*c^2*k0*(I/16*(2*c - I*k0)^5 + I/16*(2*c - I*k0)^3*k0^2 - I/16*(2*c - I*k0)*k0^4 - (I/16*k0^6)/(2*c - I*k0)) + 16*c*k0^2*(I/16*(2*c - I*k0)^5 + I/16*(2*c - I*k0)^3*k0^2 - I/16*(2*c - I*k0)*k0^4 - (I/16*k0^6)/(2*c - I*k0)) - (4*I)*k0^3*(I/16*(2*c - I*k0)^5 + I/16*(2*c - I*k0)^3*k0^2 - I/16*(2*c - I*k0)*k0^4 - (I/16*k0^6)/(2*c - I*k0)) + c*((-5*I)/128*(c - I*k0)^7 - I/32*(c - I*k0)^5*k0^2 + I/64*(c - I*k0)^3*k0^4 - I/32*(c - I*k0)*k0^6 - ((5*I)/128*k0^8)/(c - I*k0)) - I*k0*((-5*I)/128*(c - I*k0)^7 - I/32*(c - I*k0)^5*k0^2 + I/64*(c - I*k0)^3*k0^4 - I/32*(c - I*k0)*k0^6 - ((5*I)/128*k0^8)/(c - I*k0)) - 4*c*((-5*I)/128*(2*c - I*k0)^7 - I/32*(2*c - I*k0)^5*k0^2 + I/64*(2*c - I*k0)^3*k0^4 - I/32*(2*c - I*k0)*k0^6 - ((5*I)/128*k0^8)/(2*c - I*k0)) + (2*I)*k0*((-5*I)/128*(2*c - I*k0)^7 - I/32*(2*c - I*k0)^5*k0^2 + I/64*(2*c - I*k0)^3*k0^4 - I/32*(2*c - I*k0)*k0^6 - ((5*I)/128*k0^8)/(2*c - I*k0))))/k^2 - I/4*(5*c^4 - (24*I)*c^3*k0 - 12*c^2*k0^2)*(-I/2*(-((c - I*k0)^3*(2*c - I*k0))/(2*k^2) - ((c - I*k0)*(2*c - I*k0)^3)/(2*k^2))*k0^2 - ((3*I)/8*(c - I*k0)*(2*c - I*k0)*k0^4)/k^2 - I*(((c - I*k0)^3*(2*c - I*k0)^3)/(4*k^2) + (3*(c - I*k0)^4*(2*c - I*k0)*(c/k - (I*k0)/k))/(8*k) + (3*(c - I*k0)*(2*c - I*k0)^4*((2*c)/k - (I*k0)/k))/(8*k))) + (3*I)*c^2*((-3*I)/8*(-((c - I*k0)^3*(2*c - I*k0))/(2*k^2) - ((c - I*k0)*(2*c - I*k0)^3)/(2*k^2))*k0^4 - ((5*I)/16*(c - I*k0)*(2*c - I*k0)*k0^6)/k^2 - I/2*k0^2*(((c - I*k0)^3*(2*c - I*k0)^3)/(4*k^2) + (3*(c - I*k0)^4*(2*c - I*k0)*(c/k - (I*k0)/k))/(8*k) + (3*(c - I*k0)*(2*c - I*k0)^4*((2*c)/k - (I*k0)/k))/(8*k)) - I*((-5*(c - I*k0)^6*(2*c - I*k0)*(c/k - (I*k0)/k))/(16*k) - (3*(c - I*k0)^4*(2*c - I*k0)^3*(c/k - (I*k0)/k))/(16*k) - (3*(c - I*k0)^3*(2*c - I*k0)^4*((2*c)/k - (I*k0)/k))/(16*k) - (5*(c - I*k0)*(2*c - I*k0)^6*((2*c)/k - (I*k0)/k))/(16*k))))/((c - I*k0)*(2*c - I*k0)*k0), 0, ((-I*(-((c - I*k0)^3*(2*c - I*k0))/(2*k^2) - ((c - I*k0)*(2*c - I*k0)^3)/(2*k^2)) - (I/2*(c - I*k0)*(2*c - I*k0)*k0^2)/k^2)*((2*I)*c^2*((-5*(c - I*k0)^7)/(128*(2*c - I*k0)) + ((c - I*k0)^5*(2*c - I*k0))/32 + ((c - I*k0)^3*(2*c - I*k0)^3)/64 + ((c - I*k0)*(2*c - I*k0)^5)/32 - (5*(2*c - I*k0)^7)/(128*(c - I*k0))) + 3*c*((-5*(c - I*k0)^7)/(128*(2*c - I*k0)) + ((c - I*k0)^5*(2*c - I*k0))/32 + ((c - I*k0)^3*(2*c - I*k0)^3)/64 + ((c - I*k0)*(2*c - I*k0)^5)/32 - (5*(2*c - I*k0)^7)/(128*(c - I*k0)))*k0 - (4*I)*c^2*((c - I*k0)^5/(16*(2*c - I*k0)) - ((c - I*k0)^3*(2*c - I*k0))/16 - ((c - I*k0)*(2*c - I*k0)^3)/16 + (2*c - I*k0)^5/(16*(c - I*k0)))*k0^2 - I*((-5*(c - I*k0)^7)/(128*(2*c - I*k0)) + ((c - I*k0)^5*(2*c - I*k0))/32 + ((c - I*k0)^3*(2*c - I*k0)^3)/64 + ((c - I*k0)*(2*c - I*k0)^5)/32 - (5*(2*c - I*k0)^7)/(128*(c - I*k0)))*k0^2 - 6*c*((c - I*k0)^5/(16*(2*c - I*k0)) - ((c - I*k0)^3*(2*c - I*k0))/16 - ((c - I*k0)*(2*c - I*k0)^3)/16 + (2*c - I*k0)^5/(16*(c - I*k0)))*k0^3 + (2*I)*((c - I*k0)^5/(16*(2*c - I*k0)) - ((c - I*k0)^3*(2*c - I*k0))/16 - ((c - I*k0)*(2*c - I*k0)^3)/16 + (2*c - I*k0)^5/(16*(c - I*k0)))*k0^4 + 8*c^3*(I/16*(c - I*k0)^5 + I/16*(c - I*k0)^3*k0^2 - I/16*(c - I*k0)*k0^4 - (I/16*k0^6)/(c - I*k0)) - (16*I)*c^2*k0*(I/16*(c - I*k0)^5 + I/16*(c - I*k0)^3*k0^2 - I/16*(c - I*k0)*k0^4 - (I/16*k0^6)/(c - I*k0)) - 10*c*k0^2*(I/16*(c - I*k0)^5 + I/16*(c - I*k0)^3*k0^2 - I/16*(c - I*k0)*k0^4 - (I/16*k0^6)/(c - I*k0)) + (2*I)*k0^3*(I/16*(c - I*k0)^5 + I/16*(c - I*k0)^3*k0^2 - I/16*(c - I*k0)*k0^4 - (I/16*k0^6)/(c - I*k0)) - 8*c^3*(I/16*(2*c - I*k0)^5 + I/16*(2*c - I*k0)^3*k0^2 - I/16*(2*c - I*k0)*k0^4 - (I/16*k0^6)/(2*c - I*k0)) + (20*I)*c^2*k0*(I/16*(2*c - I*k0)^5 + I/16*(2*c - I*k0)^3*k0^2 - I/16*(2*c - I*k0)*k0^4 - (I/16*k0^6)/(2*c - I*k0)) + 16*c*k0^2*(I/16*(2*c - I*k0)^5 + I/16*(2*c - I*k0)^3*k0^2 - I/16*(2*c - I*k0)*k0^4 - (I/16*k0^6)/(2*c - I*k0)) - (4*I)*k0^3*(I/16*(2*c - I*k0)^5 + I/16*(2*c - I*k0)^3*k0^2 - I/16*(2*c - I*k0)*k0^4 - (I/16*k0^6)/(2*c - I*k0)) + c*((-5*I)/128*(c - I*k0)^7 - I/32*(c - I*k0)^5*k0^2 + I/64*(c - I*k0)^3*k0^4 - I/32*(c - I*k0)*k0^6 - ((5*I)/128*k0^8)/(c - I*k0)) - I*k0*((-5*I)/128*(c - I*k0)^7 - I/32*(c - I*k0)^5*k0^2 + I/64*(c - I*k0)^3*k0^4 - I/32*(c - I*k0)*k0^6 - ((5*I)/128*k0^8)/(c - I*k0)) - 4*c*((-5*I)/128*(2*c - I*k0)^7 - I/32*(2*c - I*k0)^5*k0^2 + I/64*(2*c - I*k0)^3*k0^4 - I/32*(2*c - I*k0)*k0^6 - ((5*I)/128*k0^8)/(2*c - I*k0)) + (2*I)*k0*((-5*I)/128*(2*c - I*k0)^7 - I/32*(2*c - I*k0)^5*k0^2 + I/64*(2*c - I*k0)^3*k0^4 - I/32*(2*c - I*k0)*k0^6 - ((5*I)/128*k0^8)/(2*c - I*k0))) - (I*(c - I*k0)*(2*c - I*k0)*((2*I)*c^2*((7*(c - I*k0)^9)/(256*(2*c - I*k0)) - (5*(c - I*k0)^7*(2*c - I*k0))/256 - ((c - I*k0)^5*(2*c - I*k0)^3)/128 - ((c - I*k0)^3*(2*c - I*k0)^5)/128 - (5*(c - I*k0)*(2*c - I*k0)^7)/256 + (7*(2*c - I*k0)^9)/(256*(c - I*k0))) + 3*c*((7*(c - I*k0)^9)/(256*(2*c - I*k0)) - (5*(c - I*k0)^7*(2*c - I*k0))/256 - ((c - I*k0)^5*(2*c - I*k0)^3)/128 - ((c - I*k0)^3*(2*c - I*k0)^5)/128 - (5*(c - I*k0)*(2*c - I*k0)^7)/256 + (7*(2*c - I*k0)^9)/(256*(c - I*k0)))*k0 - (4*I)*c^2*((-5*(c - I*k0)^7)/(128*(2*c - I*k0)) + ((c - I*k0)^5*(2*c - I*k0))/32 + ((c - I*k0)^3*(2*c - I*k0)^3)/64 + ((c - I*k0)*(2*c - I*k0)^5)/32 - (5*(2*c - I*k0)^7)/(128*(c - I*k0)))*k0^2 - I*((7*(c - I*k0)^9)/(256*(2*c - I*k0)) - (5*(c - I*k0)^7*(2*c - I*k0))/256 - ((c - I*k0)^5*(2*c - I*k0)^3)/128 - ((c - I*k0)^3*(2*c - I*k0)^5)/128 - (5*(c - I*k0)*(2*c - I*k0)^7)/256 + (7*(2*c - I*k0)^9)/(256*(c - I*k0)))*k0^2 - 6*c*((-5*(c - I*k0)^7)/(128*(2*c - I*k0)) + ((c - I*k0)^5*(2*c - I*k0))/32 + ((c - I*k0)^3*(2*c - I*k0)^3)/64 + ((c - I*k0)*(2*c - I*k0)^5)/32 - (5*(2*c - I*k0)^7)/(128*(c - I*k0)))*k0^3 + (2*I)*((-5*(c - I*k0)^7)/(128*(2*c - I*k0)) + ((c - I*k0)^5*(2*c - I*k0))/32 + ((c - I*k0)^3*(2*c - I*k0)^3)/64 + ((c - I*k0)*(2*c - I*k0)^5)/32 - (5*(2*c - I*k0)^7)/(128*(c - I*k0)))*k0^4 + 8*c^3*((-5*I)/128*(c - I*k0)^7 - I/32*(c - I*k0)^5*k0^2 + I/64*(c - I*k0)^3*k0^4 - I/32*(c - I*k0)*k0^6 - ((5*I)/128*k0^8)/(c - I*k0)) - (16*I)*c^2*k0*((-5*I)/128*(c - I*k0)^7 - I/32*(c - I*k0)^5*k0^2 + I/64*(c - I*k0)^3*k0^4 - I/32*(c - I*k0)*k0^6 - ((5*I)/128*k0^8)/(c - I*k0)) - 10*c*k0^2*((-5*I)/128*(c - I*k0)^7 - I/32*(c - I*k0)^5*k0^2 + I/64*(c - I*k0)^3*k0^4 - I/32*(c - I*k0)*k0^6 - ((5*I)/128*k0^8)/(c - I*k0)) + (2*I)*k0^3*((-5*I)/128*(c - I*k0)^7 - I/32*(c - I*k0)^5*k0^2 + I/64*(c - I*k0)^3*k0^4 - I/32*(c - I*k0)*k0^6 - ((5*I)/128*k0^8)/(c - I*k0)) - 8*c^3*((-5*I)/128*(2*c - I*k0)^7 - I/32*(2*c - I*k0)^5*k0^2 + I/64*(2*c - I*k0)^3*k0^4 - I/32*(2*c - I*k0)*k0^6 - ((5*I)/128*k0^8)/(2*c - I*k0)) + (20*I)*c^2*k0*((-5*I)/128*(2*c - I*k0)^7 - I/32*(2*c - I*k0)^5*k0^2 + I/64*(2*c - I*k0)^3*k0^4 - I/32*(2*c - I*k0)*k0^6 - ((5*I)/128*k0^8)/(2*c - I*k0)) + 16*c*k0^2*((-5*I)/128*(2*c - I*k0)^7 - I/32*(2*c - I*k0)^5*k0^2 + I/64*(2*c - I*k0)^3*k0^4 - I/32*(2*c - I*k0)*k0^6 - ((5*I)/128*k0^8)/(2*c - I*k0)) - (4*I)*k0^3*((-5*I)/128*(2*c - I*k0)^7 - I/32*(2*c - I*k0)^5*k0^2 + I/64*(2*c - I*k0)^3*k0^4 - I/32*(2*c - I*k0)*k0^6 - ((5*I)/128*k0^8)/(2*c - I*k0)) + c*((7*I)/256*(c - I*k0)^9 + (5*I)/256*(c - I*k0)^7*k0^2 - I/128*(c - I*k0)^5*k0^4 + I/128*(c - I*k0)^3*k0^6 - (5*I)/256*(c - I*k0)*k0^8 - ((7*I)/256*k0^10)/(c - I*k0)) - I*k0*((7*I)/256*(c - I*k0)^9 + (5*I)/256*(c - I*k0)^7*k0^2 - I/128*(c - I*k0)^5*k0^4 + I/128*(c - I*k0)^3*k0^6 - (5*I)/256*(c - I*k0)*k0^8 - ((7*I)/256*k0^10)/(c - I*k0)) - 4*c*((7*I)/256*(2*c - I*k0)^9 + (5*I)/256*(2*c - I*k0)^7*k0^2 - I/128*(2*c - I*k0)^5*k0^4 + I/128*(2*c - I*k0)^3*k0^6 - (5*I)/256*(2*c - I*k0)*k0^8 - ((7*I)/256*k0^10)/(2*c - I*k0)) + (2*I)*k0*((7*I)/256*(2*c - I*k0)^9 + (5*I)/256*(2*c - I*k0)^7*k0^2 - I/128*(2*c - I*k0)^5*k0^4 + I/128*(2*c - I*k0)^3*k0^6 - (5*I)/256*(2*c - I*k0)*k0^8 - ((7*I)/256*k0^10)/(2*c - I*k0))))/k^2 + ((2*I)*c^2*((c - I*k0)^5/(16*(2*c - I*k0)) - ((c - I*k0)^3*(2*c - I*k0))/16 - ((c - I*k0)*(2*c - I*k0)^3)/16 + (2*c - I*k0)^5/(16*(c - I*k0))) + 3*c*((c - I*k0)^5/(16*(2*c - I*k0)) - ((c - I*k0)^3*(2*c - I*k0))/16 - ((c - I*k0)*(2*c - I*k0)^3)/16 + (2*c - I*k0)^5/(16*(c - I*k0)))*k0 - (4*I)*c^2*(-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)))*k0^2 - I*((c - I*k0)^5/(16*(2*c - I*k0)) - ((c - I*k0)^3*(2*c - I*k0))/16 - ((c - I*k0)*(2*c - I*k0)^3)/16 + (2*c - I*k0)^5/(16*(c - I*k0)))*k0^2 - 6*c*(-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)))*k0^3 + (2*I)*(-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)))*k0^4 + 8*c^3*(-I/8*(c - I*k0)^3 - I/4*(c - I*k0)*k0^2 - (I/8*k0^4)/(c - I*k0)) - (16*I)*c^2*k0*(-I/8*(c - I*k0)^3 - I/4*(c - I*k0)*k0^2 - (I/8*k0^4)/(c - I*k0)) - 10*c*k0^2*(-I/8*(c - I*k0)^3 - I/4*(c - I*k0)*k0^2 - (I/8*k0^4)/(c - I*k0)) + (2*I)*k0^3*(-I/8*(c - I*k0)^3 - I/4*(c - I*k0)*k0^2 - (I/8*k0^4)/(c - I*k0)) - 8*c^3*(-I/8*(2*c - I*k0)^3 - I/4*(2*c - I*k0)*k0^2 - (I/8*k0^4)/(2*c - I*k0)) + (20*I)*c^2*k0*(-I/8*(2*c - I*k0)^3 - I/4*(2*c - I*k0)*k0^2 - (I/8*k0^4)/(2*c - I*k0)) + 16*c*k0^2*(-I/8*(2*c - I*k0)^3 - I/4*(2*c - I*k0)*k0^2 - (I/8*k0^4)/(2*c - I*k0)) - (4*I)*k0^3*(-I/8*(2*c - I*k0)^3 - I/4*(2*c - I*k0)*k0^2 - (I/8*k0^4)/(2*c - I*k0)) + c*(I/16*(c - I*k0)^5 + I/16*(c - I*k0)^3*k0^2 - I/16*(c - I*k0)*k0^4 - (I/16*k0^6)/(c - I*k0)) - I*k0*(I/16*(c - I*k0)^5 + I/16*(c - I*k0)^3*k0^2 - I/16*(c - I*k0)*k0^4 - (I/16*k0^6)/(c - I*k0)) - 4*c*(I/16*(2*c - I*k0)^5 + I/16*(2*c - I*k0)^3*k0^2 - I/16*(2*c - I*k0)*k0^4 - (I/16*k0^6)/(2*c - I*k0)) + (2*I)*k0*(I/16*(2*c - I*k0)^5 + I/16*(2*c - I*k0)^3*k0^2 - I/16*(2*c - I*k0)*k0^4 - (I/16*k0^6)/(2*c - I*k0)))*(-I/2*(-((c - I*k0)^3*(2*c - I*k0))/(2*k^2) - ((c - I*k0)*(2*c - I*k0)^3)/(2*k^2))*k0^2 - ((3*I)/8*(c - I*k0)*(2*c - I*k0)*k0^4)/k^2 - I*(((c - I*k0)^3*(2*c - I*k0)^3)/(4*k^2) + (3*(c - I*k0)^4*(2*c - I*k0)*(c/k - (I*k0)/k))/(8*k) + (3*(c - I*k0)*(2*c - I*k0)^4*((2*c)/k - (I*k0)/k))/(8*k))) - I/4*(5*c^4 - (24*I)*c^3*k0 - 12*c^2*k0^2)*((-3*I)/8*(-((c - I*k0)^3*(2*c - I*k0))/(2*k^2) - ((c - I*k0)*(2*c - I*k0)^3)/(2*k^2))*k0^4 - ((5*I)/16*(c - I*k0)*(2*c - I*k0)*k0^6)/k^2 - I/2*k0^2*(((c - I*k0)^3*(2*c - I*k0)^3)/(4*k^2) + (3*(c - I*k0)^4*(2*c - I*k0)*(c/k - (I*k0)/k))/(8*k) + (3*(c - I*k0)*(2*c - I*k0)^4*((2*c)/k - (I*k0)/k))/(8*k)) - I*((-5*(c - I*k0)^6*(2*c - I*k0)*(c/k - (I*k0)/k))/(16*k) - (3*(c - I*k0)^4*(2*c - I*k0)^3*(c/k - (I*k0)/k))/(16*k) - (3*(c - I*k0)^3*(2*c - I*k0)^4*((2*c)/k - (I*k0)/k))/(16*k) - (5*(c - I*k0)*(2*c - I*k0)^6*((2*c)/k - (I*k0)/k))/(16*k))) + (3*I)*c^2*((-5*I)/16*(-((c - I*k0)^3*(2*c - I*k0))/(2*k^2) - ((c - I*k0)*(2*c - I*k0)^3)/(2*k^2))*k0^6 - ((35*I)/128*(c - I*k0)*(2*c - I*k0)*k0^8)/k^2 - (3*I)/8*k0^4*(((c - I*k0)^3*(2*c - I*k0)^3)/(4*k^2) + (3*(c - I*k0)^4*(2*c - I*k0)*(c/k - (I*k0)/k))/(8*k) + (3*(c - I*k0)*(2*c - I*k0)^4*((2*c)/k - (I*k0)/k))/(8*k)) - I/2*k0^2*((-5*(c - I*k0)^6*(2*c - I*k0)*(c/k - (I*k0)/k))/(16*k) - (3*(c - I*k0)^4*(2*c - I*k0)^3*(c/k - (I*k0)/k))/(16*k) - (3*(c - I*k0)^3*(2*c - I*k0)^4*((2*c)/k - (I*k0)/k))/(16*k) - (5*(c - I*k0)*(2*c - I*k0)^6*((2*c)/k - (I*k0)/k))/(16*k)) - I*((35*(c - I*k0)^8*(2*c - I*k0)*(c/k - (I*k0)/k))/(128*k) + (5*(c - I*k0)^6*(2*c - I*k0)^3*(c/k - (I*k0)/k))/(32*k) + (5*(c - I*k0)^3*(2*c - I*k0)^6*((2*c)/k - (I*k0)/k))/(32*k) + (35*(c - I*k0)*(2*c - I*k0)^8*((2*c)/k - (I*k0)/k))/(128*k) + (9*(c - I*k0)^4*(2*c - I*k0)^4*(c/k - (I*k0)/k)*((2*c)/k - (I*k0)/k))/64)))/((c - I*k0)*(2*c - I*k0)*k0)}, 1, 11, 1]] diff --git a/besseltransforms/2-1-3 b/besseltransforms/2-1-3 deleted file mode 100644 index b9ff315..0000000 --- a/besseltransforms/2-1-3 +++ /dev/null @@ -1,2 +0,0 @@ -((k^2*(-3 + Sqrt[1 + k^2/(c - I*k0)^2]) + 4*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^2)/Sqrt[1 + k^2/(c - I*k0)^2] - (2*(k^2*(-3 + Sqrt[1 + k^2/(2*c - I*k0)^2]) + 4*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^2))/Sqrt[1 + k^2/(2*c - I*k0)^2] + (k^2*(-3 + Sqrt[1 + k^2/(3*c - I*k0)^2]) + 4*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^2)/Sqrt[1 + k^2/(3*c - I*k0)^2])/(k^3*k0) -SeriesData[k, Infinity, {(8*c^2)/(k*k0), (-15*(2*c^3 - I*c^2*k0))/(k*k0), 0, (35*(18*c^5 - (25*I)*c^4*k0 - 12*c^3*k0^2 + (2*I)*c^2*k0^3))/(4*k*k0), 0, (63*(-138*c^7 + (301*I)*c^6*k0 + 270*c^5*k0^2 - (125*I)*c^4*k0^3 - 30*c^3*k0^4 + (3*I)*c^2*k0^5))/(8*k*k0), 0, (165*(3110*c^9 - (9075*I)*c^8*k0 - 11592*c^7*k0^2 + (8428*I)*c^6*k0^3 + 3780*c^5*k0^4 - (1050*I)*c^4*k0^5 - 168*c^3*k0^6 + (12*I)*c^2*k0^7))/(64*k*k0)}, 2, 11, 1] diff --git a/besseltransforms/2-1-4 b/besseltransforms/2-1-4 deleted file mode 100644 index 0eb249d..0000000 --- a/besseltransforms/2-1-4 +++ /dev/null @@ -1,2 +0,0 @@ -((k^4 - 4*k^2*(-2 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^2 - 8*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^4)/(Sqrt[1 + k^2/(c - I*k0)^2]*(c - I*k0)) - (2*(k^4 - 4*k^2*(-2 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^2 - 8*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^4))/(Sqrt[1 + k^2/(2*c - I*k0)^2]*(2*c - I*k0)) + (k^4 - 4*k^2*(-2 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^2 - 8*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^4)/(Sqrt[1 + k^2/(3*c - I*k0)^2]*(3*c - I*k0)))/(k^4*k0) -SeriesData[k, Infinity, {(15*c^2)/(k*k0), (-48*(2*c^3 - I*c^2*k0))/(k*k0), (35*(25*c^4 - (24*I)*c^3*k0 - 6*c^2*k0^2))/(4*k*k0), 0, (-21*(301*c^6 - (540*I)*c^5*k0 - 375*c^4*k0^2 + (120*I)*c^3*k0^3 + 15*c^2*k0^4))/(8*k*k0), 0, (-99*(-3025*c^8 + (7728*I)*c^7*k0 + 8428*c^6*k0^2 - (5040*I)*c^5*k0^3 - 1750*c^4*k0^4 + (336*I)*c^3*k0^5 + 28*c^2*k0^6))/(64*k*k0), 0, (-143*(28501*c^10 - (93300*I)*c^9*k0 - 136125*c^8*k0^2 + (115920*I)*c^7*k0^3 + 63210*c^6*k0^4 - (22680*I)*c^5*k0^5 - 5250*c^4*k0^6 + (720*I)*c^3*k0^7 + 45*c^2*k0^8))/(128*k*k0)}, 2, 11, 1] diff --git a/besseltransforms/2-1-5 b/besseltransforms/2-1-5 deleted file mode 100644 index 2061c66..0000000 --- a/besseltransforms/2-1-5 +++ /dev/null @@ -1,2 +0,0 @@ -((k^4*(-5 + Sqrt[1 + k^2/(c - I*k0)^2]) + 4*k^2*(-5 + 3*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^2 + 16*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^4)/Sqrt[1 + k^2/(c - I*k0)^2] - (2*(k^4*(-5 + Sqrt[1 + k^2/(2*c - I*k0)^2]) + 4*k^2*(-5 + 3*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^2 + 16*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^4))/Sqrt[1 + k^2/(2*c - I*k0)^2] + (k^4*(-5 + Sqrt[1 + k^2/(3*c - I*k0)^2]) + 4*k^2*(-5 + 3*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^2 + 16*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^4)/Sqrt[1 + k^2/(3*c - I*k0)^2])/(k^5*k0) -SeriesData[k, Infinity, {(24*c^2)/(k*k0), (-105*(2*c^3 - I*c^2*k0))/(k*k0), (32*(25*c^4 - (24*I)*c^3*k0 - 6*c^2*k0^2))/(k*k0), (-315*(18*c^5 - (25*I)*c^4*k0 - 12*c^3*k0^2 + (2*I)*c^2*k0^3))/(4*k*k0), 0, (231*(138*c^7 - (301*I)*c^6*k0 - 270*c^5*k0^2 + (125*I)*c^4*k0^3 + 30*c^3*k0^4 - (3*I)*c^2*k0^5))/(8*k*k0), 0, (429*(-3110*c^9 + (9075*I)*c^8*k0 + 11592*c^7*k0^2 - (8428*I)*c^6*k0^3 - 3780*c^5*k0^4 + (1050*I)*c^4*k0^5 + 168*c^3*k0^6 - (12*I)*c^2*k0^7))/(64*k*k0)}, 2, 11, 1] diff --git a/besseltransforms/2-1-6 b/besseltransforms/2-1-6 deleted file mode 100644 index 900e941..0000000 --- a/besseltransforms/2-1-6 +++ /dev/null @@ -1,2 +0,0 @@ -((k^6 - 6*k^4*(-3 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^2 + 16*k^2*(3 - 2*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^4 - 32*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^6)/(Sqrt[1 + k^2/(c - I*k0)^2]*(c - I*k0)) - (2*(k^6 - 6*k^4*(-3 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^2 + 16*k^2*(3 - 2*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^4 - 32*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^6))/(Sqrt[1 + k^2/(2*c - I*k0)^2]*(2*c - I*k0)) + (k^6 - 6*k^4*(-3 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^2 + 16*k^2*(3 - 2*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^4 - 32*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^6)/(Sqrt[1 + k^2/(3*c - I*k0)^2]*(3*c - I*k0)))/(k^6*k0) -SeriesData[k, Infinity, {(35*c^2)/(k*k0), (-192*(2*c^3 - I*c^2*k0))/(k*k0), (315*(25*c^4 - (24*I)*c^3*k0 - 6*c^2*k0^2))/(4*k*k0), (-320*(18*c^5 - (25*I)*c^4*k0 - 12*c^3*k0^2 + (2*I)*c^2*k0^3))/(k*k0), (231*(301*c^6 - (540*I)*c^5*k0 - 375*c^4*k0^2 + (120*I)*c^3*k0^3 + 15*c^2*k0^4))/(8*k*k0), 0, (429*(-3025*c^8 + (7728*I)*c^7*k0 + 8428*c^6*k0^2 - (5040*I)*c^5*k0^3 - 1750*c^4*k0^4 + (336*I)*c^3*k0^5 + 28*c^2*k0^6))/(64*k*k0), 0, (429*(28501*c^10 - (93300*I)*c^9*k0 - 136125*c^8*k0^2 + (115920*I)*c^7*k0^3 + 63210*c^6*k0^4 - (22680*I)*c^5*k0^5 - 5250*c^4*k0^6 + (720*I)*c^3*k0^7 + 45*c^2*k0^8))/(128*k*k0)}, 2, 11, 1] diff --git a/besseltransforms/2-1-7 b/besseltransforms/2-1-7 deleted file mode 100644 index b576a37..0000000 --- a/besseltransforms/2-1-7 +++ /dev/null @@ -1,2 +0,0 @@ -((k^6*(-7 + Sqrt[1 + k^2/(c - I*k0)^2]) + 8*k^4*(-7 + 3*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^2 + 16*k^2*(-7 + 5*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^4 + 64*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^6)/Sqrt[1 + k^2/(c - I*k0)^2] - (2*(k^6*(-7 + Sqrt[1 + k^2/(2*c - I*k0)^2]) + 8*k^4*(-7 + 3*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^2 + 16*k^2*(-7 + 5*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^4 + 64*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^6))/Sqrt[1 + k^2/(2*c - I*k0)^2] + (k^6*(-7 + Sqrt[1 + k^2/(3*c - I*k0)^2]) + 8*k^4*(-7 + 3*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^2 + 16*k^2*(-7 + 5*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^4 + 64*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^6)/Sqrt[1 + k^2/(3*c - I*k0)^2])/(k^7*k0) -SeriesData[k, Infinity, {(48*c^2)/(k*k0), (-315*(2*c^3 - I*c^2*k0))/(k*k0), (160*(25*c^4 - (24*I)*c^3*k0 - 6*c^2*k0^2))/(k*k0), (-3465*(18*c^5 - (25*I)*c^4*k0 - 12*c^3*k0^2 + (2*I)*c^2*k0^3))/(4*k*k0), (128*(301*c^6 - (540*I)*c^5*k0 - 375*c^4*k0^2 + (120*I)*c^3*k0^3 + 15*c^2*k0^4))/(k*k0), (3003*(-138*c^7 + (301*I)*c^6*k0 + 270*c^5*k0^2 - (125*I)*c^4*k0^3 - 30*c^3*k0^4 + (3*I)*c^2*k0^5))/(8*k*k0), 0, (2145*(3110*c^9 - (9075*I)*c^8*k0 - 11592*c^7*k0^2 + (8428*I)*c^6*k0^3 + 3780*c^5*k0^4 - (1050*I)*c^4*k0^5 - 168*c^3*k0^6 + (12*I)*c^2*k0^7))/(64*k*k0)}, 2, 11, 1] diff --git a/besseltransforms/2-2-0 b/besseltransforms/2-2-0 deleted file mode 100644 index e69de29..0000000 diff --git a/besseltransforms/2-2-1 b/besseltransforms/2-2-1 deleted file mode 100644 index ef9e915..0000000 --- a/besseltransforms/2-2-1 +++ /dev/null @@ -1,2 +0,0 @@ -((-2*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0))/k + ((-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0))/k + (Sqrt[Pi]*(Piecewise[{{0, k^2/k0^2 <= 1}}, (2*Sqrt[k^2 - k0^2])/(k*Sqrt[Pi])] + I*Piecewise[{{(2*k0)/(k*Sqrt[Pi]), k0^2/k^2 < 1}, {(2*(k0 - Sqrt[-k^2 + k0^2]))/(k*Sqrt[Pi]), k0^2/k^2 > 1}}, 0]))/2)/k0^2 -Piecewise[{{SeriesData[k, Infinity, {c^2/k0^2, 0, (3*c^2)/2 - (7*c^4)/(4*k0^2) + ((3*I)*c^3)/k0, 0, (31*c^6 - (90*I)*c^5*k0 - 105*c^4*k0^2 + (60*I)*c^3*k0^3 + 15*c^2*k0^4)/(8*k0^2), 0, (-5*(127*c^8 - (504*I)*c^7*k0 - 868*c^6*k0^2 + (840*I)*c^5*k0^3 + 490*c^4*k0^4 - (168*I)*c^3*k0^5 - 28*c^2*k0^6))/(64*k0^2), 0, (7*(511*c^10 - (2550*I)*c^9*k0 - 5715*c^8*k0^2 + (7560*I)*c^7*k0^3 + 6510*c^6*k0^4 - (3780*I)*c^5*k0^5 - 1470*c^4*k0^6 + (360*I)*c^3*k0^7 + 45*c^2*k0^8))/(128*k0^2)}, 2, 11, 1], (k0 <= 0 && k^2/k0^2 > 1) || k0 > 0}}, SeriesData[k, Infinity, {-k0^(-2), 0, (2*c^2 + k0^2)/(2*k0^2), 0, ((c*(c - I*k0)^3)/4 - (c*(2*c - I*k0)^3)/4 - I/4*(c - I*k0)^3*k0 + I/8*(2*c - I*k0)^3*k0)/k0^2, 0, (-(c*(c - I*k0)^5)/8 + (c*(2*c - I*k0)^5)/8 + I/8*(c - I*k0)^5*k0 - I/16*(2*c - I*k0)^5*k0)/k0^2, 0, ((5*c*(c - I*k0)^7)/64 - (5*c*(2*c - I*k0)^7)/64 - (5*I)/64*(c - I*k0)^7*k0 + (5*I)/128*(2*c - I*k0)^7*k0)/k0^2, 0, ((-7*c*(c - I*k0)^9)/128 + (7*c*(2*c - I*k0)^9)/128 + (7*I)/128*(c - I*k0)^9*k0 - (7*I)/256*(2*c - I*k0)^9*k0)/k0^2}, 0, 11, 1]] diff --git a/besseltransforms/2-2-2 b/besseltransforms/2-2-2 deleted file mode 100644 index 16eff75..0000000 --- a/besseltransforms/2-2-2 +++ /dev/null @@ -1,2 +0,0 @@ -(-1 + (4*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^2)/k^2 - (2*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^2)/k^2 + Sqrt[Pi]*(I*Piecewise[{{0, k^2/k0^2 <= 1}}, (2*k0*Sqrt[k^2 - k0^2])/(k^2*Sqrt[Pi])] + Piecewise[{{(k^2 + 2*k0*(-k0 + Sqrt[-k^2 + k0^2]))/(k^2*Sqrt[Pi]), k^2/k0^2 < 1}, {(1 - (2*k0^2)/k^2)/Sqrt[Pi], k^2/k0^2 > 1}}, 0]))/(2*k0^2) -SeriesData[k, Infinity, {(2*c^2)/k0^2, (-3*(c^3 - I*c^2*k0))/k0^2, 0, (5*(3*c^5 - (7*I)*c^4*k0 - 6*c^3*k0^2 + (2*I)*c^2*k0^3))/(4*k0^2), 0, (-7*(9*c^7 - (31*I)*c^6*k0 - 45*c^5*k0^2 + (35*I)*c^4*k0^3 + 15*c^3*k0^4 - (3*I)*c^2*k0^5))/(8*k0^2), 0, (15*(85*c^9 - (381*I)*c^8*k0 - 756*c^7*k0^2 + (868*I)*c^6*k0^3 + 630*c^5*k0^4 - (294*I)*c^4*k0^5 - 84*c^3*k0^6 + (12*I)*c^2*k0^7))/(64*k0^2)}, 2, 11, 1] diff --git a/besseltransforms/2-2-3 b/besseltransforms/2-2-3 deleted file mode 100644 index d78923c..0000000 --- a/besseltransforms/2-2-3 +++ /dev/null @@ -1,2 +0,0 @@ -(k^2*(-3 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0) + 4*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^3 - 2*k^2*(-3 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0) - 8*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^3 + k^2*(-3 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0) + 4*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^3)/(3*k^3*k0^2) -SeriesData[k, Infinity, {(3*c^2)/k0^2, (-16*c^3)/k0^2 + ((8*I)*c^2)/k0, (-15*c^2)/2 + (125*c^4)/(4*k0^2) - ((30*I)*c^3)/k0, 0, (-7*(301*c^6 - (540*I)*c^5*k0 - 375*c^4*k0^2 + (120*I)*c^3*k0^3 + 15*c^2*k0^4))/(24*k0^2), 0, (9*(3025*c^8 - (7728*I)*c^7*k0 - 8428*c^6*k0^2 + (5040*I)*c^5*k0^3 + 1750*c^4*k0^4 - (336*I)*c^3*k0^5 - 28*c^2*k0^6))/(64*k0^2), 0, (-11*(28501*c^10 - (93300*I)*c^9*k0 - 136125*c^8*k0^2 + (115920*I)*c^7*k0^3 + 63210*c^6*k0^4 - (22680*I)*c^5*k0^5 - 5250*c^4*k0^6 + (720*I)*c^3*k0^7 + 45*c^2*k0^8))/(128*k0^2)}, 2, 11, 1] diff --git a/besseltransforms/2-2-4 b/besseltransforms/2-2-4 deleted file mode 100644 index 3da9cf6..0000000 --- a/besseltransforms/2-2-4 +++ /dev/null @@ -1,2 +0,0 @@ --(2*k^2*(-2 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^2 + 4*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^4 - 4*k^2*(-2 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^2 - 8*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^4 + 2*k^2*(-2 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^2 + 4*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^4)/(2*k^4*k0^2) -SeriesData[k, Infinity, {(4*c^2)/k0^2, (-30*c^3)/k0^2 + ((15*I)*c^2)/k0, -24*c^2 + (100*c^4)/k0^2 - ((96*I)*c^3)/k0, 105*c^3 - (315*c^5)/(2*k0^2) + ((875*I)/4*c^4)/k0 - (35*I)/2*c^2*k0, 0, (21*(138*c^7 - (301*I)*c^6*k0 - 270*c^5*k0^2 + (125*I)*c^4*k0^3 + 30*c^3*k0^4 - (3*I)*c^2*k0^5))/(8*k0^2), 0, (-33*(3110*c^9 - (9075*I)*c^8*k0 - 11592*c^7*k0^2 + (8428*I)*c^6*k0^3 + 3780*c^5*k0^4 - (1050*I)*c^4*k0^5 - 168*c^3*k0^6 + (12*I)*c^2*k0^7))/(64*k0^2)}, 2, 11, 1] diff --git a/besseltransforms/2-2-5 b/besseltransforms/2-2-5 deleted file mode 100644 index 39aa789..0000000 --- a/besseltransforms/2-2-5 +++ /dev/null @@ -1,2 +0,0 @@ -(-2*(k^4*(-5 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0) + 4*k^2*(-5 + 3*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^3 + 16*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^5) + k^4*(-5 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0) + 4*k^2*(-5 + 3*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^3 + 16*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^5 + k^4*(-5 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0) + 4*k^2*(-5 + 3*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^3 + 16*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^5)/(5*k^5*k0^2) -SeriesData[k, Infinity, {(5*c^2)/k0^2, (-24*(2*c^3 - I*c^2*k0))/k0^2, (35*(25*c^4 - (24*I)*c^3*k0 - 6*c^2*k0^2))/(4*k0^2), (-32*(18*c^5 - (25*I)*c^4*k0 - 12*c^3*k0^2 + (2*I)*c^2*k0^3))/k0^2, (21*(301*c^6 - (540*I)*c^5*k0 - 375*c^4*k0^2 + (120*I)*c^3*k0^3 + 15*c^2*k0^4))/(8*k0^2), 0, ((-165*(c - I*k0)^8)/128 + (165*(2*c - I*k0)^8)/64 - (165*(3*c - I*k0)^8)/128)/(5*k0^2), 0, ((143*(c - I*k0)^10)/256 - (143*(2*c - I*k0)^10)/128 + (143*(3*c - I*k0)^10)/256)/(5*k0^2)}, 2, 11, 1] diff --git a/besseltransforms/2-2-6 b/besseltransforms/2-2-6 deleted file mode 100644 index edf6ace..0000000 --- a/besseltransforms/2-2-6 +++ /dev/null @@ -1,2 +0,0 @@ -(-3*k^4*(-3 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^2 + 8*k^2*(3 - 2*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^4 - 16*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^6 + 6*k^4*(-3 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^2 + 16*k^2*(-3 + 2*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^4 + 32*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^6 - 3*k^4*(-3 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^2 + 8*k^2*(3 - 2*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^4 - 16*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^6)/(3*k^6*k0^2) -SeriesData[k, Infinity, {(6*c^2)/k0^2, (-35*(2*c^3 - I*c^2*k0))/k0^2, (16*(25*c^4 - (24*I)*c^3*k0 - 6*c^2*k0^2))/k0^2, (-315*(18*c^5 - (25*I)*c^4*k0 - 12*c^3*k0^2 + (2*I)*c^2*k0^3))/(4*k0^2), (16*(c - I*k0)^6 - 32*(2*c - I*k0)^6 + 16*(3*c - I*k0)^6)/(3*k0^2), ((-99*(c - I*k0)^7)/16 + (99*(2*c - I*k0)^7)/8 - (99*(3*c - I*k0)^7)/16)/(3*k0^2), 0, ((143*(c - I*k0)^9)/128 - (143*(2*c - I*k0)^9)/64 + (143*(3*c - I*k0)^9)/128)/(3*k0^2)}, 2, 11, 1] diff --git a/besseltransforms/2-2-7 b/besseltransforms/2-2-7 deleted file mode 100644 index ee5cf53..0000000 --- a/besseltransforms/2-2-7 +++ /dev/null @@ -1,2 +0,0 @@ -(-2*(k^6*(-7 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0) + 8*k^4*(-7 + 3*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^3 + 16*k^2*(-7 + 5*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^5 + 64*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^7) + k^6*(-7 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0) + 8*k^4*(-7 + 3*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^3 + 16*k^2*(-7 + 5*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^5 + 64*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^7 + k^6*(-7 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0) + 8*k^4*(-7 + 3*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^3 + 16*k^2*(-7 + 5*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^5 + 64*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^7)/(7*k^7*k0^2) -SeriesData[k, Infinity, {(7*c^2)/k0^2, (-48*(2*c^3 - I*c^2*k0))/k0^2, (105*(25*c^4 - (24*I)*c^3*k0 - 6*c^2*k0^2))/(4*k0^2), (-160*(18*c^5 - (25*I)*c^4*k0 - 12*c^3*k0^2 + (2*I)*c^2*k0^3))/k0^2, (231*(301*c^6 - (540*I)*c^5*k0 - 375*c^4*k0^2 + (120*I)*c^3*k0^3 + 15*c^2*k0^4))/(8*k0^2), (-64*(c - I*k0)^7 + 128*(2*c - I*k0)^7 - 64*(3*c - I*k0)^7)/(7*k0^2), ((3003*(c - I*k0)^8)/128 - (3003*(2*c - I*k0)^8)/64 + (3003*(3*c - I*k0)^8)/128)/(7*k0^2), 0, ((-1001*(c - I*k0)^10)/256 + (1001*(2*c - I*k0)^10)/128 - (1001*(3*c - I*k0)^10)/256)/(7*k0^2)}, 2, 11, 1] diff --git a/besseltransforms/2-3-0 b/besseltransforms/2-3-0 deleted file mode 100644 index e69de29..0000000 diff --git a/besseltransforms/2-3-1 b/besseltransforms/2-3-1 deleted file mode 100644 index 42b69b8..0000000 --- a/besseltransforms/2-3-1 +++ /dev/null @@ -1,9 +0,0 @@ -Integrate[(E^(I*k0*x)*(-1 + E^(-(c*x)))^2*BesselJ[1, k*x])/(k0^3*x^2), {x, 0, Infinity}, Assumptions -> n == 1 && q == 3 && κ == 2] - - -2 c x + I k0 x c x 2 2 2 4 4 6 6 8 8 Pi 2 2 4 4 6 6 8 8 Pi - -(E (-1 + E ) (8 k x (-14783093325 + 1452971520 k x - 309657600 k x + 251658240 k x + 2147483648 k x ) Cos[-- + k x] - 3 (156043762875 - 11416204800 k x + 1589575680 k x - 587202560 k x + 2147483648 k x ) Sin[-- + k x])) - 4 4 -Integrate::idiv: Integral of ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ does not converge on {0, Infinity}. - 19/2 3 23/2 - 8589934592 k k0 Sqrt[2 Pi] x -Series[Integrate[(E^(I*k0*x)*(-1 + E^(-(c*x)))^2*BesselJ[1, k*x])/(k0^3*x^2), {x, 0, Infinity}, Assumptions -> n == 1 && q == 3 && κ == 2], {k, Infinity, 10}] diff --git a/besseltransforms/2-3-2 b/besseltransforms/2-3-2 deleted file mode 100644 index 52a4158..0000000 --- a/besseltransforms/2-3-2 +++ /dev/null @@ -1,2 +0,0 @@ -(-4*(-3 + 2*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0) - (8*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^3)/k^2 + 2*(-3 + 2*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0) + (4*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^3)/k^2 + 3*k0*Sqrt[Pi]*(Piecewise[{{0, k^2/k0^2 <= 1}}, (4*(k^2 - k0^2)^(3/2))/(3*k^2*k0*Sqrt[Pi])] + I*Piecewise[{{(-2*(2*k0*(k0 - Sqrt[-k^2 + k0^2]) + k^2*(-3 + (2*Sqrt[-k^2 + k0^2])/k0)))/(3*k^2*Sqrt[Pi]), k^2/k0^2 < 1}, {(2*(1 - (2*k0^2)/(3*k^2)))/Sqrt[Pi], k^2/k0^2 > 1}}, 0]))/(12*k0^3) -SeriesData[k, Infinity, {c^2/k0^3, (-2*(c^3 - I*c^2*k0))/k0^3, (7*c^4 - (12*I)*c^3*k0 - 6*c^2*k0^2)/(4*k0^3), 0, (-31*c^6 + (90*I)*c^5*k0 + 105*c^4*k0^2 - (60*I)*c^3*k0^3 - 15*c^2*k0^4)/(24*k0^3), 0, (127*c^8 - (504*I)*c^7*k0 - 868*c^6*k0^2 + (840*I)*c^5*k0^3 + 490*c^4*k0^4 - (168*I)*c^3*k0^5 - 28*c^2*k0^6)/(64*k0^3), 0, (-511*c^10 + (2550*I)*c^9*k0 + 5715*c^8*k0^2 - (7560*I)*c^7*k0^3 - 6510*c^6*k0^4 + (3780*I)*c^5*k0^5 + 1470*c^4*k0^6 - (360*I)*c^3*k0^7 - 45*c^2*k0^8)/(128*k0^3)}, 1, 11, 1] diff --git a/besseltransforms/2-3-3 b/besseltransforms/2-3-3 deleted file mode 100644 index 99e8566..0000000 --- a/besseltransforms/2-3-3 +++ /dev/null @@ -1,2 +0,0 @@ -(k^2*(3 - 2*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^2 - 2*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^4 + 2*k^2*(-3 + 2*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^2 + 4*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^4 + k^2*(3 - 2*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^2 - 2*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^4)/(6*k^3*k0^3) -SeriesData[k, Infinity, {c^2/k0^3, (-3*(2*c^3 - I*c^2*k0))/k0^3, (2*(25*c^4 - (24*I)*c^3*k0 - 6*c^2*k0^2))/(3*k0^3), (-5*(18*c^5 - (25*I)*c^4*k0 - 12*c^3*k0^2 + (2*I)*c^2*k0^3))/(4*k0^3), 0, ((c - I*k0)^7/8 - (2*c - I*k0)^7/4 + (3*c - I*k0)^7/8)/(6*k0^3), 0, ((-3*(c - I*k0)^9)/64 + (3*(2*c - I*k0)^9)/32 - (3*(3*c - I*k0)^9)/64)/(6*k0^3), 0, ((3*(c - I*k0)^11)/128 - (3*(2*c - I*k0)^11)/64 + (3*(3*c - I*k0)^11)/128)/(6*k0^3)}, 1, 11, 1] diff --git a/besseltransforms/2-3-4 b/besseltransforms/2-3-4 deleted file mode 100644 index f7f8b9b..0000000 --- a/besseltransforms/2-3-4 +++ /dev/null @@ -1,2 +0,0 @@ -(-2*(k^4*(-15 + 4*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0) + 4*k^2*(-10 + 7*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^3 + 24*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^5) + k^4*(-15 + 4*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0) + 4*k^2*(-10 + 7*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^3 + 24*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^5 + k^4*(-15 + 4*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0) + 4*k^2*(-10 + 7*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^3 + 24*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^5)/(60*k^4*k0^3) -SeriesData[k, Infinity, {c^2/k0^3, (-4*(2*c^3 - I*c^2*k0))/k0^3, (5*(25*c^4 - (24*I)*c^3*k0 - 6*c^2*k0^2))/(4*k0^3), (-4*(18*c^5 - (25*I)*c^4*k0 - 12*c^3*k0^2 + (2*I)*c^2*k0^3))/k0^3, (7*(301*c^6 - (540*I)*c^5*k0 - 375*c^4*k0^2 + (120*I)*c^3*k0^3 + 15*c^2*k0^4))/(24*k0^3), 0, ((-45*(c - I*k0)^8)/32 + (45*(2*c - I*k0)^8)/16 - (45*(3*c - I*k0)^8)/32)/(60*k0^3), 0, ((33*(c - I*k0)^10)/64 - (33*(2*c - I*k0)^10)/32 + (33*(3*c - I*k0)^10)/64)/(60*k0^3)}, 1, 11, 1] diff --git a/besseltransforms/2-3-5 b/besseltransforms/2-3-5 deleted file mode 100644 index 19de25b..0000000 --- a/besseltransforms/2-3-5 +++ /dev/null @@ -1,2 +0,0 @@ -(6*k^4*(5 - 2*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^2 + 4*k^2*(15 - 11*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^4 - 32*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^6 + 12*k^4*(-5 + 2*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^2 + 8*k^2*(-15 + 11*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^4 + 64*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^6 + 6*k^4*(5 - 2*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^2 + 4*k^2*(15 - 11*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^4 - 32*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^6)/(60*k^5*k0^3) -SeriesData[k, Infinity, {c^2/k0^3, (-5*(2*c^3 - I*c^2*k0))/k0^3, (2*(25*c^4 - (24*I)*c^3*k0 - 6*c^2*k0^2))/k0^3, (-35*(18*c^5 - (25*I)*c^4*k0 - 12*c^3*k0^2 + (2*I)*c^2*k0^3))/(4*k0^3), (32*(c - I*k0)^6 - 64*(2*c - I*k0)^6 + 32*(3*c - I*k0)^6)/(60*k0^3), ((-45*(c - I*k0)^7)/4 + (45*(2*c - I*k0)^7)/2 - (45*(3*c - I*k0)^7)/4)/(60*k0^3), 0, ((55*(c - I*k0)^9)/32 - (55*(2*c - I*k0)^9)/16 + (55*(3*c - I*k0)^9)/32)/(60*k0^3), 0, ((-39*(c - I*k0)^11)/64 + (39*(2*c - I*k0)^11)/32 - (39*(3*c - I*k0)^11)/64)/(60*k0^3)}, 1, 11, 1] diff --git a/besseltransforms/2-3-6 b/besseltransforms/2-3-6 deleted file mode 100644 index 36b5ad4..0000000 --- a/besseltransforms/2-3-6 +++ /dev/null @@ -1,2 +0,0 @@ -(-2*(k^6*(-35 + 6*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0) + 6*k^4*(-35 + 17*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^3 + 16*k^2*(-21 + 16*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^5 + 160*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^7) + k^6*(-35 + 6*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0) + 6*k^4*(-35 + 17*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^3 + 16*k^2*(-21 + 16*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^5 + 160*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^7 + k^6*(-35 + 6*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0) + 6*k^4*(-35 + 17*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^3 + 16*k^2*(-21 + 16*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^5 + 160*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^7)/(210*k^6*k0^3) -SeriesData[k, Infinity, {c^2/k0^3, (-6*(2*c^3 - I*c^2*k0))/k0^3, (35*(25*c^4 - (24*I)*c^3*k0 - 6*c^2*k0^2))/(12*k0^3), (-16*(18*c^5 - (25*I)*c^4*k0 - 12*c^3*k0^2 + (2*I)*c^2*k0^3))/k0^3, (21*(301*c^6 - (540*I)*c^5*k0 - 375*c^4*k0^2 + (120*I)*c^3*k0^3 + 15*c^2*k0^4))/(8*k0^3), (-160*(c - I*k0)^7 + 320*(2*c - I*k0)^7 - 160*(3*c - I*k0)^7)/(210*k0^3), ((3465*(c - I*k0)^8)/64 - (3465*(2*c - I*k0)^8)/32 + (3465*(3*c - I*k0)^8)/64)/(210*k0^3), 0, ((-1001*(c - I*k0)^10)/128 + (1001*(2*c - I*k0)^10)/64 - (1001*(3*c - I*k0)^10)/128)/(210*k0^3)}, 1, 11, 1] diff --git a/besseltransforms/2-3-7 b/besseltransforms/2-3-7 deleted file mode 100644 index cae73a7..0000000 --- a/besseltransforms/2-3-7 +++ /dev/null @@ -1,2 +0,0 @@ -((7*k^8 + 24*k^6*(7 - 2*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^2 + 16*k^4*(42 - 23*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^4 + 64*k^2*(14 - 11*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^6 - 384*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^8)/(336*k^7) - (7*k^8 + 24*k^6*(7 - 2*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^2 + 16*k^4*(42 - 23*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^4 + 64*k^2*(14 - 11*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^6 - 384*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^8)/(168*k^7) + (7*k^8 + 24*k^6*(7 - 2*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^2 + 16*k^4*(42 - 23*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^4 + 64*k^2*(14 - 11*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^6 - 384*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^8)/(336*k^7))/k0^3 -SeriesData[k, Infinity, {c^2/k0^3, (-7*(2*c^3 - I*c^2*k0))/k0^3, (4*(25*c^4 - (24*I)*c^3*k0 - 6*c^2*k0^2))/k0^3, (-105*(18*c^5 - (25*I)*c^4*k0 - 12*c^3*k0^2 + (2*I)*c^2*k0^3))/(4*k0^3), (16*(301*c^6 - (540*I)*c^5*k0 - 375*c^4*k0^2 + (120*I)*c^3*k0^3 + 15*c^2*k0^4))/(3*k0^3), ((-33*(c - I*k0)^7)/16 + (33*(2*c - I*k0)^7)/8 - (33*(3*c - I*k0)^7)/16)/k0^3, ((8*(c - I*k0)^8)/7 - (16*(2*c - I*k0)^8)/7 + (8*(3*c - I*k0)^8)/7)/k0^3, ((-143*(c - I*k0)^9)/384 + (143*(2*c - I*k0)^9)/192 - (143*(3*c - I*k0)^9)/384)/k0^3, 0, ((13*(c - I*k0)^11)/256 - (13*(2*c - I*k0)^11)/128 + (13*(3*c - I*k0)^11)/256)/k0^3}, 1, 11, 1] diff --git a/besseltransforms/3-1-0 b/besseltransforms/3-1-0 deleted file mode 100644 index 2dd4e66..0000000 --- a/besseltransforms/3-1-0 +++ /dev/null @@ -1,2 +0,0 @@ -(-3/(Sqrt[1 + k^2/(c - I*k0)^2]*(c - I*k0)) + 3/(Sqrt[1 + k^2/(2*c - I*k0)^2]*(2*c - I*k0)) - 1/(Sqrt[1 + k^2/(3*c - I*k0)^2]*(3*c - I*k0)) + (Sqrt[Pi]*(I*Piecewise[{{0, k0^2/k^2 <= 1}}, k/(Sqrt[-k^2 + k0^2]*Sqrt[Pi])] + Piecewise[{{k/(Sqrt[k^2 - k0^2]*Sqrt[Pi]), k0^2/k^2 < 1}}, 0]))/k)/k0 -SeriesData[k, Infinity, {(-9*(3*c^4 - (2*I)*c^3*k0))/(2*k^3*k0), 0, ((-9*(3*c^4 - (2*I)*c^3*k0)*(((-((c - I*k0)^3*(2*c - I*k0))/(2*k^2) - ((c - I*k0)*(2*c - I*k0)^3)/(2*k^2))*(3*c - I*k0))/k - ((c - I*k0)*(2*c - I*k0)*(3*c - I*k0)^3)/(2*k^3) + ((c - I*k0)*(2*c - I*k0)*(3*c - I*k0)*k0^2)/(2*k^3)))/2 + ((c - I*k0)*(2*c - I*k0)*(3*c - I*k0)*(6*c^3*(((c - I*k0)^5/(16*(2*c - I*k0)) - ((c - I*k0)^3*(2*c - I*k0))/16 - ((c - I*k0)*(2*c - I*k0)^3)/16 + (2*c - I*k0)^5/(16*(c - I*k0)))/(3*c - I*k0) + ((-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)))*(3*c - I*k0))/2 - (((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*(3*c - I*k0)^3)/8 + (3*c - I*k0)^5/(16*(c - I*k0)*(2*c - I*k0))) - (11*I)*c^2*(((c - I*k0)^5/(16*(2*c - I*k0)) - ((c - I*k0)^3*(2*c - I*k0))/16 - ((c - I*k0)*(2*c - I*k0)^3)/16 + (2*c - I*k0)^5/(16*(c - I*k0)))/(3*c - I*k0) + ((-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)))*(3*c - I*k0))/2 - (((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*(3*c - I*k0)^3)/8 + (3*c - I*k0)^5/(16*(c - I*k0)*(2*c - I*k0)))*k0 - 6*c*(((c - I*k0)^5/(16*(2*c - I*k0)) - ((c - I*k0)^3*(2*c - I*k0))/16 - ((c - I*k0)*(2*c - I*k0)^3)/16 + (2*c - I*k0)^5/(16*(c - I*k0)))/(3*c - I*k0) + ((-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)))*(3*c - I*k0))/2 - (((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*(3*c - I*k0)^3)/8 + (3*c - I*k0)^5/(16*(c - I*k0)*(2*c - I*k0)))*k0^2 + I*(((c - I*k0)^5/(16*(2*c - I*k0)) - ((c - I*k0)^3*(2*c - I*k0))/16 - ((c - I*k0)*(2*c - I*k0)^3)/16 + (2*c - I*k0)^5/(16*(c - I*k0)))/(3*c - I*k0) + ((-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)))*(3*c - I*k0))/2 - (((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*(3*c - I*k0)^3)/8 + (3*c - I*k0)^5/(16*(c - I*k0)*(2*c - I*k0)))*k0^3 - 2*c^2*((c - I*k0)^5/(16*(2*c - I*k0)) - ((c - I*k0)^3*(2*c - I*k0))/16 - ((c - I*k0)*(2*c - I*k0)^3)/16 + (2*c - I*k0)^5/(16*(c - I*k0)) - ((-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)))*k0^2)/2 - (((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*k0^4)/8 - k0^6/(16*(c - I*k0)*(2*c - I*k0))) + (3*I)*c*k0*((c - I*k0)^5/(16*(2*c - I*k0)) - ((c - I*k0)^3*(2*c - I*k0))/16 - ((c - I*k0)*(2*c - I*k0)^3)/16 + (2*c - I*k0)^5/(16*(c - I*k0)) - ((-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)))*k0^2)/2 - (((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*k0^4)/8 - k0^6/(16*(c - I*k0)*(2*c - I*k0))) + k0^2*((c - I*k0)^5/(16*(2*c - I*k0)) - ((c - I*k0)^3*(2*c - I*k0))/16 - ((c - I*k0)*(2*c - I*k0)^3)/16 + (2*c - I*k0)^5/(16*(c - I*k0)) - ((-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)))*k0^2)/2 - (((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*k0^4)/8 - k0^6/(16*(c - I*k0)*(2*c - I*k0))) + 9*c^2*((c - I*k0)^5/(16*(3*c - I*k0)) - ((c - I*k0)^3*(3*c - I*k0))/16 - ((c - I*k0)*(3*c - I*k0)^3)/16 + (3*c - I*k0)^5/(16*(c - I*k0)) - ((-(c - I*k0)^3/(8*(3*c - I*k0)) + ((c - I*k0)*(3*c - I*k0))/4 - (3*c - I*k0)^3/(8*(c - I*k0)))*k0^2)/2 - (((c - I*k0)/(2*(3*c - I*k0)) + (3*c - I*k0)/(2*(c - I*k0)))*k0^4)/8 - k0^6/(16*(c - I*k0)*(3*c - I*k0))) - (12*I)*c*k0*((c - I*k0)^5/(16*(3*c - I*k0)) - ((c - I*k0)^3*(3*c - I*k0))/16 - ((c - I*k0)*(3*c - I*k0)^3)/16 + (3*c - I*k0)^5/(16*(c - I*k0)) - ((-(c - I*k0)^3/(8*(3*c - I*k0)) + ((c - I*k0)*(3*c - I*k0))/4 - (3*c - I*k0)^3/(8*(c - I*k0)))*k0^2)/2 - (((c - I*k0)/(2*(3*c - I*k0)) + (3*c - I*k0)/(2*(c - I*k0)))*k0^4)/8 - k0^6/(16*(c - I*k0)*(3*c - I*k0))) - 3*k0^2*((c - I*k0)^5/(16*(3*c - I*k0)) - ((c - I*k0)^3*(3*c - I*k0))/16 - ((c - I*k0)*(3*c - I*k0)^3)/16 + (3*c - I*k0)^5/(16*(c - I*k0)) - ((-(c - I*k0)^3/(8*(3*c - I*k0)) + ((c - I*k0)*(3*c - I*k0))/4 - (3*c - I*k0)^3/(8*(c - I*k0)))*k0^2)/2 - (((c - I*k0)/(2*(3*c - I*k0)) + (3*c - I*k0)/(2*(c - I*k0)))*k0^4)/8 - k0^6/(16*(c - I*k0)*(3*c - I*k0))) - 18*c^2*((2*c - I*k0)^5/(16*(3*c - I*k0)) - ((2*c - I*k0)^3*(3*c - I*k0))/16 - ((2*c - I*k0)*(3*c - I*k0)^3)/16 + (3*c - I*k0)^5/(16*(2*c - I*k0)) - ((-(2*c - I*k0)^3/(8*(3*c - I*k0)) + ((2*c - I*k0)*(3*c - I*k0))/4 - (3*c - I*k0)^3/(8*(2*c - I*k0)))*k0^2)/2 - (((2*c - I*k0)/(2*(3*c - I*k0)) + (3*c - I*k0)/(2*(2*c - I*k0)))*k0^4)/8 - k0^6/(16*(2*c - I*k0)*(3*c - I*k0))) + (15*I)*c*k0*((2*c - I*k0)^5/(16*(3*c - I*k0)) - ((2*c - I*k0)^3*(3*c - I*k0))/16 - ((2*c - I*k0)*(3*c - I*k0)^3)/16 + (3*c - I*k0)^5/(16*(2*c - I*k0)) - ((-(2*c - I*k0)^3/(8*(3*c - I*k0)) + ((2*c - I*k0)*(3*c - I*k0))/4 - (3*c - I*k0)^3/(8*(2*c - I*k0)))*k0^2)/2 - (((2*c - I*k0)/(2*(3*c - I*k0)) + (3*c - I*k0)/(2*(2*c - I*k0)))*k0^4)/8 - k0^6/(16*(2*c - I*k0)*(3*c - I*k0))) + 3*k0^2*((2*c - I*k0)^5/(16*(3*c - I*k0)) - ((2*c - I*k0)^3*(3*c - I*k0))/16 - ((2*c - I*k0)*(3*c - I*k0)^3)/16 + (3*c - I*k0)^5/(16*(2*c - I*k0)) - ((-(2*c - I*k0)^3/(8*(3*c - I*k0)) + ((2*c - I*k0)*(3*c - I*k0))/4 - (3*c - I*k0)^3/(8*(2*c - I*k0)))*k0^2)/2 - (((2*c - I*k0)/(2*(3*c - I*k0)) + (3*c - I*k0)/(2*(2*c - I*k0)))*k0^4)/8 - k0^6/(16*(2*c - I*k0)*(3*c - I*k0)))))/k^3)/((c - I*k0)*(2*c - I*k0)*(3*c - I*k0)*k0), 0, ((((-((c - I*k0)^3*(2*c - I*k0))/(2*k^2) - ((c - I*k0)*(2*c - I*k0)^3)/(2*k^2))*(3*c - I*k0))/k - ((c - I*k0)*(2*c - I*k0)*(3*c - I*k0)^3)/(2*k^3) + ((c - I*k0)*(2*c - I*k0)*(3*c - I*k0)*k0^2)/(2*k^3))*(6*c^3*(((c - I*k0)^5/(16*(2*c - I*k0)) - ((c - I*k0)^3*(2*c - I*k0))/16 - ((c - I*k0)*(2*c - I*k0)^3)/16 + (2*c - I*k0)^5/(16*(c - I*k0)))/(3*c - I*k0) + ((-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)))*(3*c - I*k0))/2 - (((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*(3*c - I*k0)^3)/8 + (3*c - I*k0)^5/(16*(c - I*k0)*(2*c - I*k0))) - (11*I)*c^2*(((c - I*k0)^5/(16*(2*c - I*k0)) - ((c - I*k0)^3*(2*c - I*k0))/16 - ((c - I*k0)*(2*c - I*k0)^3)/16 + (2*c - I*k0)^5/(16*(c - I*k0)))/(3*c - I*k0) + ((-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)))*(3*c - I*k0))/2 - (((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*(3*c - I*k0)^3)/8 + (3*c - I*k0)^5/(16*(c - I*k0)*(2*c - I*k0)))*k0 - 6*c*(((c - I*k0)^5/(16*(2*c - I*k0)) - ((c - I*k0)^3*(2*c - I*k0))/16 - ((c - I*k0)*(2*c - I*k0)^3)/16 + (2*c - I*k0)^5/(16*(c - I*k0)))/(3*c - I*k0) + ((-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)))*(3*c - I*k0))/2 - (((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*(3*c - I*k0)^3)/8 + (3*c - I*k0)^5/(16*(c - I*k0)*(2*c - I*k0)))*k0^2 + I*(((c - I*k0)^5/(16*(2*c - I*k0)) - ((c - I*k0)^3*(2*c - I*k0))/16 - ((c - I*k0)*(2*c - I*k0)^3)/16 + (2*c - I*k0)^5/(16*(c - I*k0)))/(3*c - I*k0) + ((-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)))*(3*c - I*k0))/2 - (((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*(3*c - I*k0)^3)/8 + (3*c - I*k0)^5/(16*(c - I*k0)*(2*c - I*k0)))*k0^3 - 2*c^2*((c - I*k0)^5/(16*(2*c - I*k0)) - ((c - I*k0)^3*(2*c - I*k0))/16 - ((c - I*k0)*(2*c - I*k0)^3)/16 + (2*c - I*k0)^5/(16*(c - I*k0)) - ((-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)))*k0^2)/2 - (((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*k0^4)/8 - k0^6/(16*(c - I*k0)*(2*c - I*k0))) + (3*I)*c*k0*((c - I*k0)^5/(16*(2*c - I*k0)) - ((c - I*k0)^3*(2*c - I*k0))/16 - ((c - I*k0)*(2*c - I*k0)^3)/16 + (2*c - I*k0)^5/(16*(c - I*k0)) - ((-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)))*k0^2)/2 - (((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*k0^4)/8 - k0^6/(16*(c - I*k0)*(2*c - I*k0))) + k0^2*((c - I*k0)^5/(16*(2*c - I*k0)) - ((c - I*k0)^3*(2*c - I*k0))/16 - ((c - I*k0)*(2*c - I*k0)^3)/16 + (2*c - I*k0)^5/(16*(c - I*k0)) - ((-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)))*k0^2)/2 - (((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*k0^4)/8 - k0^6/(16*(c - I*k0)*(2*c - I*k0))) + 9*c^2*((c - I*k0)^5/(16*(3*c - I*k0)) - ((c - I*k0)^3*(3*c - I*k0))/16 - ((c - I*k0)*(3*c - I*k0)^3)/16 + (3*c - I*k0)^5/(16*(c - I*k0)) - ((-(c - I*k0)^3/(8*(3*c - I*k0)) + ((c - I*k0)*(3*c - I*k0))/4 - (3*c - I*k0)^3/(8*(c - I*k0)))*k0^2)/2 - (((c - I*k0)/(2*(3*c - I*k0)) + (3*c - I*k0)/(2*(c - I*k0)))*k0^4)/8 - k0^6/(16*(c - I*k0)*(3*c - I*k0))) - (12*I)*c*k0*((c - I*k0)^5/(16*(3*c - I*k0)) - ((c - I*k0)^3*(3*c - I*k0))/16 - ((c - I*k0)*(3*c - I*k0)^3)/16 + (3*c - I*k0)^5/(16*(c - I*k0)) - ((-(c - I*k0)^3/(8*(3*c - I*k0)) + ((c - I*k0)*(3*c - I*k0))/4 - (3*c - I*k0)^3/(8*(c - I*k0)))*k0^2)/2 - (((c - I*k0)/(2*(3*c - I*k0)) + (3*c - I*k0)/(2*(c - I*k0)))*k0^4)/8 - k0^6/(16*(c - I*k0)*(3*c - I*k0))) - 3*k0^2*((c - I*k0)^5/(16*(3*c - I*k0)) - ((c - I*k0)^3*(3*c - I*k0))/16 - ((c - I*k0)*(3*c - I*k0)^3)/16 + (3*c - I*k0)^5/(16*(c - I*k0)) - ((-(c - I*k0)^3/(8*(3*c - I*k0)) + ((c - I*k0)*(3*c - I*k0))/4 - (3*c - I*k0)^3/(8*(c - I*k0)))*k0^2)/2 - (((c - I*k0)/(2*(3*c - I*k0)) + (3*c - I*k0)/(2*(c - I*k0)))*k0^4)/8 - k0^6/(16*(c - I*k0)*(3*c - I*k0))) - 18*c^2*((2*c - I*k0)^5/(16*(3*c - I*k0)) - ((2*c - I*k0)^3*(3*c - I*k0))/16 - ((2*c - I*k0)*(3*c - I*k0)^3)/16 + (3*c - I*k0)^5/(16*(2*c - I*k0)) - ((-(2*c - I*k0)^3/(8*(3*c - I*k0)) + ((2*c - I*k0)*(3*c - I*k0))/4 - (3*c - I*k0)^3/(8*(2*c - I*k0)))*k0^2)/2 - (((2*c - I*k0)/(2*(3*c - I*k0)) + (3*c - I*k0)/(2*(2*c - I*k0)))*k0^4)/8 - k0^6/(16*(2*c - I*k0)*(3*c - I*k0))) + (15*I)*c*k0*((2*c - I*k0)^5/(16*(3*c - I*k0)) - ((2*c - I*k0)^3*(3*c - I*k0))/16 - ((2*c - I*k0)*(3*c - I*k0)^3)/16 + (3*c - I*k0)^5/(16*(2*c - I*k0)) - ((-(2*c - I*k0)^3/(8*(3*c - I*k0)) + ((2*c - I*k0)*(3*c - I*k0))/4 - (3*c - I*k0)^3/(8*(2*c - I*k0)))*k0^2)/2 - (((2*c - I*k0)/(2*(3*c - I*k0)) + (3*c - I*k0)/(2*(2*c - I*k0)))*k0^4)/8 - k0^6/(16*(2*c - I*k0)*(3*c - I*k0))) + 3*k0^2*((2*c - I*k0)^5/(16*(3*c - I*k0)) - ((2*c - I*k0)^3*(3*c - I*k0))/16 - ((2*c - I*k0)*(3*c - I*k0)^3)/16 + (3*c - I*k0)^5/(16*(2*c - I*k0)) - ((-(2*c - I*k0)^3/(8*(3*c - I*k0)) + ((2*c - I*k0)*(3*c - I*k0))/4 - (3*c - I*k0)^3/(8*(2*c - I*k0)))*k0^2)/2 - (((2*c - I*k0)/(2*(3*c - I*k0)) + (3*c - I*k0)/(2*(2*c - I*k0)))*k0^4)/8 - k0^6/(16*(2*c - I*k0)*(3*c - I*k0)))) + ((c - I*k0)*(2*c - I*k0)*(3*c - I*k0)*(6*c^3*(((-5*(c - I*k0)^7)/(128*(2*c - I*k0)) + ((c - I*k0)^5*(2*c - I*k0))/32 + ((c - I*k0)^3*(2*c - I*k0)^3)/64 + ((c - I*k0)*(2*c - I*k0)^5)/32 - (5*(2*c - I*k0)^7)/(128*(c - I*k0)))/(3*c - I*k0) + (((c - I*k0)^5/(16*(2*c - I*k0)) - ((c - I*k0)^3*(2*c - I*k0))/16 - ((c - I*k0)*(2*c - I*k0)^3)/16 + (2*c - I*k0)^5/(16*(c - I*k0)))*(3*c - I*k0))/2 - ((-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)))*(3*c - I*k0)^3)/8 + (((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*(3*c - I*k0)^5)/16 - (5*(3*c - I*k0)^7)/(128*(c - I*k0)*(2*c - I*k0))) - (11*I)*c^2*(((-5*(c - I*k0)^7)/(128*(2*c - I*k0)) + ((c - I*k0)^5*(2*c - I*k0))/32 + ((c - I*k0)^3*(2*c - I*k0)^3)/64 + ((c - I*k0)*(2*c - I*k0)^5)/32 - (5*(2*c - I*k0)^7)/(128*(c - I*k0)))/(3*c - I*k0) + (((c - I*k0)^5/(16*(2*c - I*k0)) - ((c - I*k0)^3*(2*c - I*k0))/16 - ((c - I*k0)*(2*c - I*k0)^3)/16 + (2*c - I*k0)^5/(16*(c - I*k0)))*(3*c - I*k0))/2 - ((-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)))*(3*c - I*k0)^3)/8 + (((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*(3*c - I*k0)^5)/16 - (5*(3*c - I*k0)^7)/(128*(c - I*k0)*(2*c - I*k0)))*k0 - 6*c*(((-5*(c - I*k0)^7)/(128*(2*c - I*k0)) + ((c - I*k0)^5*(2*c - I*k0))/32 + ((c - I*k0)^3*(2*c - I*k0)^3)/64 + ((c - I*k0)*(2*c - I*k0)^5)/32 - (5*(2*c - I*k0)^7)/(128*(c - I*k0)))/(3*c - I*k0) + (((c - I*k0)^5/(16*(2*c - I*k0)) - ((c - I*k0)^3*(2*c - I*k0))/16 - ((c - I*k0)*(2*c - I*k0)^3)/16 + (2*c - I*k0)^5/(16*(c - I*k0)))*(3*c - I*k0))/2 - ((-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)))*(3*c - I*k0)^3)/8 + (((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*(3*c - I*k0)^5)/16 - (5*(3*c - I*k0)^7)/(128*(c - I*k0)*(2*c - I*k0)))*k0^2 + I*(((-5*(c - I*k0)^7)/(128*(2*c - I*k0)) + ((c - I*k0)^5*(2*c - I*k0))/32 + ((c - I*k0)^3*(2*c - I*k0)^3)/64 + ((c - I*k0)*(2*c - I*k0)^5)/32 - (5*(2*c - I*k0)^7)/(128*(c - I*k0)))/(3*c - I*k0) + (((c - I*k0)^5/(16*(2*c - I*k0)) - ((c - I*k0)^3*(2*c - I*k0))/16 - ((c - I*k0)*(2*c - I*k0)^3)/16 + (2*c - I*k0)^5/(16*(c - I*k0)))*(3*c - I*k0))/2 - ((-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)))*(3*c - I*k0)^3)/8 + (((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*(3*c - I*k0)^5)/16 - (5*(3*c - I*k0)^7)/(128*(c - I*k0)*(2*c - I*k0)))*k0^3 - 2*c^2*((-5*(c - I*k0)^7)/(128*(2*c - I*k0)) + ((c - I*k0)^5*(2*c - I*k0))/32 + ((c - I*k0)^3*(2*c - I*k0)^3)/64 + ((c - I*k0)*(2*c - I*k0)^5)/32 - (5*(2*c - I*k0)^7)/(128*(c - I*k0)) - (((c - I*k0)^5/(16*(2*c - I*k0)) - ((c - I*k0)^3*(2*c - I*k0))/16 - ((c - I*k0)*(2*c - I*k0)^3)/16 + (2*c - I*k0)^5/(16*(c - I*k0)))*k0^2)/2 - ((-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)))*k0^4)/8 - (((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*k0^6)/16 - (5*k0^8)/(128*(c - I*k0)*(2*c - I*k0))) + (3*I)*c*k0*((-5*(c - I*k0)^7)/(128*(2*c - I*k0)) + ((c - I*k0)^5*(2*c - I*k0))/32 + ((c - I*k0)^3*(2*c - I*k0)^3)/64 + ((c - I*k0)*(2*c - I*k0)^5)/32 - (5*(2*c - I*k0)^7)/(128*(c - I*k0)) - (((c - I*k0)^5/(16*(2*c - I*k0)) - ((c - I*k0)^3*(2*c - I*k0))/16 - ((c - I*k0)*(2*c - I*k0)^3)/16 + (2*c - I*k0)^5/(16*(c - I*k0)))*k0^2)/2 - ((-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)))*k0^4)/8 - (((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*k0^6)/16 - (5*k0^8)/(128*(c - I*k0)*(2*c - I*k0))) + k0^2*((-5*(c - I*k0)^7)/(128*(2*c - I*k0)) + ((c - I*k0)^5*(2*c - I*k0))/32 + ((c - I*k0)^3*(2*c - I*k0)^3)/64 + ((c - I*k0)*(2*c - I*k0)^5)/32 - (5*(2*c - I*k0)^7)/(128*(c - I*k0)) - (((c - I*k0)^5/(16*(2*c - I*k0)) - ((c - I*k0)^3*(2*c - I*k0))/16 - ((c - I*k0)*(2*c - I*k0)^3)/16 + (2*c - I*k0)^5/(16*(c - I*k0)))*k0^2)/2 - ((-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)))*k0^4)/8 - (((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*k0^6)/16 - (5*k0^8)/(128*(c - I*k0)*(2*c - I*k0))) + 9*c^2*((-5*(c - I*k0)^7)/(128*(3*c - I*k0)) + ((c - I*k0)^5*(3*c - I*k0))/32 + ((c - I*k0)^3*(3*c - I*k0)^3)/64 + ((c - I*k0)*(3*c - I*k0)^5)/32 - (5*(3*c - I*k0)^7)/(128*(c - I*k0)) - (((c - I*k0)^5/(16*(3*c - I*k0)) - ((c - I*k0)^3*(3*c - I*k0))/16 - ((c - I*k0)*(3*c - I*k0)^3)/16 + (3*c - I*k0)^5/(16*(c - I*k0)))*k0^2)/2 - ((-(c - I*k0)^3/(8*(3*c - I*k0)) + ((c - I*k0)*(3*c - I*k0))/4 - (3*c - I*k0)^3/(8*(c - I*k0)))*k0^4)/8 - (((c - I*k0)/(2*(3*c - I*k0)) + (3*c - I*k0)/(2*(c - I*k0)))*k0^6)/16 - (5*k0^8)/(128*(c - I*k0)*(3*c - I*k0))) - (12*I)*c*k0*((-5*(c - I*k0)^7)/(128*(3*c - I*k0)) + ((c - I*k0)^5*(3*c - I*k0))/32 + ((c - I*k0)^3*(3*c - I*k0)^3)/64 + ((c - I*k0)*(3*c - I*k0)^5)/32 - (5*(3*c - I*k0)^7)/(128*(c - I*k0)) - (((c - I*k0)^5/(16*(3*c - I*k0)) - ((c - I*k0)^3*(3*c - I*k0))/16 - ((c - I*k0)*(3*c - I*k0)^3)/16 + (3*c - I*k0)^5/(16*(c - I*k0)))*k0^2)/2 - ((-(c - I*k0)^3/(8*(3*c - I*k0)) + ((c - I*k0)*(3*c - I*k0))/4 - (3*c - I*k0)^3/(8*(c - I*k0)))*k0^4)/8 - (((c - I*k0)/(2*(3*c - I*k0)) + (3*c - I*k0)/(2*(c - I*k0)))*k0^6)/16 - (5*k0^8)/(128*(c - I*k0)*(3*c - I*k0))) - 3*k0^2*((-5*(c - I*k0)^7)/(128*(3*c - I*k0)) + ((c - I*k0)^5*(3*c - I*k0))/32 + ((c - I*k0)^3*(3*c - I*k0)^3)/64 + ((c - I*k0)*(3*c - I*k0)^5)/32 - (5*(3*c - I*k0)^7)/(128*(c - I*k0)) - (((c - I*k0)^5/(16*(3*c - I*k0)) - ((c - I*k0)^3*(3*c - I*k0))/16 - ((c - I*k0)*(3*c - I*k0)^3)/16 + (3*c - I*k0)^5/(16*(c - I*k0)))*k0^2)/2 - ((-(c - I*k0)^3/(8*(3*c - I*k0)) + ((c - I*k0)*(3*c - I*k0))/4 - (3*c - I*k0)^3/(8*(c - I*k0)))*k0^4)/8 - (((c - I*k0)/(2*(3*c - I*k0)) + (3*c - I*k0)/(2*(c - I*k0)))*k0^6)/16 - (5*k0^8)/(128*(c - I*k0)*(3*c - I*k0))) - 18*c^2*((-5*(2*c - I*k0)^7)/(128*(3*c - I*k0)) + ((2*c - I*k0)^5*(3*c - I*k0))/32 + ((2*c - I*k0)^3*(3*c - I*k0)^3)/64 + ((2*c - I*k0)*(3*c - I*k0)^5)/32 - (5*(3*c - I*k0)^7)/(128*(2*c - I*k0)) - (((2*c - I*k0)^5/(16*(3*c - I*k0)) - ((2*c - I*k0)^3*(3*c - I*k0))/16 - ((2*c - I*k0)*(3*c - I*k0)^3)/16 + (3*c - I*k0)^5/(16*(2*c - I*k0)))*k0^2)/2 - ((-(2*c - I*k0)^3/(8*(3*c - I*k0)) + ((2*c - I*k0)*(3*c - I*k0))/4 - (3*c - I*k0)^3/(8*(2*c - I*k0)))*k0^4)/8 - (((2*c - I*k0)/(2*(3*c - I*k0)) + (3*c - I*k0)/(2*(2*c - I*k0)))*k0^6)/16 - (5*k0^8)/(128*(2*c - I*k0)*(3*c - I*k0))) + (15*I)*c*k0*((-5*(2*c - I*k0)^7)/(128*(3*c - I*k0)) + ((2*c - I*k0)^5*(3*c - I*k0))/32 + ((2*c - I*k0)^3*(3*c - I*k0)^3)/64 + ((2*c - I*k0)*(3*c - I*k0)^5)/32 - (5*(3*c - I*k0)^7)/(128*(2*c - I*k0)) - (((2*c - I*k0)^5/(16*(3*c - I*k0)) - ((2*c - I*k0)^3*(3*c - I*k0))/16 - ((2*c - I*k0)*(3*c - I*k0)^3)/16 + (3*c - I*k0)^5/(16*(2*c - I*k0)))*k0^2)/2 - ((-(2*c - I*k0)^3/(8*(3*c - I*k0)) + ((2*c - I*k0)*(3*c - I*k0))/4 - (3*c - I*k0)^3/(8*(2*c - I*k0)))*k0^4)/8 - (((2*c - I*k0)/(2*(3*c - I*k0)) + (3*c - I*k0)/(2*(2*c - I*k0)))*k0^6)/16 - (5*k0^8)/(128*(2*c - I*k0)*(3*c - I*k0))) + 3*k0^2*((-5*(2*c - I*k0)^7)/(128*(3*c - I*k0)) + ((2*c - I*k0)^5*(3*c - I*k0))/32 + ((2*c - I*k0)^3*(3*c - I*k0)^3)/64 + ((2*c - I*k0)*(3*c - I*k0)^5)/32 - (5*(3*c - I*k0)^7)/(128*(2*c - I*k0)) - (((2*c - I*k0)^5/(16*(3*c - I*k0)) - ((2*c - I*k0)^3*(3*c - I*k0))/16 - ((2*c - I*k0)*(3*c - I*k0)^3)/16 + (3*c - I*k0)^5/(16*(2*c - I*k0)))*k0^2)/2 - ((-(2*c - I*k0)^3/(8*(3*c - I*k0)) + ((2*c - I*k0)*(3*c - I*k0))/4 - (3*c - I*k0)^3/(8*(2*c - I*k0)))*k0^4)/8 - (((2*c - I*k0)/(2*(3*c - I*k0)) + (3*c - I*k0)/(2*(2*c - I*k0)))*k0^6)/16 - (5*k0^8)/(128*(2*c - I*k0)*(3*c - I*k0)))))/k^3 - (9*(3*c^4 - (2*I)*c^3*k0)*(-((-((c - I*k0)^3*(2*c - I*k0))/(2*k^2) - ((c - I*k0)*(2*c - I*k0)^3)/(2*k^2))*(3*c - I*k0)^3)/(2*k) + ((((-((c - I*k0)^3*(2*c - I*k0))/(2*k^2) - ((c - I*k0)*(2*c - I*k0)^3)/(2*k^2))*(3*c - I*k0))/k - ((c - I*k0)*(2*c - I*k0)*(3*c - I*k0)^3)/(2*k^3))*k0^2)/2 + (3*(c - I*k0)*(2*c - I*k0)*(3*c - I*k0)*k0^4)/(8*k^3) + (3*(c - I*k0)*(2*c - I*k0)*(3*c - I*k0)^4*((3*c)/k - (I*k0)/k))/(8*k^2) + ((3*c - I*k0)*(((c - I*k0)^3*(2*c - I*k0)^3)/(4*k^2) + (3*(c - I*k0)^4*(2*c - I*k0)*(c/k - (I*k0)/k))/(8*k) + (3*(c - I*k0)*(2*c - I*k0)^4*((2*c)/k - (I*k0)/k))/(8*k)))/k))/2)/((c - I*k0)*(2*c - I*k0)*(3*c - I*k0)*k0), 0, ((((-((c - I*k0)^3*(2*c - I*k0))/(2*k^2) - ((c - I*k0)*(2*c - I*k0)^3)/(2*k^2))*(3*c - I*k0))/k - ((c - I*k0)*(2*c - I*k0)*(3*c - I*k0)^3)/(2*k^3) + ((c - I*k0)*(2*c - I*k0)*(3*c - I*k0)*k0^2)/(2*k^3))*(6*c^3*(((-5*(c - I*k0)^7)/(128*(2*c - I*k0)) + ((c - I*k0)^5*(2*c - I*k0))/32 + ((c - I*k0)^3*(2*c - I*k0)^3)/64 + ((c - I*k0)*(2*c - I*k0)^5)/32 - (5*(2*c - I*k0)^7)/(128*(c - I*k0)))/(3*c - I*k0) + (((c - I*k0)^5/(16*(2*c - I*k0)) - ((c - I*k0)^3*(2*c - I*k0))/16 - ((c - I*k0)*(2*c - I*k0)^3)/16 + (2*c - I*k0)^5/(16*(c - I*k0)))*(3*c - I*k0))/2 - ((-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)))*(3*c - I*k0)^3)/8 + (((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*(3*c - I*k0)^5)/16 - (5*(3*c - I*k0)^7)/(128*(c - I*k0)*(2*c - I*k0))) - (11*I)*c^2*(((-5*(c - I*k0)^7)/(128*(2*c - I*k0)) + ((c - I*k0)^5*(2*c - I*k0))/32 + ((c - I*k0)^3*(2*c - I*k0)^3)/64 + ((c - I*k0)*(2*c - I*k0)^5)/32 - (5*(2*c - I*k0)^7)/(128*(c - I*k0)))/(3*c - I*k0) + (((c - I*k0)^5/(16*(2*c - I*k0)) - ((c - I*k0)^3*(2*c - I*k0))/16 - ((c - I*k0)*(2*c - I*k0)^3)/16 + (2*c - I*k0)^5/(16*(c - I*k0)))*(3*c - I*k0))/2 - ((-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)))*(3*c - I*k0)^3)/8 + (((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*(3*c - I*k0)^5)/16 - (5*(3*c - I*k0)^7)/(128*(c - I*k0)*(2*c - I*k0)))*k0 - 6*c*(((-5*(c - I*k0)^7)/(128*(2*c - I*k0)) + ((c - I*k0)^5*(2*c - I*k0))/32 + ((c - I*k0)^3*(2*c - I*k0)^3)/64 + ((c - I*k0)*(2*c - I*k0)^5)/32 - (5*(2*c - I*k0)^7)/(128*(c - I*k0)))/(3*c - I*k0) + (((c - I*k0)^5/(16*(2*c - I*k0)) - ((c - I*k0)^3*(2*c - I*k0))/16 - ((c - I*k0)*(2*c - I*k0)^3)/16 + (2*c - I*k0)^5/(16*(c - I*k0)))*(3*c - I*k0))/2 - ((-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)))*(3*c - I*k0)^3)/8 + (((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*(3*c - I*k0)^5)/16 - (5*(3*c - I*k0)^7)/(128*(c - I*k0)*(2*c - I*k0)))*k0^2 + I*(((-5*(c - I*k0)^7)/(128*(2*c - I*k0)) + ((c - I*k0)^5*(2*c - I*k0))/32 + ((c - I*k0)^3*(2*c - I*k0)^3)/64 + ((c - I*k0)*(2*c - I*k0)^5)/32 - (5*(2*c - I*k0)^7)/(128*(c - I*k0)))/(3*c - I*k0) + (((c - I*k0)^5/(16*(2*c - I*k0)) - ((c - I*k0)^3*(2*c - I*k0))/16 - ((c - I*k0)*(2*c - I*k0)^3)/16 + (2*c - I*k0)^5/(16*(c - I*k0)))*(3*c - I*k0))/2 - ((-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)))*(3*c - I*k0)^3)/8 + (((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*(3*c - I*k0)^5)/16 - (5*(3*c - I*k0)^7)/(128*(c - I*k0)*(2*c - I*k0)))*k0^3 - 2*c^2*((-5*(c - I*k0)^7)/(128*(2*c - I*k0)) + ((c - I*k0)^5*(2*c - I*k0))/32 + ((c - I*k0)^3*(2*c - I*k0)^3)/64 + ((c - I*k0)*(2*c - I*k0)^5)/32 - (5*(2*c - I*k0)^7)/(128*(c - I*k0)) - (((c - I*k0)^5/(16*(2*c - I*k0)) - ((c - I*k0)^3*(2*c - I*k0))/16 - ((c - I*k0)*(2*c - I*k0)^3)/16 + (2*c - I*k0)^5/(16*(c - I*k0)))*k0^2)/2 - ((-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)))*k0^4)/8 - (((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*k0^6)/16 - (5*k0^8)/(128*(c - I*k0)*(2*c - I*k0))) + (3*I)*c*k0*((-5*(c - I*k0)^7)/(128*(2*c - I*k0)) + ((c - I*k0)^5*(2*c - I*k0))/32 + ((c - I*k0)^3*(2*c - I*k0)^3)/64 + ((c - I*k0)*(2*c - I*k0)^5)/32 - (5*(2*c - I*k0)^7)/(128*(c - I*k0)) - (((c - I*k0)^5/(16*(2*c - I*k0)) - ((c - I*k0)^3*(2*c - I*k0))/16 - ((c - I*k0)*(2*c - I*k0)^3)/16 + (2*c - I*k0)^5/(16*(c - I*k0)))*k0^2)/2 - ((-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)))*k0^4)/8 - (((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*k0^6)/16 - (5*k0^8)/(128*(c - I*k0)*(2*c - I*k0))) + k0^2*((-5*(c - I*k0)^7)/(128*(2*c - I*k0)) + ((c - I*k0)^5*(2*c - I*k0))/32 + ((c - I*k0)^3*(2*c - I*k0)^3)/64 + ((c - I*k0)*(2*c - I*k0)^5)/32 - (5*(2*c - I*k0)^7)/(128*(c - I*k0)) - (((c - I*k0)^5/(16*(2*c - I*k0)) - ((c - I*k0)^3*(2*c - I*k0))/16 - ((c - I*k0)*(2*c - I*k0)^3)/16 + (2*c - I*k0)^5/(16*(c - I*k0)))*k0^2)/2 - ((-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)))*k0^4)/8 - (((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*k0^6)/16 - (5*k0^8)/(128*(c - I*k0)*(2*c - I*k0))) + 9*c^2*((-5*(c - I*k0)^7)/(128*(3*c - I*k0)) + ((c - I*k0)^5*(3*c - I*k0))/32 + ((c - I*k0)^3*(3*c - I*k0)^3)/64 + ((c - I*k0)*(3*c - I*k0)^5)/32 - (5*(3*c - I*k0)^7)/(128*(c - I*k0)) - (((c - I*k0)^5/(16*(3*c - I*k0)) - ((c - I*k0)^3*(3*c - I*k0))/16 - ((c - I*k0)*(3*c - I*k0)^3)/16 + (3*c - I*k0)^5/(16*(c - I*k0)))*k0^2)/2 - ((-(c - I*k0)^3/(8*(3*c - I*k0)) + ((c - I*k0)*(3*c - I*k0))/4 - (3*c - I*k0)^3/(8*(c - I*k0)))*k0^4)/8 - (((c - I*k0)/(2*(3*c - I*k0)) + (3*c - I*k0)/(2*(c - I*k0)))*k0^6)/16 - (5*k0^8)/(128*(c - I*k0)*(3*c - I*k0))) - (12*I)*c*k0*((-5*(c - I*k0)^7)/(128*(3*c - I*k0)) + ((c - I*k0)^5*(3*c - I*k0))/32 + ((c - I*k0)^3*(3*c - I*k0)^3)/64 + ((c - I*k0)*(3*c - I*k0)^5)/32 - (5*(3*c - I*k0)^7)/(128*(c - I*k0)) - (((c - I*k0)^5/(16*(3*c - I*k0)) - ((c - I*k0)^3*(3*c - I*k0))/16 - ((c - I*k0)*(3*c - I*k0)^3)/16 + (3*c - I*k0)^5/(16*(c - I*k0)))*k0^2)/2 - ((-(c - I*k0)^3/(8*(3*c - I*k0)) + ((c - I*k0)*(3*c - I*k0))/4 - (3*c - I*k0)^3/(8*(c - I*k0)))*k0^4)/8 - (((c - I*k0)/(2*(3*c - I*k0)) + (3*c - I*k0)/(2*(c - I*k0)))*k0^6)/16 - (5*k0^8)/(128*(c - I*k0)*(3*c - I*k0))) - 3*k0^2*((-5*(c - I*k0)^7)/(128*(3*c - I*k0)) + ((c - I*k0)^5*(3*c - I*k0))/32 + ((c - I*k0)^3*(3*c - I*k0)^3)/64 + ((c - I*k0)*(3*c - I*k0)^5)/32 - (5*(3*c - I*k0)^7)/(128*(c - I*k0)) - (((c - I*k0)^5/(16*(3*c - I*k0)) - ((c - I*k0)^3*(3*c - I*k0))/16 - ((c - I*k0)*(3*c - I*k0)^3)/16 + (3*c - I*k0)^5/(16*(c - I*k0)))*k0^2)/2 - ((-(c - I*k0)^3/(8*(3*c - I*k0)) + ((c - I*k0)*(3*c - I*k0))/4 - (3*c - I*k0)^3/(8*(c - I*k0)))*k0^4)/8 - (((c - I*k0)/(2*(3*c - I*k0)) + (3*c - I*k0)/(2*(c - I*k0)))*k0^6)/16 - (5*k0^8)/(128*(c - I*k0)*(3*c - I*k0))) - 18*c^2*((-5*(2*c - I*k0)^7)/(128*(3*c - I*k0)) + ((2*c - I*k0)^5*(3*c - I*k0))/32 + ((2*c - I*k0)^3*(3*c - I*k0)^3)/64 + ((2*c - I*k0)*(3*c - I*k0)^5)/32 - (5*(3*c - I*k0)^7)/(128*(2*c - I*k0)) - (((2*c - I*k0)^5/(16*(3*c - I*k0)) - ((2*c - I*k0)^3*(3*c - I*k0))/16 - ((2*c - I*k0)*(3*c - I*k0)^3)/16 + (3*c - I*k0)^5/(16*(2*c - I*k0)))*k0^2)/2 - ((-(2*c - I*k0)^3/(8*(3*c - I*k0)) + ((2*c - I*k0)*(3*c - I*k0))/4 - (3*c - I*k0)^3/(8*(2*c - I*k0)))*k0^4)/8 - (((2*c - I*k0)/(2*(3*c - I*k0)) + (3*c - I*k0)/(2*(2*c - I*k0)))*k0^6)/16 - (5*k0^8)/(128*(2*c - I*k0)*(3*c - I*k0))) + (15*I)*c*k0*((-5*(2*c - I*k0)^7)/(128*(3*c - I*k0)) + ((2*c - I*k0)^5*(3*c - I*k0))/32 + ((2*c - I*k0)^3*(3*c - I*k0)^3)/64 + ((2*c - I*k0)*(3*c - I*k0)^5)/32 - (5*(3*c - I*k0)^7)/(128*(2*c - I*k0)) - (((2*c - I*k0)^5/(16*(3*c - I*k0)) - ((2*c - I*k0)^3*(3*c - I*k0))/16 - ((2*c - I*k0)*(3*c - I*k0)^3)/16 + (3*c - I*k0)^5/(16*(2*c - I*k0)))*k0^2)/2 - ((-(2*c - I*k0)^3/(8*(3*c - I*k0)) + ((2*c - I*k0)*(3*c - I*k0))/4 - (3*c - I*k0)^3/(8*(2*c - I*k0)))*k0^4)/8 - (((2*c - I*k0)/(2*(3*c - I*k0)) + (3*c - I*k0)/(2*(2*c - I*k0)))*k0^6)/16 - (5*k0^8)/(128*(2*c - I*k0)*(3*c - I*k0))) + 3*k0^2*((-5*(2*c - I*k0)^7)/(128*(3*c - I*k0)) + ((2*c - I*k0)^5*(3*c - I*k0))/32 + ((2*c - I*k0)^3*(3*c - I*k0)^3)/64 + ((2*c - I*k0)*(3*c - I*k0)^5)/32 - (5*(3*c - I*k0)^7)/(128*(2*c - I*k0)) - (((2*c - I*k0)^5/(16*(3*c - I*k0)) - ((2*c - I*k0)^3*(3*c - I*k0))/16 - ((2*c - I*k0)*(3*c - I*k0)^3)/16 + (3*c - I*k0)^5/(16*(2*c - I*k0)))*k0^2)/2 - ((-(2*c - I*k0)^3/(8*(3*c - I*k0)) + ((2*c - I*k0)*(3*c - I*k0))/4 - (3*c - I*k0)^3/(8*(2*c - I*k0)))*k0^4)/8 - (((2*c - I*k0)/(2*(3*c - I*k0)) + (3*c - I*k0)/(2*(2*c - I*k0)))*k0^6)/16 - (5*k0^8)/(128*(2*c - I*k0)*(3*c - I*k0)))) + ((c - I*k0)*(2*c - I*k0)*(3*c - I*k0)*(6*c^3*(((7*(c - I*k0)^9)/(256*(2*c - I*k0)) - (5*(c - I*k0)^7*(2*c - I*k0))/256 - ((c - I*k0)^5*(2*c - I*k0)^3)/128 - ((c - I*k0)^3*(2*c - I*k0)^5)/128 - (5*(c - I*k0)*(2*c - I*k0)^7)/256 + (7*(2*c - I*k0)^9)/(256*(c - I*k0)))/(3*c - I*k0) + (((-5*(c - I*k0)^7)/(128*(2*c - I*k0)) + ((c - I*k0)^5*(2*c - I*k0))/32 + ((c - I*k0)^3*(2*c - I*k0)^3)/64 + ((c - I*k0)*(2*c - I*k0)^5)/32 - (5*(2*c - I*k0)^7)/(128*(c - I*k0)))*(3*c - I*k0))/2 - (((c - I*k0)^5/(16*(2*c - I*k0)) - ((c - I*k0)^3*(2*c - I*k0))/16 - ((c - I*k0)*(2*c - I*k0)^3)/16 + (2*c - I*k0)^5/(16*(c - I*k0)))*(3*c - I*k0)^3)/8 + ((-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)))*(3*c - I*k0)^5)/16 - (5*((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*(3*c - I*k0)^7)/128 + (7*(3*c - I*k0)^9)/(256*(c - I*k0)*(2*c - I*k0))) - (11*I)*c^2*(((7*(c - I*k0)^9)/(256*(2*c - I*k0)) - (5*(c - I*k0)^7*(2*c - I*k0))/256 - ((c - I*k0)^5*(2*c - I*k0)^3)/128 - ((c - I*k0)^3*(2*c - I*k0)^5)/128 - (5*(c - I*k0)*(2*c - I*k0)^7)/256 + (7*(2*c - I*k0)^9)/(256*(c - I*k0)))/(3*c - I*k0) + (((-5*(c - I*k0)^7)/(128*(2*c - I*k0)) + ((c - I*k0)^5*(2*c - I*k0))/32 + ((c - I*k0)^3*(2*c - I*k0)^3)/64 + ((c - I*k0)*(2*c - I*k0)^5)/32 - (5*(2*c - I*k0)^7)/(128*(c - I*k0)))*(3*c - I*k0))/2 - (((c - I*k0)^5/(16*(2*c - I*k0)) - ((c - I*k0)^3*(2*c - I*k0))/16 - ((c - I*k0)*(2*c - I*k0)^3)/16 + (2*c - I*k0)^5/(16*(c - I*k0)))*(3*c - I*k0)^3)/8 + ((-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)))*(3*c - I*k0)^5)/16 - (5*((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*(3*c - I*k0)^7)/128 + (7*(3*c - I*k0)^9)/(256*(c - I*k0)*(2*c - I*k0)))*k0 - 6*c*(((7*(c - I*k0)^9)/(256*(2*c - I*k0)) - (5*(c - I*k0)^7*(2*c - I*k0))/256 - ((c - I*k0)^5*(2*c - I*k0)^3)/128 - ((c - I*k0)^3*(2*c - I*k0)^5)/128 - (5*(c - I*k0)*(2*c - I*k0)^7)/256 + (7*(2*c - I*k0)^9)/(256*(c - I*k0)))/(3*c - I*k0) + (((-5*(c - I*k0)^7)/(128*(2*c - I*k0)) + ((c - I*k0)^5*(2*c - I*k0))/32 + ((c - I*k0)^3*(2*c - I*k0)^3)/64 + ((c - I*k0)*(2*c - I*k0)^5)/32 - (5*(2*c - I*k0)^7)/(128*(c - I*k0)))*(3*c - I*k0))/2 - (((c - I*k0)^5/(16*(2*c - I*k0)) - ((c - I*k0)^3*(2*c - I*k0))/16 - ((c - I*k0)*(2*c - I*k0)^3)/16 + (2*c - I*k0)^5/(16*(c - I*k0)))*(3*c - I*k0)^3)/8 + ((-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)))*(3*c - I*k0)^5)/16 - (5*((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*(3*c - I*k0)^7)/128 + (7*(3*c - I*k0)^9)/(256*(c - I*k0)*(2*c - I*k0)))*k0^2 + I*(((7*(c - I*k0)^9)/(256*(2*c - I*k0)) - (5*(c - I*k0)^7*(2*c - I*k0))/256 - ((c - I*k0)^5*(2*c - I*k0)^3)/128 - ((c - I*k0)^3*(2*c - I*k0)^5)/128 - (5*(c - I*k0)*(2*c - I*k0)^7)/256 + (7*(2*c - I*k0)^9)/(256*(c - I*k0)))/(3*c - I*k0) + (((-5*(c - I*k0)^7)/(128*(2*c - I*k0)) + ((c - I*k0)^5*(2*c - I*k0))/32 + ((c - I*k0)^3*(2*c - I*k0)^3)/64 + ((c - I*k0)*(2*c - I*k0)^5)/32 - (5*(2*c - I*k0)^7)/(128*(c - I*k0)))*(3*c - I*k0))/2 - (((c - I*k0)^5/(16*(2*c - I*k0)) - ((c - I*k0)^3*(2*c - I*k0))/16 - ((c - I*k0)*(2*c - I*k0)^3)/16 + (2*c - I*k0)^5/(16*(c - I*k0)))*(3*c - I*k0)^3)/8 + ((-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)))*(3*c - I*k0)^5)/16 - (5*((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*(3*c - I*k0)^7)/128 + (7*(3*c - I*k0)^9)/(256*(c - I*k0)*(2*c - I*k0)))*k0^3 - 2*c^2*((7*(c - I*k0)^9)/(256*(2*c - I*k0)) - (5*(c - I*k0)^7*(2*c - I*k0))/256 - ((c - I*k0)^5*(2*c - I*k0)^3)/128 - ((c - I*k0)^3*(2*c - I*k0)^5)/128 - (5*(c - I*k0)*(2*c - I*k0)^7)/256 + (7*(2*c - I*k0)^9)/(256*(c - I*k0)) - (((-5*(c - I*k0)^7)/(128*(2*c - I*k0)) + ((c - I*k0)^5*(2*c - I*k0))/32 + ((c - I*k0)^3*(2*c - I*k0)^3)/64 + ((c - I*k0)*(2*c - I*k0)^5)/32 - (5*(2*c - I*k0)^7)/(128*(c - I*k0)))*k0^2)/2 - (((c - I*k0)^5/(16*(2*c - I*k0)) - ((c - I*k0)^3*(2*c - I*k0))/16 - ((c - I*k0)*(2*c - I*k0)^3)/16 + (2*c - I*k0)^5/(16*(c - I*k0)))*k0^4)/8 - ((-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)))*k0^6)/16 - (5*((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*k0^8)/128 - (7*k0^10)/(256*(c - I*k0)*(2*c - I*k0))) + (3*I)*c*k0*((7*(c - I*k0)^9)/(256*(2*c - I*k0)) - (5*(c - I*k0)^7*(2*c - I*k0))/256 - ((c - I*k0)^5*(2*c - I*k0)^3)/128 - ((c - I*k0)^3*(2*c - I*k0)^5)/128 - (5*(c - I*k0)*(2*c - I*k0)^7)/256 + (7*(2*c - I*k0)^9)/(256*(c - I*k0)) - (((-5*(c - I*k0)^7)/(128*(2*c - I*k0)) + ((c - I*k0)^5*(2*c - I*k0))/32 + ((c - I*k0)^3*(2*c - I*k0)^3)/64 + ((c - I*k0)*(2*c - I*k0)^5)/32 - (5*(2*c - I*k0)^7)/(128*(c - I*k0)))*k0^2)/2 - (((c - I*k0)^5/(16*(2*c - I*k0)) - ((c - I*k0)^3*(2*c - I*k0))/16 - ((c - I*k0)*(2*c - I*k0)^3)/16 + (2*c - I*k0)^5/(16*(c - I*k0)))*k0^4)/8 - ((-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)))*k0^6)/16 - (5*((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*k0^8)/128 - (7*k0^10)/(256*(c - I*k0)*(2*c - I*k0))) + k0^2*((7*(c - I*k0)^9)/(256*(2*c - I*k0)) - (5*(c - I*k0)^7*(2*c - I*k0))/256 - ((c - I*k0)^5*(2*c - I*k0)^3)/128 - ((c - I*k0)^3*(2*c - I*k0)^5)/128 - (5*(c - I*k0)*(2*c - I*k0)^7)/256 + (7*(2*c - I*k0)^9)/(256*(c - I*k0)) - (((-5*(c - I*k0)^7)/(128*(2*c - I*k0)) + ((c - I*k0)^5*(2*c - I*k0))/32 + ((c - I*k0)^3*(2*c - I*k0)^3)/64 + ((c - I*k0)*(2*c - I*k0)^5)/32 - (5*(2*c - I*k0)^7)/(128*(c - I*k0)))*k0^2)/2 - (((c - I*k0)^5/(16*(2*c - I*k0)) - ((c - I*k0)^3*(2*c - I*k0))/16 - ((c - I*k0)*(2*c - I*k0)^3)/16 + (2*c - I*k0)^5/(16*(c - I*k0)))*k0^4)/8 - ((-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)))*k0^6)/16 - (5*((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*k0^8)/128 - (7*k0^10)/(256*(c - I*k0)*(2*c - I*k0))) + 9*c^2*((7*(c - I*k0)^9)/(256*(3*c - I*k0)) - (5*(c - I*k0)^7*(3*c - I*k0))/256 - ((c - I*k0)^5*(3*c - I*k0)^3)/128 - ((c - I*k0)^3*(3*c - I*k0)^5)/128 - (5*(c - I*k0)*(3*c - I*k0)^7)/256 + (7*(3*c - I*k0)^9)/(256*(c - I*k0)) - (((-5*(c - I*k0)^7)/(128*(3*c - I*k0)) + ((c - I*k0)^5*(3*c - I*k0))/32 + ((c - I*k0)^3*(3*c - I*k0)^3)/64 + ((c - I*k0)*(3*c - I*k0)^5)/32 - (5*(3*c - I*k0)^7)/(128*(c - I*k0)))*k0^2)/2 - (((c - I*k0)^5/(16*(3*c - I*k0)) - ((c - I*k0)^3*(3*c - I*k0))/16 - ((c - I*k0)*(3*c - I*k0)^3)/16 + (3*c - I*k0)^5/(16*(c - I*k0)))*k0^4)/8 - ((-(c - I*k0)^3/(8*(3*c - I*k0)) + ((c - I*k0)*(3*c - I*k0))/4 - (3*c - I*k0)^3/(8*(c - I*k0)))*k0^6)/16 - (5*((c - I*k0)/(2*(3*c - I*k0)) + (3*c - I*k0)/(2*(c - I*k0)))*k0^8)/128 - (7*k0^10)/(256*(c - I*k0)*(3*c - I*k0))) - (12*I)*c*k0*((7*(c - I*k0)^9)/(256*(3*c - I*k0)) - (5*(c - I*k0)^7*(3*c - I*k0))/256 - ((c - I*k0)^5*(3*c - I*k0)^3)/128 - ((c - I*k0)^3*(3*c - I*k0)^5)/128 - (5*(c - I*k0)*(3*c - I*k0)^7)/256 + (7*(3*c - I*k0)^9)/(256*(c - I*k0)) - (((-5*(c - I*k0)^7)/(128*(3*c - I*k0)) + ((c - I*k0)^5*(3*c - I*k0))/32 + ((c - I*k0)^3*(3*c - I*k0)^3)/64 + ((c - I*k0)*(3*c - I*k0)^5)/32 - (5*(3*c - I*k0)^7)/(128*(c - I*k0)))*k0^2)/2 - (((c - I*k0)^5/(16*(3*c - I*k0)) - ((c - I*k0)^3*(3*c - I*k0))/16 - ((c - I*k0)*(3*c - I*k0)^3)/16 + (3*c - I*k0)^5/(16*(c - I*k0)))*k0^4)/8 - ((-(c - I*k0)^3/(8*(3*c - I*k0)) + ((c - I*k0)*(3*c - I*k0))/4 - (3*c - I*k0)^3/(8*(c - I*k0)))*k0^6)/16 - (5*((c - I*k0)/(2*(3*c - I*k0)) + (3*c - I*k0)/(2*(c - I*k0)))*k0^8)/128 - (7*k0^10)/(256*(c - I*k0)*(3*c - I*k0))) - 3*k0^2*((7*(c - I*k0)^9)/(256*(3*c - I*k0)) - (5*(c - I*k0)^7*(3*c - I*k0))/256 - ((c - I*k0)^5*(3*c - I*k0)^3)/128 - ((c - I*k0)^3*(3*c - I*k0)^5)/128 - (5*(c - I*k0)*(3*c - I*k0)^7)/256 + (7*(3*c - I*k0)^9)/(256*(c - I*k0)) - (((-5*(c - I*k0)^7)/(128*(3*c - I*k0)) + ((c - I*k0)^5*(3*c - I*k0))/32 + ((c - I*k0)^3*(3*c - I*k0)^3)/64 + ((c - I*k0)*(3*c - I*k0)^5)/32 - (5*(3*c - I*k0)^7)/(128*(c - I*k0)))*k0^2)/2 - (((c - I*k0)^5/(16*(3*c - I*k0)) - ((c - I*k0)^3*(3*c - I*k0))/16 - ((c - I*k0)*(3*c - I*k0)^3)/16 + (3*c - I*k0)^5/(16*(c - I*k0)))*k0^4)/8 - ((-(c - I*k0)^3/(8*(3*c - I*k0)) + ((c - I*k0)*(3*c - I*k0))/4 - (3*c - I*k0)^3/(8*(c - I*k0)))*k0^6)/16 - (5*((c - I*k0)/(2*(3*c - I*k0)) + (3*c - I*k0)/(2*(c - I*k0)))*k0^8)/128 - (7*k0^10)/(256*(c - I*k0)*(3*c - I*k0))) - 18*c^2*((7*(2*c - I*k0)^9)/(256*(3*c - I*k0)) - (5*(2*c - I*k0)^7*(3*c - I*k0))/256 - ((2*c - I*k0)^5*(3*c - I*k0)^3)/128 - ((2*c - I*k0)^3*(3*c - I*k0)^5)/128 - (5*(2*c - I*k0)*(3*c - I*k0)^7)/256 + (7*(3*c - I*k0)^9)/(256*(2*c - I*k0)) - (((-5*(2*c - I*k0)^7)/(128*(3*c - I*k0)) + ((2*c - I*k0)^5*(3*c - I*k0))/32 + ((2*c - I*k0)^3*(3*c - I*k0)^3)/64 + ((2*c - I*k0)*(3*c - I*k0)^5)/32 - (5*(3*c - I*k0)^7)/(128*(2*c - I*k0)))*k0^2)/2 - (((2*c - I*k0)^5/(16*(3*c - I*k0)) - ((2*c - I*k0)^3*(3*c - I*k0))/16 - ((2*c - I*k0)*(3*c - I*k0)^3)/16 + (3*c - I*k0)^5/(16*(2*c - I*k0)))*k0^4)/8 - ((-(2*c - I*k0)^3/(8*(3*c - I*k0)) + ((2*c - I*k0)*(3*c - I*k0))/4 - (3*c - I*k0)^3/(8*(2*c - I*k0)))*k0^6)/16 - (5*((2*c - I*k0)/(2*(3*c - I*k0)) + (3*c - I*k0)/(2*(2*c - I*k0)))*k0^8)/128 - (7*k0^10)/(256*(2*c - I*k0)*(3*c - I*k0))) + (15*I)*c*k0*((7*(2*c - I*k0)^9)/(256*(3*c - I*k0)) - (5*(2*c - I*k0)^7*(3*c - I*k0))/256 - ((2*c - I*k0)^5*(3*c - I*k0)^3)/128 - ((2*c - I*k0)^3*(3*c - I*k0)^5)/128 - (5*(2*c - I*k0)*(3*c - I*k0)^7)/256 + (7*(3*c - I*k0)^9)/(256*(2*c - I*k0)) - (((-5*(2*c - I*k0)^7)/(128*(3*c - I*k0)) + ((2*c - I*k0)^5*(3*c - I*k0))/32 + ((2*c - I*k0)^3*(3*c - I*k0)^3)/64 + ((2*c - I*k0)*(3*c - I*k0)^5)/32 - (5*(3*c - I*k0)^7)/(128*(2*c - I*k0)))*k0^2)/2 - (((2*c - I*k0)^5/(16*(3*c - I*k0)) - ((2*c - I*k0)^3*(3*c - I*k0))/16 - ((2*c - I*k0)*(3*c - I*k0)^3)/16 + (3*c - I*k0)^5/(16*(2*c - I*k0)))*k0^4)/8 - ((-(2*c - I*k0)^3/(8*(3*c - I*k0)) + ((2*c - I*k0)*(3*c - I*k0))/4 - (3*c - I*k0)^3/(8*(2*c - I*k0)))*k0^6)/16 - (5*((2*c - I*k0)/(2*(3*c - I*k0)) + (3*c - I*k0)/(2*(2*c - I*k0)))*k0^8)/128 - (7*k0^10)/(256*(2*c - I*k0)*(3*c - I*k0))) + 3*k0^2*((7*(2*c - I*k0)^9)/(256*(3*c - I*k0)) - (5*(2*c - I*k0)^7*(3*c - I*k0))/256 - ((2*c - I*k0)^5*(3*c - I*k0)^3)/128 - ((2*c - I*k0)^3*(3*c - I*k0)^5)/128 - (5*(2*c - I*k0)*(3*c - I*k0)^7)/256 + (7*(3*c - I*k0)^9)/(256*(2*c - I*k0)) - (((-5*(2*c - I*k0)^7)/(128*(3*c - I*k0)) + ((2*c - I*k0)^5*(3*c - I*k0))/32 + ((2*c - I*k0)^3*(3*c - I*k0)^3)/64 + ((2*c - I*k0)*(3*c - I*k0)^5)/32 - (5*(3*c - I*k0)^7)/(128*(2*c - I*k0)))*k0^2)/2 - (((2*c - I*k0)^5/(16*(3*c - I*k0)) - ((2*c - I*k0)^3*(3*c - I*k0))/16 - ((2*c - I*k0)*(3*c - I*k0)^3)/16 + (3*c - I*k0)^5/(16*(2*c - I*k0)))*k0^4)/8 - ((-(2*c - I*k0)^3/(8*(3*c - I*k0)) + ((2*c - I*k0)*(3*c - I*k0))/4 - (3*c - I*k0)^3/(8*(2*c - I*k0)))*k0^6)/16 - (5*((2*c - I*k0)/(2*(3*c - I*k0)) + (3*c - I*k0)/(2*(2*c - I*k0)))*k0^8)/128 - (7*k0^10)/(256*(2*c - I*k0)*(3*c - I*k0)))))/k^3 + (6*c^3*(((c - I*k0)^5/(16*(2*c - I*k0)) - ((c - I*k0)^3*(2*c - I*k0))/16 - ((c - I*k0)*(2*c - I*k0)^3)/16 + (2*c - I*k0)^5/(16*(c - I*k0)))/(3*c - I*k0) + ((-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)))*(3*c - I*k0))/2 - (((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*(3*c - I*k0)^3)/8 + (3*c - I*k0)^5/(16*(c - I*k0)*(2*c - I*k0))) - (11*I)*c^2*(((c - I*k0)^5/(16*(2*c - I*k0)) - ((c - I*k0)^3*(2*c - I*k0))/16 - ((c - I*k0)*(2*c - I*k0)^3)/16 + (2*c - I*k0)^5/(16*(c - I*k0)))/(3*c - I*k0) + ((-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)))*(3*c - I*k0))/2 - (((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*(3*c - I*k0)^3)/8 + (3*c - I*k0)^5/(16*(c - I*k0)*(2*c - I*k0)))*k0 - 6*c*(((c - I*k0)^5/(16*(2*c - I*k0)) - ((c - I*k0)^3*(2*c - I*k0))/16 - ((c - I*k0)*(2*c - I*k0)^3)/16 + (2*c - I*k0)^5/(16*(c - I*k0)))/(3*c - I*k0) + ((-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)))*(3*c - I*k0))/2 - (((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*(3*c - I*k0)^3)/8 + (3*c - I*k0)^5/(16*(c - I*k0)*(2*c - I*k0)))*k0^2 + I*(((c - I*k0)^5/(16*(2*c - I*k0)) - ((c - I*k0)^3*(2*c - I*k0))/16 - ((c - I*k0)*(2*c - I*k0)^3)/16 + (2*c - I*k0)^5/(16*(c - I*k0)))/(3*c - I*k0) + ((-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)))*(3*c - I*k0))/2 - (((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*(3*c - I*k0)^3)/8 + (3*c - I*k0)^5/(16*(c - I*k0)*(2*c - I*k0)))*k0^3 - 2*c^2*((c - I*k0)^5/(16*(2*c - I*k0)) - ((c - I*k0)^3*(2*c - I*k0))/16 - ((c - I*k0)*(2*c - I*k0)^3)/16 + (2*c - I*k0)^5/(16*(c - I*k0)) - ((-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)))*k0^2)/2 - (((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*k0^4)/8 - k0^6/(16*(c - I*k0)*(2*c - I*k0))) + (3*I)*c*k0*((c - I*k0)^5/(16*(2*c - I*k0)) - ((c - I*k0)^3*(2*c - I*k0))/16 - ((c - I*k0)*(2*c - I*k0)^3)/16 + (2*c - I*k0)^5/(16*(c - I*k0)) - ((-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)))*k0^2)/2 - (((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*k0^4)/8 - k0^6/(16*(c - I*k0)*(2*c - I*k0))) + k0^2*((c - I*k0)^5/(16*(2*c - I*k0)) - ((c - I*k0)^3*(2*c - I*k0))/16 - ((c - I*k0)*(2*c - I*k0)^3)/16 + (2*c - I*k0)^5/(16*(c - I*k0)) - ((-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)))*k0^2)/2 - (((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*k0^4)/8 - k0^6/(16*(c - I*k0)*(2*c - I*k0))) + 9*c^2*((c - I*k0)^5/(16*(3*c - I*k0)) - ((c - I*k0)^3*(3*c - I*k0))/16 - ((c - I*k0)*(3*c - I*k0)^3)/16 + (3*c - I*k0)^5/(16*(c - I*k0)) - ((-(c - I*k0)^3/(8*(3*c - I*k0)) + ((c - I*k0)*(3*c - I*k0))/4 - (3*c - I*k0)^3/(8*(c - I*k0)))*k0^2)/2 - (((c - I*k0)/(2*(3*c - I*k0)) + (3*c - I*k0)/(2*(c - I*k0)))*k0^4)/8 - k0^6/(16*(c - I*k0)*(3*c - I*k0))) - (12*I)*c*k0*((c - I*k0)^5/(16*(3*c - I*k0)) - ((c - I*k0)^3*(3*c - I*k0))/16 - ((c - I*k0)*(3*c - I*k0)^3)/16 + (3*c - I*k0)^5/(16*(c - I*k0)) - ((-(c - I*k0)^3/(8*(3*c - I*k0)) + ((c - I*k0)*(3*c - I*k0))/4 - (3*c - I*k0)^3/(8*(c - I*k0)))*k0^2)/2 - (((c - I*k0)/(2*(3*c - I*k0)) + (3*c - I*k0)/(2*(c - I*k0)))*k0^4)/8 - k0^6/(16*(c - I*k0)*(3*c - I*k0))) - 3*k0^2*((c - I*k0)^5/(16*(3*c - I*k0)) - ((c - I*k0)^3*(3*c - I*k0))/16 - ((c - I*k0)*(3*c - I*k0)^3)/16 + (3*c - I*k0)^5/(16*(c - I*k0)) - ((-(c - I*k0)^3/(8*(3*c - I*k0)) + ((c - I*k0)*(3*c - I*k0))/4 - (3*c - I*k0)^3/(8*(c - I*k0)))*k0^2)/2 - (((c - I*k0)/(2*(3*c - I*k0)) + (3*c - I*k0)/(2*(c - I*k0)))*k0^4)/8 - k0^6/(16*(c - I*k0)*(3*c - I*k0))) - 18*c^2*((2*c - I*k0)^5/(16*(3*c - I*k0)) - ((2*c - I*k0)^3*(3*c - I*k0))/16 - ((2*c - I*k0)*(3*c - I*k0)^3)/16 + (3*c - I*k0)^5/(16*(2*c - I*k0)) - ((-(2*c - I*k0)^3/(8*(3*c - I*k0)) + ((2*c - I*k0)*(3*c - I*k0))/4 - (3*c - I*k0)^3/(8*(2*c - I*k0)))*k0^2)/2 - (((2*c - I*k0)/(2*(3*c - I*k0)) + (3*c - I*k0)/(2*(2*c - I*k0)))*k0^4)/8 - k0^6/(16*(2*c - I*k0)*(3*c - I*k0))) + (15*I)*c*k0*((2*c - I*k0)^5/(16*(3*c - I*k0)) - ((2*c - I*k0)^3*(3*c - I*k0))/16 - ((2*c - I*k0)*(3*c - I*k0)^3)/16 + (3*c - I*k0)^5/(16*(2*c - I*k0)) - ((-(2*c - I*k0)^3/(8*(3*c - I*k0)) + ((2*c - I*k0)*(3*c - I*k0))/4 - (3*c - I*k0)^3/(8*(2*c - I*k0)))*k0^2)/2 - (((2*c - I*k0)/(2*(3*c - I*k0)) + (3*c - I*k0)/(2*(2*c - I*k0)))*k0^4)/8 - k0^6/(16*(2*c - I*k0)*(3*c - I*k0))) + 3*k0^2*((2*c - I*k0)^5/(16*(3*c - I*k0)) - ((2*c - I*k0)^3*(3*c - I*k0))/16 - ((2*c - I*k0)*(3*c - I*k0)^3)/16 + (3*c - I*k0)^5/(16*(2*c - I*k0)) - ((-(2*c - I*k0)^3/(8*(3*c - I*k0)) + ((2*c - I*k0)*(3*c - I*k0))/4 - (3*c - I*k0)^3/(8*(2*c - I*k0)))*k0^2)/2 - (((2*c - I*k0)/(2*(3*c - I*k0)) + (3*c - I*k0)/(2*(2*c - I*k0)))*k0^4)/8 - k0^6/(16*(2*c - I*k0)*(3*c - I*k0))))*(-((-((c - I*k0)^3*(2*c - I*k0))/(2*k^2) - ((c - I*k0)*(2*c - I*k0)^3)/(2*k^2))*(3*c - I*k0)^3)/(2*k) + ((((-((c - I*k0)^3*(2*c - I*k0))/(2*k^2) - ((c - I*k0)*(2*c - I*k0)^3)/(2*k^2))*(3*c - I*k0))/k - ((c - I*k0)*(2*c - I*k0)*(3*c - I*k0)^3)/(2*k^3))*k0^2)/2 + (3*(c - I*k0)*(2*c - I*k0)*(3*c - I*k0)*k0^4)/(8*k^3) + (3*(c - I*k0)*(2*c - I*k0)*(3*c - I*k0)^4*((3*c)/k - (I*k0)/k))/(8*k^2) + ((3*c - I*k0)*(((c - I*k0)^3*(2*c - I*k0)^3)/(4*k^2) + (3*(c - I*k0)^4*(2*c - I*k0)*(c/k - (I*k0)/k))/(8*k) + (3*(c - I*k0)*(2*c - I*k0)^4*((2*c)/k - (I*k0)/k))/(8*k)))/k) - (9*(3*c^4 - (2*I)*c^3*k0)*((3*(((-((c - I*k0)^3*(2*c - I*k0))/(2*k^2) - ((c - I*k0)*(2*c - I*k0)^3)/(2*k^2))*(3*c - I*k0))/k - ((c - I*k0)*(2*c - I*k0)*(3*c - I*k0)^3)/(2*k^3))*k0^4)/8 + (5*(c - I*k0)*(2*c - I*k0)*(3*c - I*k0)*k0^6)/(16*k^3) + (3*(-((c - I*k0)^3*(2*c - I*k0))/(2*k^2) - ((c - I*k0)*(2*c - I*k0)^3)/(2*k^2))*(3*c - I*k0)^4*((3*c)/k - (I*k0)/k))/8 - (5*(c - I*k0)*(2*c - I*k0)*(3*c - I*k0)^6*((3*c)/k - (I*k0)/k))/(16*k^2) - ((3*c - I*k0)^3*(((c - I*k0)^3*(2*c - I*k0)^3)/(4*k^2) + (3*(c - I*k0)^4*(2*c - I*k0)*(c/k - (I*k0)/k))/(8*k) + (3*(c - I*k0)*(2*c - I*k0)^4*((2*c)/k - (I*k0)/k))/(8*k)))/(2*k) + ((3*c - I*k0)*((-5*(c - I*k0)^6*(2*c - I*k0)*(c/k - (I*k0)/k))/(16*k) - (3*(c - I*k0)^4*(2*c - I*k0)^3*(c/k - (I*k0)/k))/(16*k) - (3*(c - I*k0)^3*(2*c - I*k0)^4*((2*c)/k - (I*k0)/k))/(16*k) - (5*(c - I*k0)*(2*c - I*k0)^6*((2*c)/k - (I*k0)/k))/(16*k)))/k + (k0^2*(-((-((c - I*k0)^3*(2*c - I*k0))/(2*k^2) - ((c - I*k0)*(2*c - I*k0)^3)/(2*k^2))*(3*c - I*k0)^3)/(2*k) + (3*(c - I*k0)*(2*c - I*k0)*(3*c - I*k0)^4*((3*c)/k - (I*k0)/k))/(8*k^2) + ((3*c - I*k0)*(((c - I*k0)^3*(2*c - I*k0)^3)/(4*k^2) + (3*(c - I*k0)^4*(2*c - I*k0)*(c/k - (I*k0)/k))/(8*k) + (3*(c - I*k0)*(2*c - I*k0)^4*((2*c)/k - (I*k0)/k))/(8*k)))/k))/2))/2)/((c - I*k0)*(2*c - I*k0)*(3*c - I*k0)*k0), 0, ((((-((c - I*k0)^3*(2*c - I*k0))/(2*k^2) - ((c - I*k0)*(2*c - I*k0)^3)/(2*k^2))*(3*c - I*k0))/k - ((c - I*k0)*(2*c - I*k0)*(3*c - I*k0)^3)/(2*k^3) + ((c - I*k0)*(2*c - I*k0)*(3*c - I*k0)*k0^2)/(2*k^3))*(6*c^3*(((7*(c - I*k0)^9)/(256*(2*c - I*k0)) - (5*(c - I*k0)^7*(2*c - I*k0))/256 - ((c - I*k0)^5*(2*c - I*k0)^3)/128 - ((c - I*k0)^3*(2*c - I*k0)^5)/128 - (5*(c - I*k0)*(2*c - I*k0)^7)/256 + (7*(2*c - I*k0)^9)/(256*(c - I*k0)))/(3*c - I*k0) + (((-5*(c - I*k0)^7)/(128*(2*c - I*k0)) + ((c - I*k0)^5*(2*c - I*k0))/32 + ((c - I*k0)^3*(2*c - I*k0)^3)/64 + ((c - I*k0)*(2*c - I*k0)^5)/32 - (5*(2*c - I*k0)^7)/(128*(c - I*k0)))*(3*c - I*k0))/2 - (((c - I*k0)^5/(16*(2*c - I*k0)) - ((c - I*k0)^3*(2*c - I*k0))/16 - ((c - I*k0)*(2*c - I*k0)^3)/16 + (2*c - I*k0)^5/(16*(c - I*k0)))*(3*c - I*k0)^3)/8 + ((-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)))*(3*c - I*k0)^5)/16 - (5*((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*(3*c - I*k0)^7)/128 + (7*(3*c - I*k0)^9)/(256*(c - I*k0)*(2*c - I*k0))) - (11*I)*c^2*(((7*(c - I*k0)^9)/(256*(2*c - I*k0)) - (5*(c - I*k0)^7*(2*c - I*k0))/256 - ((c - I*k0)^5*(2*c - I*k0)^3)/128 - ((c - I*k0)^3*(2*c - I*k0)^5)/128 - (5*(c - I*k0)*(2*c - I*k0)^7)/256 + (7*(2*c - I*k0)^9)/(256*(c - I*k0)))/(3*c - I*k0) + (((-5*(c - I*k0)^7)/(128*(2*c - I*k0)) + ((c - I*k0)^5*(2*c - I*k0))/32 + ((c - I*k0)^3*(2*c - I*k0)^3)/64 + ((c - I*k0)*(2*c - I*k0)^5)/32 - (5*(2*c - I*k0)^7)/(128*(c - I*k0)))*(3*c - I*k0))/2 - (((c - I*k0)^5/(16*(2*c - I*k0)) - ((c - I*k0)^3*(2*c - I*k0))/16 - ((c - I*k0)*(2*c - I*k0)^3)/16 + (2*c - I*k0)^5/(16*(c - I*k0)))*(3*c - I*k0)^3)/8 + ((-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)))*(3*c - I*k0)^5)/16 - (5*((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*(3*c - I*k0)^7)/128 + (7*(3*c - I*k0)^9)/(256*(c - I*k0)*(2*c - I*k0)))*k0 - 6*c*(((7*(c - I*k0)^9)/(256*(2*c - I*k0)) - (5*(c - I*k0)^7*(2*c - I*k0))/256 - ((c - I*k0)^5*(2*c - I*k0)^3)/128 - ((c - I*k0)^3*(2*c - I*k0)^5)/128 - (5*(c - I*k0)*(2*c - I*k0)^7)/256 + (7*(2*c - I*k0)^9)/(256*(c - I*k0)))/(3*c - I*k0) + (((-5*(c - I*k0)^7)/(128*(2*c - I*k0)) + ((c - I*k0)^5*(2*c - I*k0))/32 + ((c - I*k0)^3*(2*c - I*k0)^3)/64 + ((c - I*k0)*(2*c - I*k0)^5)/32 - (5*(2*c - I*k0)^7)/(128*(c - I*k0)))*(3*c - I*k0))/2 - (((c - I*k0)^5/(16*(2*c - I*k0)) - ((c - I*k0)^3*(2*c - I*k0))/16 - ((c - I*k0)*(2*c - I*k0)^3)/16 + (2*c - I*k0)^5/(16*(c - I*k0)))*(3*c - I*k0)^3)/8 + ((-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)))*(3*c - I*k0)^5)/16 - (5*((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*(3*c - I*k0)^7)/128 + (7*(3*c - I*k0)^9)/(256*(c - I*k0)*(2*c - I*k0)))*k0^2 + I*(((7*(c - I*k0)^9)/(256*(2*c - I*k0)) - (5*(c - I*k0)^7*(2*c - I*k0))/256 - ((c - I*k0)^5*(2*c - I*k0)^3)/128 - ((c - I*k0)^3*(2*c - I*k0)^5)/128 - (5*(c - I*k0)*(2*c - I*k0)^7)/256 + (7*(2*c - I*k0)^9)/(256*(c - I*k0)))/(3*c - I*k0) + (((-5*(c - I*k0)^7)/(128*(2*c - I*k0)) + ((c - I*k0)^5*(2*c - I*k0))/32 + ((c - I*k0)^3*(2*c - I*k0)^3)/64 + ((c - I*k0)*(2*c - I*k0)^5)/32 - (5*(2*c - I*k0)^7)/(128*(c - I*k0)))*(3*c - I*k0))/2 - (((c - I*k0)^5/(16*(2*c - I*k0)) - ((c - I*k0)^3*(2*c - I*k0))/16 - ((c - I*k0)*(2*c - I*k0)^3)/16 + (2*c - I*k0)^5/(16*(c - I*k0)))*(3*c - I*k0)^3)/8 + ((-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)))*(3*c - I*k0)^5)/16 - (5*((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*(3*c - I*k0)^7)/128 + (7*(3*c - I*k0)^9)/(256*(c - I*k0)*(2*c - I*k0)))*k0^3 - 2*c^2*((7*(c - I*k0)^9)/(256*(2*c - I*k0)) - (5*(c - I*k0)^7*(2*c - I*k0))/256 - ((c - I*k0)^5*(2*c - I*k0)^3)/128 - ((c - I*k0)^3*(2*c - I*k0)^5)/128 - (5*(c - I*k0)*(2*c - I*k0)^7)/256 + (7*(2*c - I*k0)^9)/(256*(c - I*k0)) - (((-5*(c - I*k0)^7)/(128*(2*c - I*k0)) + ((c - I*k0)^5*(2*c - I*k0))/32 + ((c - I*k0)^3*(2*c - I*k0)^3)/64 + ((c - I*k0)*(2*c - I*k0)^5)/32 - (5*(2*c - I*k0)^7)/(128*(c - I*k0)))*k0^2)/2 - (((c - I*k0)^5/(16*(2*c - I*k0)) - ((c - I*k0)^3*(2*c - I*k0))/16 - ((c - I*k0)*(2*c - I*k0)^3)/16 + (2*c - I*k0)^5/(16*(c - I*k0)))*k0^4)/8 - ((-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)))*k0^6)/16 - (5*((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*k0^8)/128 - (7*k0^10)/(256*(c - I*k0)*(2*c - I*k0))) + (3*I)*c*k0*((7*(c - I*k0)^9)/(256*(2*c - I*k0)) - (5*(c - I*k0)^7*(2*c - I*k0))/256 - ((c - I*k0)^5*(2*c - I*k0)^3)/128 - ((c - I*k0)^3*(2*c - I*k0)^5)/128 - (5*(c - I*k0)*(2*c - I*k0)^7)/256 + (7*(2*c - I*k0)^9)/(256*(c - I*k0)) - (((-5*(c - I*k0)^7)/(128*(2*c - I*k0)) + ((c - I*k0)^5*(2*c - I*k0))/32 + ((c - I*k0)^3*(2*c - I*k0)^3)/64 + ((c - I*k0)*(2*c - I*k0)^5)/32 - (5*(2*c - I*k0)^7)/(128*(c - I*k0)))*k0^2)/2 - (((c - I*k0)^5/(16*(2*c - I*k0)) - ((c - I*k0)^3*(2*c - I*k0))/16 - ((c - I*k0)*(2*c - I*k0)^3)/16 + (2*c - I*k0)^5/(16*(c - I*k0)))*k0^4)/8 - ((-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)))*k0^6)/16 - (5*((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*k0^8)/128 - (7*k0^10)/(256*(c - I*k0)*(2*c - I*k0))) + k0^2*((7*(c - I*k0)^9)/(256*(2*c - I*k0)) - (5*(c - I*k0)^7*(2*c - I*k0))/256 - ((c - I*k0)^5*(2*c - I*k0)^3)/128 - ((c - I*k0)^3*(2*c - I*k0)^5)/128 - (5*(c - I*k0)*(2*c - I*k0)^7)/256 + (7*(2*c - I*k0)^9)/(256*(c - I*k0)) - (((-5*(c - I*k0)^7)/(128*(2*c - I*k0)) + ((c - I*k0)^5*(2*c - I*k0))/32 + ((c - I*k0)^3*(2*c - I*k0)^3)/64 + ((c - I*k0)*(2*c - I*k0)^5)/32 - (5*(2*c - I*k0)^7)/(128*(c - I*k0)))*k0^2)/2 - (((c - I*k0)^5/(16*(2*c - I*k0)) - ((c - I*k0)^3*(2*c - I*k0))/16 - ((c - I*k0)*(2*c - I*k0)^3)/16 + (2*c - I*k0)^5/(16*(c - I*k0)))*k0^4)/8 - ((-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)))*k0^6)/16 - (5*((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*k0^8)/128 - (7*k0^10)/(256*(c - I*k0)*(2*c - I*k0))) + 9*c^2*((7*(c - I*k0)^9)/(256*(3*c - I*k0)) - (5*(c - I*k0)^7*(3*c - I*k0))/256 - ((c - I*k0)^5*(3*c - I*k0)^3)/128 - ((c - I*k0)^3*(3*c - I*k0)^5)/128 - (5*(c - I*k0)*(3*c - I*k0)^7)/256 + (7*(3*c - I*k0)^9)/(256*(c - I*k0)) - (((-5*(c - I*k0)^7)/(128*(3*c - I*k0)) + ((c - I*k0)^5*(3*c - I*k0))/32 + ((c - I*k0)^3*(3*c - I*k0)^3)/64 + ((c - I*k0)*(3*c - I*k0)^5)/32 - (5*(3*c - I*k0)^7)/(128*(c - I*k0)))*k0^2)/2 - (((c - I*k0)^5/(16*(3*c - I*k0)) - ((c - I*k0)^3*(3*c - I*k0))/16 - ((c - I*k0)*(3*c - I*k0)^3)/16 + (3*c - I*k0)^5/(16*(c - I*k0)))*k0^4)/8 - ((-(c - I*k0)^3/(8*(3*c - I*k0)) + ((c - I*k0)*(3*c - I*k0))/4 - (3*c - I*k0)^3/(8*(c - I*k0)))*k0^6)/16 - (5*((c - I*k0)/(2*(3*c - I*k0)) + (3*c - I*k0)/(2*(c - I*k0)))*k0^8)/128 - (7*k0^10)/(256*(c - I*k0)*(3*c - I*k0))) - (12*I)*c*k0*((7*(c - I*k0)^9)/(256*(3*c - I*k0)) - (5*(c - I*k0)^7*(3*c - I*k0))/256 - ((c - I*k0)^5*(3*c - I*k0)^3)/128 - ((c - I*k0)^3*(3*c - I*k0)^5)/128 - (5*(c - I*k0)*(3*c - I*k0)^7)/256 + (7*(3*c - I*k0)^9)/(256*(c - I*k0)) - (((-5*(c - I*k0)^7)/(128*(3*c - I*k0)) + ((c - I*k0)^5*(3*c - I*k0))/32 + ((c - I*k0)^3*(3*c - I*k0)^3)/64 + ((c - I*k0)*(3*c - I*k0)^5)/32 - (5*(3*c - I*k0)^7)/(128*(c - I*k0)))*k0^2)/2 - (((c - I*k0)^5/(16*(3*c - I*k0)) - ((c - I*k0)^3*(3*c - I*k0))/16 - ((c - I*k0)*(3*c - I*k0)^3)/16 + (3*c - I*k0)^5/(16*(c - I*k0)))*k0^4)/8 - ((-(c - I*k0)^3/(8*(3*c - I*k0)) + ((c - I*k0)*(3*c - I*k0))/4 - (3*c - I*k0)^3/(8*(c - I*k0)))*k0^6)/16 - (5*((c - I*k0)/(2*(3*c - I*k0)) + (3*c - I*k0)/(2*(c - I*k0)))*k0^8)/128 - (7*k0^10)/(256*(c - I*k0)*(3*c - I*k0))) - 3*k0^2*((7*(c - I*k0)^9)/(256*(3*c - I*k0)) - (5*(c - I*k0)^7*(3*c - I*k0))/256 - ((c - I*k0)^5*(3*c - I*k0)^3)/128 - ((c - I*k0)^3*(3*c - I*k0)^5)/128 - (5*(c - I*k0)*(3*c - I*k0)^7)/256 + (7*(3*c - I*k0)^9)/(256*(c - I*k0)) - (((-5*(c - I*k0)^7)/(128*(3*c - I*k0)) + ((c - I*k0)^5*(3*c - I*k0))/32 + ((c - I*k0)^3*(3*c - I*k0)^3)/64 + ((c - I*k0)*(3*c - I*k0)^5)/32 - (5*(3*c - I*k0)^7)/(128*(c - I*k0)))*k0^2)/2 - (((c - I*k0)^5/(16*(3*c - I*k0)) - ((c - I*k0)^3*(3*c - I*k0))/16 - ((c - I*k0)*(3*c - I*k0)^3)/16 + (3*c - I*k0)^5/(16*(c - I*k0)))*k0^4)/8 - ((-(c - I*k0)^3/(8*(3*c - I*k0)) + ((c - I*k0)*(3*c - I*k0))/4 - (3*c - I*k0)^3/(8*(c - I*k0)))*k0^6)/16 - (5*((c - I*k0)/(2*(3*c - I*k0)) + (3*c - I*k0)/(2*(c - I*k0)))*k0^8)/128 - (7*k0^10)/(256*(c - I*k0)*(3*c - I*k0))) - 18*c^2*((7*(2*c - I*k0)^9)/(256*(3*c - I*k0)) - (5*(2*c - I*k0)^7*(3*c - I*k0))/256 - ((2*c - I*k0)^5*(3*c - I*k0)^3)/128 - ((2*c - I*k0)^3*(3*c - I*k0)^5)/128 - (5*(2*c - I*k0)*(3*c - I*k0)^7)/256 + (7*(3*c - I*k0)^9)/(256*(2*c - I*k0)) - (((-5*(2*c - I*k0)^7)/(128*(3*c - I*k0)) + ((2*c - I*k0)^5*(3*c - I*k0))/32 + ((2*c - I*k0)^3*(3*c - I*k0)^3)/64 + ((2*c - I*k0)*(3*c - I*k0)^5)/32 - (5*(3*c - I*k0)^7)/(128*(2*c - I*k0)))*k0^2)/2 - (((2*c - I*k0)^5/(16*(3*c - I*k0)) - ((2*c - I*k0)^3*(3*c - I*k0))/16 - ((2*c - I*k0)*(3*c - I*k0)^3)/16 + (3*c - I*k0)^5/(16*(2*c - I*k0)))*k0^4)/8 - ((-(2*c - I*k0)^3/(8*(3*c - I*k0)) + ((2*c - I*k0)*(3*c - I*k0))/4 - (3*c - I*k0)^3/(8*(2*c - I*k0)))*k0^6)/16 - (5*((2*c - I*k0)/(2*(3*c - I*k0)) + (3*c - I*k0)/(2*(2*c - I*k0)))*k0^8)/128 - (7*k0^10)/(256*(2*c - I*k0)*(3*c - I*k0))) + (15*I)*c*k0*((7*(2*c - I*k0)^9)/(256*(3*c - I*k0)) - (5*(2*c - I*k0)^7*(3*c - I*k0))/256 - ((2*c - I*k0)^5*(3*c - I*k0)^3)/128 - ((2*c - I*k0)^3*(3*c - I*k0)^5)/128 - (5*(2*c - I*k0)*(3*c - I*k0)^7)/256 + (7*(3*c - I*k0)^9)/(256*(2*c - I*k0)) - (((-5*(2*c - I*k0)^7)/(128*(3*c - I*k0)) + ((2*c - I*k0)^5*(3*c - I*k0))/32 + ((2*c - I*k0)^3*(3*c - I*k0)^3)/64 + ((2*c - I*k0)*(3*c - I*k0)^5)/32 - (5*(3*c - I*k0)^7)/(128*(2*c - I*k0)))*k0^2)/2 - (((2*c - I*k0)^5/(16*(3*c - I*k0)) - ((2*c - I*k0)^3*(3*c - I*k0))/16 - ((2*c - I*k0)*(3*c - I*k0)^3)/16 + (3*c - I*k0)^5/(16*(2*c - I*k0)))*k0^4)/8 - ((-(2*c - I*k0)^3/(8*(3*c - I*k0)) + ((2*c - I*k0)*(3*c - I*k0))/4 - (3*c - I*k0)^3/(8*(2*c - I*k0)))*k0^6)/16 - (5*((2*c - I*k0)/(2*(3*c - I*k0)) + (3*c - I*k0)/(2*(2*c - I*k0)))*k0^8)/128 - (7*k0^10)/(256*(2*c - I*k0)*(3*c - I*k0))) + 3*k0^2*((7*(2*c - I*k0)^9)/(256*(3*c - I*k0)) - (5*(2*c - I*k0)^7*(3*c - I*k0))/256 - ((2*c - I*k0)^5*(3*c - I*k0)^3)/128 - ((2*c - I*k0)^3*(3*c - I*k0)^5)/128 - (5*(2*c - I*k0)*(3*c - I*k0)^7)/256 + (7*(3*c - I*k0)^9)/(256*(2*c - I*k0)) - (((-5*(2*c - I*k0)^7)/(128*(3*c - I*k0)) + ((2*c - I*k0)^5*(3*c - I*k0))/32 + ((2*c - I*k0)^3*(3*c - I*k0)^3)/64 + ((2*c - I*k0)*(3*c - I*k0)^5)/32 - (5*(3*c - I*k0)^7)/(128*(2*c - I*k0)))*k0^2)/2 - (((2*c - I*k0)^5/(16*(3*c - I*k0)) - ((2*c - I*k0)^3*(3*c - I*k0))/16 - ((2*c - I*k0)*(3*c - I*k0)^3)/16 + (3*c - I*k0)^5/(16*(2*c - I*k0)))*k0^4)/8 - ((-(2*c - I*k0)^3/(8*(3*c - I*k0)) + ((2*c - I*k0)*(3*c - I*k0))/4 - (3*c - I*k0)^3/(8*(2*c - I*k0)))*k0^6)/16 - (5*((2*c - I*k0)/(2*(3*c - I*k0)) + (3*c - I*k0)/(2*(2*c - I*k0)))*k0^8)/128 - (7*k0^10)/(256*(2*c - I*k0)*(3*c - I*k0)))) + ((c - I*k0)*(2*c - I*k0)*(3*c - I*k0)*(6*c^3*(((-21*(c - I*k0)^11)/(1024*(2*c - I*k0)) + (7*(c - I*k0)^9*(2*c - I*k0))/512 + (5*(c - I*k0)^7*(2*c - I*k0)^3)/1024 + ((c - I*k0)^5*(2*c - I*k0)^5)/256 + (5*(c - I*k0)^3*(2*c - I*k0)^7)/1024 + (7*(c - I*k0)*(2*c - I*k0)^9)/512 - (21*(2*c - I*k0)^11)/(1024*(c - I*k0)))/(3*c - I*k0) + (((7*(c - I*k0)^9)/(256*(2*c - I*k0)) - (5*(c - I*k0)^7*(2*c - I*k0))/256 - ((c - I*k0)^5*(2*c - I*k0)^3)/128 - ((c - I*k0)^3*(2*c - I*k0)^5)/128 - (5*(c - I*k0)*(2*c - I*k0)^7)/256 + (7*(2*c - I*k0)^9)/(256*(c - I*k0)))*(3*c - I*k0))/2 - (((-5*(c - I*k0)^7)/(128*(2*c - I*k0)) + ((c - I*k0)^5*(2*c - I*k0))/32 + ((c - I*k0)^3*(2*c - I*k0)^3)/64 + ((c - I*k0)*(2*c - I*k0)^5)/32 - (5*(2*c - I*k0)^7)/(128*(c - I*k0)))*(3*c - I*k0)^3)/8 + (((c - I*k0)^5/(16*(2*c - I*k0)) - ((c - I*k0)^3*(2*c - I*k0))/16 - ((c - I*k0)*(2*c - I*k0)^3)/16 + (2*c - I*k0)^5/(16*(c - I*k0)))*(3*c - I*k0)^5)/16 - (5*(-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)))*(3*c - I*k0)^7)/128 + (7*((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*(3*c - I*k0)^9)/256 - (21*(3*c - I*k0)^11)/(1024*(c - I*k0)*(2*c - I*k0))) - (11*I)*c^2*(((-21*(c - I*k0)^11)/(1024*(2*c - I*k0)) + (7*(c - I*k0)^9*(2*c - I*k0))/512 + (5*(c - I*k0)^7*(2*c - I*k0)^3)/1024 + ((c - I*k0)^5*(2*c - I*k0)^5)/256 + (5*(c - I*k0)^3*(2*c - I*k0)^7)/1024 + (7*(c - I*k0)*(2*c - I*k0)^9)/512 - (21*(2*c - I*k0)^11)/(1024*(c - I*k0)))/(3*c - I*k0) + (((7*(c - I*k0)^9)/(256*(2*c - I*k0)) - (5*(c - I*k0)^7*(2*c - I*k0))/256 - ((c - I*k0)^5*(2*c - I*k0)^3)/128 - ((c - I*k0)^3*(2*c - I*k0)^5)/128 - (5*(c - I*k0)*(2*c - I*k0)^7)/256 + (7*(2*c - I*k0)^9)/(256*(c - I*k0)))*(3*c - I*k0))/2 - (((-5*(c - I*k0)^7)/(128*(2*c - I*k0)) + ((c - I*k0)^5*(2*c - I*k0))/32 + ((c - I*k0)^3*(2*c - I*k0)^3)/64 + ((c - I*k0)*(2*c - I*k0)^5)/32 - (5*(2*c - I*k0)^7)/(128*(c - I*k0)))*(3*c - I*k0)^3)/8 + (((c - I*k0)^5/(16*(2*c - I*k0)) - ((c - I*k0)^3*(2*c - I*k0))/16 - ((c - I*k0)*(2*c - I*k0)^3)/16 + (2*c - I*k0)^5/(16*(c - I*k0)))*(3*c - I*k0)^5)/16 - (5*(-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)))*(3*c - I*k0)^7)/128 + (7*((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*(3*c - I*k0)^9)/256 - (21*(3*c - I*k0)^11)/(1024*(c - I*k0)*(2*c - I*k0)))*k0 - 6*c*(((-21*(c - I*k0)^11)/(1024*(2*c - I*k0)) + (7*(c - I*k0)^9*(2*c - I*k0))/512 + (5*(c - I*k0)^7*(2*c - I*k0)^3)/1024 + ((c - I*k0)^5*(2*c - I*k0)^5)/256 + (5*(c - I*k0)^3*(2*c - I*k0)^7)/1024 + (7*(c - I*k0)*(2*c - I*k0)^9)/512 - (21*(2*c - I*k0)^11)/(1024*(c - I*k0)))/(3*c - I*k0) + (((7*(c - I*k0)^9)/(256*(2*c - I*k0)) - (5*(c - I*k0)^7*(2*c - I*k0))/256 - ((c - I*k0)^5*(2*c - I*k0)^3)/128 - ((c - I*k0)^3*(2*c - I*k0)^5)/128 - (5*(c - I*k0)*(2*c - I*k0)^7)/256 + (7*(2*c - I*k0)^9)/(256*(c - I*k0)))*(3*c - I*k0))/2 - (((-5*(c - I*k0)^7)/(128*(2*c - I*k0)) + ((c - I*k0)^5*(2*c - I*k0))/32 + ((c - I*k0)^3*(2*c - I*k0)^3)/64 + ((c - I*k0)*(2*c - I*k0)^5)/32 - (5*(2*c - I*k0)^7)/(128*(c - I*k0)))*(3*c - I*k0)^3)/8 + (((c - I*k0)^5/(16*(2*c - I*k0)) - ((c - I*k0)^3*(2*c - I*k0))/16 - ((c - I*k0)*(2*c - I*k0)^3)/16 + (2*c - I*k0)^5/(16*(c - I*k0)))*(3*c - I*k0)^5)/16 - (5*(-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)))*(3*c - I*k0)^7)/128 + (7*((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*(3*c - I*k0)^9)/256 - (21*(3*c - I*k0)^11)/(1024*(c - I*k0)*(2*c - I*k0)))*k0^2 + I*(((-21*(c - I*k0)^11)/(1024*(2*c - I*k0)) + (7*(c - I*k0)^9*(2*c - I*k0))/512 + (5*(c - I*k0)^7*(2*c - I*k0)^3)/1024 + ((c - I*k0)^5*(2*c - I*k0)^5)/256 + (5*(c - I*k0)^3*(2*c - I*k0)^7)/1024 + (7*(c - I*k0)*(2*c - I*k0)^9)/512 - (21*(2*c - I*k0)^11)/(1024*(c - I*k0)))/(3*c - I*k0) + (((7*(c - I*k0)^9)/(256*(2*c - I*k0)) - (5*(c - I*k0)^7*(2*c - I*k0))/256 - ((c - I*k0)^5*(2*c - I*k0)^3)/128 - ((c - I*k0)^3*(2*c - I*k0)^5)/128 - (5*(c - I*k0)*(2*c - I*k0)^7)/256 + (7*(2*c - I*k0)^9)/(256*(c - I*k0)))*(3*c - I*k0))/2 - (((-5*(c - I*k0)^7)/(128*(2*c - I*k0)) + ((c - I*k0)^5*(2*c - I*k0))/32 + ((c - I*k0)^3*(2*c - I*k0)^3)/64 + ((c - I*k0)*(2*c - I*k0)^5)/32 - (5*(2*c - I*k0)^7)/(128*(c - I*k0)))*(3*c - I*k0)^3)/8 + (((c - I*k0)^5/(16*(2*c - I*k0)) - ((c - I*k0)^3*(2*c - I*k0))/16 - ((c - I*k0)*(2*c - I*k0)^3)/16 + (2*c - I*k0)^5/(16*(c - I*k0)))*(3*c - I*k0)^5)/16 - (5*(-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)))*(3*c - I*k0)^7)/128 + (7*((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*(3*c - I*k0)^9)/256 - (21*(3*c - I*k0)^11)/(1024*(c - I*k0)*(2*c - I*k0)))*k0^3 - 2*c^2*((-21*(c - I*k0)^11)/(1024*(2*c - I*k0)) + (7*(c - I*k0)^9*(2*c - I*k0))/512 + (5*(c - I*k0)^7*(2*c - I*k0)^3)/1024 + ((c - I*k0)^5*(2*c - I*k0)^5)/256 + (5*(c - I*k0)^3*(2*c - I*k0)^7)/1024 + (7*(c - I*k0)*(2*c - I*k0)^9)/512 - (21*(2*c - I*k0)^11)/(1024*(c - I*k0)) - (((7*(c - I*k0)^9)/(256*(2*c - I*k0)) - (5*(c - I*k0)^7*(2*c - I*k0))/256 - ((c - I*k0)^5*(2*c - I*k0)^3)/128 - ((c - I*k0)^3*(2*c - I*k0)^5)/128 - (5*(c - I*k0)*(2*c - I*k0)^7)/256 + (7*(2*c - I*k0)^9)/(256*(c - I*k0)))*k0^2)/2 - (((-5*(c - I*k0)^7)/(128*(2*c - I*k0)) + ((c - I*k0)^5*(2*c - I*k0))/32 + ((c - I*k0)^3*(2*c - I*k0)^3)/64 + ((c - I*k0)*(2*c - I*k0)^5)/32 - (5*(2*c - I*k0)^7)/(128*(c - I*k0)))*k0^4)/8 - (((c - I*k0)^5/(16*(2*c - I*k0)) - ((c - I*k0)^3*(2*c - I*k0))/16 - ((c - I*k0)*(2*c - I*k0)^3)/16 + (2*c - I*k0)^5/(16*(c - I*k0)))*k0^6)/16 - (5*(-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)))*k0^8)/128 - (7*((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*k0^10)/256 - (21*k0^12)/(1024*(c - I*k0)*(2*c - I*k0))) + (3*I)*c*k0*((-21*(c - I*k0)^11)/(1024*(2*c - I*k0)) + (7*(c - I*k0)^9*(2*c - I*k0))/512 + (5*(c - I*k0)^7*(2*c - I*k0)^3)/1024 + ((c - I*k0)^5*(2*c - I*k0)^5)/256 + (5*(c - I*k0)^3*(2*c - I*k0)^7)/1024 + (7*(c - I*k0)*(2*c - I*k0)^9)/512 - (21*(2*c - I*k0)^11)/(1024*(c - I*k0)) - (((7*(c - I*k0)^9)/(256*(2*c - I*k0)) - (5*(c - I*k0)^7*(2*c - I*k0))/256 - ((c - I*k0)^5*(2*c - I*k0)^3)/128 - ((c - I*k0)^3*(2*c - I*k0)^5)/128 - (5*(c - I*k0)*(2*c - I*k0)^7)/256 + (7*(2*c - I*k0)^9)/(256*(c - I*k0)))*k0^2)/2 - (((-5*(c - I*k0)^7)/(128*(2*c - I*k0)) + ((c - I*k0)^5*(2*c - I*k0))/32 + ((c - I*k0)^3*(2*c - I*k0)^3)/64 + ((c - I*k0)*(2*c - I*k0)^5)/32 - (5*(2*c - I*k0)^7)/(128*(c - I*k0)))*k0^4)/8 - (((c - I*k0)^5/(16*(2*c - I*k0)) - ((c - I*k0)^3*(2*c - I*k0))/16 - ((c - I*k0)*(2*c - I*k0)^3)/16 + (2*c - I*k0)^5/(16*(c - I*k0)))*k0^6)/16 - (5*(-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)))*k0^8)/128 - (7*((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*k0^10)/256 - (21*k0^12)/(1024*(c - I*k0)*(2*c - I*k0))) + k0^2*((-21*(c - I*k0)^11)/(1024*(2*c - I*k0)) + (7*(c - I*k0)^9*(2*c - I*k0))/512 + (5*(c - I*k0)^7*(2*c - I*k0)^3)/1024 + ((c - I*k0)^5*(2*c - I*k0)^5)/256 + (5*(c - I*k0)^3*(2*c - I*k0)^7)/1024 + (7*(c - I*k0)*(2*c - I*k0)^9)/512 - (21*(2*c - I*k0)^11)/(1024*(c - I*k0)) - (((7*(c - I*k0)^9)/(256*(2*c - I*k0)) - (5*(c - I*k0)^7*(2*c - I*k0))/256 - ((c - I*k0)^5*(2*c - I*k0)^3)/128 - ((c - I*k0)^3*(2*c - I*k0)^5)/128 - (5*(c - I*k0)*(2*c - I*k0)^7)/256 + (7*(2*c - I*k0)^9)/(256*(c - I*k0)))*k0^2)/2 - (((-5*(c - I*k0)^7)/(128*(2*c - I*k0)) + ((c - I*k0)^5*(2*c - I*k0))/32 + ((c - I*k0)^3*(2*c - I*k0)^3)/64 + ((c - I*k0)*(2*c - I*k0)^5)/32 - (5*(2*c - I*k0)^7)/(128*(c - I*k0)))*k0^4)/8 - (((c - I*k0)^5/(16*(2*c - I*k0)) - ((c - I*k0)^3*(2*c - I*k0))/16 - ((c - I*k0)*(2*c - I*k0)^3)/16 + (2*c - I*k0)^5/(16*(c - I*k0)))*k0^6)/16 - (5*(-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)))*k0^8)/128 - (7*((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*k0^10)/256 - (21*k0^12)/(1024*(c - I*k0)*(2*c - I*k0))) + 9*c^2*((-21*(c - I*k0)^11)/(1024*(3*c - I*k0)) + (7*(c - I*k0)^9*(3*c - I*k0))/512 + (5*(c - I*k0)^7*(3*c - I*k0)^3)/1024 + ((c - I*k0)^5*(3*c - I*k0)^5)/256 + (5*(c - I*k0)^3*(3*c - I*k0)^7)/1024 + (7*(c - I*k0)*(3*c - I*k0)^9)/512 - (21*(3*c - I*k0)^11)/(1024*(c - I*k0)) - (((7*(c - I*k0)^9)/(256*(3*c - I*k0)) - (5*(c - I*k0)^7*(3*c - I*k0))/256 - ((c - I*k0)^5*(3*c - I*k0)^3)/128 - ((c - I*k0)^3*(3*c - I*k0)^5)/128 - (5*(c - I*k0)*(3*c - I*k0)^7)/256 + (7*(3*c - I*k0)^9)/(256*(c - I*k0)))*k0^2)/2 - (((-5*(c - I*k0)^7)/(128*(3*c - I*k0)) + ((c - I*k0)^5*(3*c - I*k0))/32 + ((c - I*k0)^3*(3*c - I*k0)^3)/64 + ((c - I*k0)*(3*c - I*k0)^5)/32 - (5*(3*c - I*k0)^7)/(128*(c - I*k0)))*k0^4)/8 - (((c - I*k0)^5/(16*(3*c - I*k0)) - ((c - I*k0)^3*(3*c - I*k0))/16 - ((c - I*k0)*(3*c - I*k0)^3)/16 + (3*c - I*k0)^5/(16*(c - I*k0)))*k0^6)/16 - (5*(-(c - I*k0)^3/(8*(3*c - I*k0)) + ((c - I*k0)*(3*c - I*k0))/4 - (3*c - I*k0)^3/(8*(c - I*k0)))*k0^8)/128 - (7*((c - I*k0)/(2*(3*c - I*k0)) + (3*c - I*k0)/(2*(c - I*k0)))*k0^10)/256 - (21*k0^12)/(1024*(c - I*k0)*(3*c - I*k0))) - (12*I)*c*k0*((-21*(c - I*k0)^11)/(1024*(3*c - I*k0)) + (7*(c - I*k0)^9*(3*c - I*k0))/512 + (5*(c - I*k0)^7*(3*c - I*k0)^3)/1024 + ((c - I*k0)^5*(3*c - I*k0)^5)/256 + (5*(c - I*k0)^3*(3*c - I*k0)^7)/1024 + (7*(c - I*k0)*(3*c - I*k0)^9)/512 - (21*(3*c - I*k0)^11)/(1024*(c - I*k0)) - (((7*(c - I*k0)^9)/(256*(3*c - I*k0)) - (5*(c - I*k0)^7*(3*c - I*k0))/256 - ((c - I*k0)^5*(3*c - I*k0)^3)/128 - ((c - I*k0)^3*(3*c - I*k0)^5)/128 - (5*(c - I*k0)*(3*c - I*k0)^7)/256 + (7*(3*c - I*k0)^9)/(256*(c - I*k0)))*k0^2)/2 - (((-5*(c - I*k0)^7)/(128*(3*c - I*k0)) + ((c - I*k0)^5*(3*c - I*k0))/32 + ((c - I*k0)^3*(3*c - I*k0)^3)/64 + ((c - I*k0)*(3*c - I*k0)^5)/32 - (5*(3*c - I*k0)^7)/(128*(c - I*k0)))*k0^4)/8 - (((c - I*k0)^5/(16*(3*c - I*k0)) - ((c - I*k0)^3*(3*c - I*k0))/16 - ((c - I*k0)*(3*c - I*k0)^3)/16 + (3*c - I*k0)^5/(16*(c - I*k0)))*k0^6)/16 - (5*(-(c - I*k0)^3/(8*(3*c - I*k0)) + ((c - I*k0)*(3*c - I*k0))/4 - (3*c - I*k0)^3/(8*(c - I*k0)))*k0^8)/128 - (7*((c - I*k0)/(2*(3*c - I*k0)) + (3*c - I*k0)/(2*(c - I*k0)))*k0^10)/256 - (21*k0^12)/(1024*(c - I*k0)*(3*c - I*k0))) - 3*k0^2*((-21*(c - I*k0)^11)/(1024*(3*c - I*k0)) + (7*(c - I*k0)^9*(3*c - I*k0))/512 + (5*(c - I*k0)^7*(3*c - I*k0)^3)/1024 + ((c - I*k0)^5*(3*c - I*k0)^5)/256 + (5*(c - I*k0)^3*(3*c - I*k0)^7)/1024 + (7*(c - I*k0)*(3*c - I*k0)^9)/512 - (21*(3*c - I*k0)^11)/(1024*(c - I*k0)) - (((7*(c - I*k0)^9)/(256*(3*c - I*k0)) - (5*(c - I*k0)^7*(3*c - I*k0))/256 - ((c - I*k0)^5*(3*c - I*k0)^3)/128 - ((c - I*k0)^3*(3*c - I*k0)^5)/128 - (5*(c - I*k0)*(3*c - I*k0)^7)/256 + (7*(3*c - I*k0)^9)/(256*(c - I*k0)))*k0^2)/2 - (((-5*(c - I*k0)^7)/(128*(3*c - I*k0)) + ((c - I*k0)^5*(3*c - I*k0))/32 + ((c - I*k0)^3*(3*c - I*k0)^3)/64 + ((c - I*k0)*(3*c - I*k0)^5)/32 - (5*(3*c - I*k0)^7)/(128*(c - I*k0)))*k0^4)/8 - (((c - I*k0)^5/(16*(3*c - I*k0)) - ((c - I*k0)^3*(3*c - I*k0))/16 - ((c - I*k0)*(3*c - I*k0)^3)/16 + (3*c - I*k0)^5/(16*(c - I*k0)))*k0^6)/16 - (5*(-(c - I*k0)^3/(8*(3*c - I*k0)) + ((c - I*k0)*(3*c - I*k0))/4 - (3*c - I*k0)^3/(8*(c - I*k0)))*k0^8)/128 - (7*((c - I*k0)/(2*(3*c - I*k0)) + (3*c - I*k0)/(2*(c - I*k0)))*k0^10)/256 - (21*k0^12)/(1024*(c - I*k0)*(3*c - I*k0))) - 18*c^2*((-21*(2*c - I*k0)^11)/(1024*(3*c - I*k0)) + (7*(2*c - I*k0)^9*(3*c - I*k0))/512 + (5*(2*c - I*k0)^7*(3*c - I*k0)^3)/1024 + ((2*c - I*k0)^5*(3*c - I*k0)^5)/256 + (5*(2*c - I*k0)^3*(3*c - I*k0)^7)/1024 + (7*(2*c - I*k0)*(3*c - I*k0)^9)/512 - (21*(3*c - I*k0)^11)/(1024*(2*c - I*k0)) - (((7*(2*c - I*k0)^9)/(256*(3*c - I*k0)) - (5*(2*c - I*k0)^7*(3*c - I*k0))/256 - ((2*c - I*k0)^5*(3*c - I*k0)^3)/128 - ((2*c - I*k0)^3*(3*c - I*k0)^5)/128 - (5*(2*c - I*k0)*(3*c - I*k0)^7)/256 + (7*(3*c - I*k0)^9)/(256*(2*c - I*k0)))*k0^2)/2 - (((-5*(2*c - I*k0)^7)/(128*(3*c - I*k0)) + ((2*c - I*k0)^5*(3*c - I*k0))/32 + ((2*c - I*k0)^3*(3*c - I*k0)^3)/64 + ((2*c - I*k0)*(3*c - I*k0)^5)/32 - (5*(3*c - I*k0)^7)/(128*(2*c - I*k0)))*k0^4)/8 - (((2*c - I*k0)^5/(16*(3*c - I*k0)) - ((2*c - I*k0)^3*(3*c - I*k0))/16 - ((2*c - I*k0)*(3*c - I*k0)^3)/16 + (3*c - I*k0)^5/(16*(2*c - I*k0)))*k0^6)/16 - (5*(-(2*c - I*k0)^3/(8*(3*c - I*k0)) + ((2*c - I*k0)*(3*c - I*k0))/4 - (3*c - I*k0)^3/(8*(2*c - I*k0)))*k0^8)/128 - (7*((2*c - I*k0)/(2*(3*c - I*k0)) + (3*c - I*k0)/(2*(2*c - I*k0)))*k0^10)/256 - (21*k0^12)/(1024*(2*c - I*k0)*(3*c - I*k0))) + (15*I)*c*k0*((-21*(2*c - I*k0)^11)/(1024*(3*c - I*k0)) + (7*(2*c - I*k0)^9*(3*c - I*k0))/512 + (5*(2*c - I*k0)^7*(3*c - I*k0)^3)/1024 + ((2*c - I*k0)^5*(3*c - I*k0)^5)/256 + (5*(2*c - I*k0)^3*(3*c - I*k0)^7)/1024 + (7*(2*c - I*k0)*(3*c - I*k0)^9)/512 - (21*(3*c - I*k0)^11)/(1024*(2*c - I*k0)) - (((7*(2*c - I*k0)^9)/(256*(3*c - I*k0)) - (5*(2*c - I*k0)^7*(3*c - I*k0))/256 - ((2*c - I*k0)^5*(3*c - I*k0)^3)/128 - ((2*c - I*k0)^3*(3*c - I*k0)^5)/128 - (5*(2*c - I*k0)*(3*c - I*k0)^7)/256 + (7*(3*c - I*k0)^9)/(256*(2*c - I*k0)))*k0^2)/2 - (((-5*(2*c - I*k0)^7)/(128*(3*c - I*k0)) + ((2*c - I*k0)^5*(3*c - I*k0))/32 + ((2*c - I*k0)^3*(3*c - I*k0)^3)/64 + ((2*c - I*k0)*(3*c - I*k0)^5)/32 - (5*(3*c - I*k0)^7)/(128*(2*c - I*k0)))*k0^4)/8 - (((2*c - I*k0)^5/(16*(3*c - I*k0)) - ((2*c - I*k0)^3*(3*c - I*k0))/16 - ((2*c - I*k0)*(3*c - I*k0)^3)/16 + (3*c - I*k0)^5/(16*(2*c - I*k0)))*k0^6)/16 - (5*(-(2*c - I*k0)^3/(8*(3*c - I*k0)) + ((2*c - I*k0)*(3*c - I*k0))/4 - (3*c - I*k0)^3/(8*(2*c - I*k0)))*k0^8)/128 - (7*((2*c - I*k0)/(2*(3*c - I*k0)) + (3*c - I*k0)/(2*(2*c - I*k0)))*k0^10)/256 - (21*k0^12)/(1024*(2*c - I*k0)*(3*c - I*k0))) + 3*k0^2*((-21*(2*c - I*k0)^11)/(1024*(3*c - I*k0)) + (7*(2*c - I*k0)^9*(3*c - I*k0))/512 + (5*(2*c - I*k0)^7*(3*c - I*k0)^3)/1024 + ((2*c - I*k0)^5*(3*c - I*k0)^5)/256 + (5*(2*c - I*k0)^3*(3*c - I*k0)^7)/1024 + (7*(2*c - I*k0)*(3*c - I*k0)^9)/512 - (21*(3*c - I*k0)^11)/(1024*(2*c - I*k0)) - (((7*(2*c - I*k0)^9)/(256*(3*c - I*k0)) - (5*(2*c - I*k0)^7*(3*c - I*k0))/256 - ((2*c - I*k0)^5*(3*c - I*k0)^3)/128 - ((2*c - I*k0)^3*(3*c - I*k0)^5)/128 - (5*(2*c - I*k0)*(3*c - I*k0)^7)/256 + (7*(3*c - I*k0)^9)/(256*(2*c - I*k0)))*k0^2)/2 - (((-5*(2*c - I*k0)^7)/(128*(3*c - I*k0)) + ((2*c - I*k0)^5*(3*c - I*k0))/32 + ((2*c - I*k0)^3*(3*c - I*k0)^3)/64 + ((2*c - I*k0)*(3*c - I*k0)^5)/32 - (5*(3*c - I*k0)^7)/(128*(2*c - I*k0)))*k0^4)/8 - (((2*c - I*k0)^5/(16*(3*c - I*k0)) - ((2*c - I*k0)^3*(3*c - I*k0))/16 - ((2*c - I*k0)*(3*c - I*k0)^3)/16 + (3*c - I*k0)^5/(16*(2*c - I*k0)))*k0^6)/16 - (5*(-(2*c - I*k0)^3/(8*(3*c - I*k0)) + ((2*c - I*k0)*(3*c - I*k0))/4 - (3*c - I*k0)^3/(8*(2*c - I*k0)))*k0^8)/128 - (7*((2*c - I*k0)/(2*(3*c - I*k0)) + (3*c - I*k0)/(2*(2*c - I*k0)))*k0^10)/256 - (21*k0^12)/(1024*(2*c - I*k0)*(3*c - I*k0)))))/k^3 + (6*c^3*(((-5*(c - I*k0)^7)/(128*(2*c - I*k0)) + ((c - I*k0)^5*(2*c - I*k0))/32 + ((c - I*k0)^3*(2*c - I*k0)^3)/64 + ((c - I*k0)*(2*c - I*k0)^5)/32 - (5*(2*c - I*k0)^7)/(128*(c - I*k0)))/(3*c - I*k0) + (((c - I*k0)^5/(16*(2*c - I*k0)) - ((c - I*k0)^3*(2*c - I*k0))/16 - ((c - I*k0)*(2*c - I*k0)^3)/16 + (2*c - I*k0)^5/(16*(c - I*k0)))*(3*c - I*k0))/2 - ((-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)))*(3*c - I*k0)^3)/8 + (((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*(3*c - I*k0)^5)/16 - (5*(3*c - I*k0)^7)/(128*(c - I*k0)*(2*c - I*k0))) - (11*I)*c^2*(((-5*(c - I*k0)^7)/(128*(2*c - I*k0)) + ((c - I*k0)^5*(2*c - I*k0))/32 + ((c - I*k0)^3*(2*c - I*k0)^3)/64 + ((c - I*k0)*(2*c - I*k0)^5)/32 - (5*(2*c - I*k0)^7)/(128*(c - I*k0)))/(3*c - I*k0) + (((c - I*k0)^5/(16*(2*c - I*k0)) - ((c - I*k0)^3*(2*c - I*k0))/16 - ((c - I*k0)*(2*c - I*k0)^3)/16 + (2*c - I*k0)^5/(16*(c - I*k0)))*(3*c - I*k0))/2 - ((-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)))*(3*c - I*k0)^3)/8 + (((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*(3*c - I*k0)^5)/16 - (5*(3*c - I*k0)^7)/(128*(c - I*k0)*(2*c - I*k0)))*k0 - 6*c*(((-5*(c - I*k0)^7)/(128*(2*c - I*k0)) + ((c - I*k0)^5*(2*c - I*k0))/32 + ((c - I*k0)^3*(2*c - I*k0)^3)/64 + ((c - I*k0)*(2*c - I*k0)^5)/32 - (5*(2*c - I*k0)^7)/(128*(c - I*k0)))/(3*c - I*k0) + (((c - I*k0)^5/(16*(2*c - I*k0)) - ((c - I*k0)^3*(2*c - I*k0))/16 - ((c - I*k0)*(2*c - I*k0)^3)/16 + (2*c - I*k0)^5/(16*(c - I*k0)))*(3*c - I*k0))/2 - ((-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)))*(3*c - I*k0)^3)/8 + (((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*(3*c - I*k0)^5)/16 - (5*(3*c - I*k0)^7)/(128*(c - I*k0)*(2*c - I*k0)))*k0^2 + I*(((-5*(c - I*k0)^7)/(128*(2*c - I*k0)) + ((c - I*k0)^5*(2*c - I*k0))/32 + ((c - I*k0)^3*(2*c - I*k0)^3)/64 + ((c - I*k0)*(2*c - I*k0)^5)/32 - (5*(2*c - I*k0)^7)/(128*(c - I*k0)))/(3*c - I*k0) + (((c - I*k0)^5/(16*(2*c - I*k0)) - ((c - I*k0)^3*(2*c - I*k0))/16 - ((c - I*k0)*(2*c - I*k0)^3)/16 + (2*c - I*k0)^5/(16*(c - I*k0)))*(3*c - I*k0))/2 - ((-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)))*(3*c - I*k0)^3)/8 + (((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*(3*c - I*k0)^5)/16 - (5*(3*c - I*k0)^7)/(128*(c - I*k0)*(2*c - I*k0)))*k0^3 - 2*c^2*((-5*(c - I*k0)^7)/(128*(2*c - I*k0)) + ((c - I*k0)^5*(2*c - I*k0))/32 + ((c - I*k0)^3*(2*c - I*k0)^3)/64 + ((c - I*k0)*(2*c - I*k0)^5)/32 - (5*(2*c - I*k0)^7)/(128*(c - I*k0)) - (((c - I*k0)^5/(16*(2*c - I*k0)) - ((c - I*k0)^3*(2*c - I*k0))/16 - ((c - I*k0)*(2*c - I*k0)^3)/16 + (2*c - I*k0)^5/(16*(c - I*k0)))*k0^2)/2 - ((-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)))*k0^4)/8 - (((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*k0^6)/16 - (5*k0^8)/(128*(c - I*k0)*(2*c - I*k0))) + (3*I)*c*k0*((-5*(c - I*k0)^7)/(128*(2*c - I*k0)) + ((c - I*k0)^5*(2*c - I*k0))/32 + ((c - I*k0)^3*(2*c - I*k0)^3)/64 + ((c - I*k0)*(2*c - I*k0)^5)/32 - (5*(2*c - I*k0)^7)/(128*(c - I*k0)) - (((c - I*k0)^5/(16*(2*c - I*k0)) - ((c - I*k0)^3*(2*c - I*k0))/16 - ((c - I*k0)*(2*c - I*k0)^3)/16 + (2*c - I*k0)^5/(16*(c - I*k0)))*k0^2)/2 - ((-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)))*k0^4)/8 - (((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*k0^6)/16 - (5*k0^8)/(128*(c - I*k0)*(2*c - I*k0))) + k0^2*((-5*(c - I*k0)^7)/(128*(2*c - I*k0)) + ((c - I*k0)^5*(2*c - I*k0))/32 + ((c - I*k0)^3*(2*c - I*k0)^3)/64 + ((c - I*k0)*(2*c - I*k0)^5)/32 - (5*(2*c - I*k0)^7)/(128*(c - I*k0)) - (((c - I*k0)^5/(16*(2*c - I*k0)) - ((c - I*k0)^3*(2*c - I*k0))/16 - ((c - I*k0)*(2*c - I*k0)^3)/16 + (2*c - I*k0)^5/(16*(c - I*k0)))*k0^2)/2 - ((-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)))*k0^4)/8 - (((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*k0^6)/16 - (5*k0^8)/(128*(c - I*k0)*(2*c - I*k0))) + 9*c^2*((-5*(c - I*k0)^7)/(128*(3*c - I*k0)) + ((c - I*k0)^5*(3*c - I*k0))/32 + ((c - I*k0)^3*(3*c - I*k0)^3)/64 + ((c - I*k0)*(3*c - I*k0)^5)/32 - (5*(3*c - I*k0)^7)/(128*(c - I*k0)) - (((c - I*k0)^5/(16*(3*c - I*k0)) - ((c - I*k0)^3*(3*c - I*k0))/16 - ((c - I*k0)*(3*c - I*k0)^3)/16 + (3*c - I*k0)^5/(16*(c - I*k0)))*k0^2)/2 - ((-(c - I*k0)^3/(8*(3*c - I*k0)) + ((c - I*k0)*(3*c - I*k0))/4 - (3*c - I*k0)^3/(8*(c - I*k0)))*k0^4)/8 - (((c - I*k0)/(2*(3*c - I*k0)) + (3*c - I*k0)/(2*(c - I*k0)))*k0^6)/16 - (5*k0^8)/(128*(c - I*k0)*(3*c - I*k0))) - (12*I)*c*k0*((-5*(c - I*k0)^7)/(128*(3*c - I*k0)) + ((c - I*k0)^5*(3*c - I*k0))/32 + ((c - I*k0)^3*(3*c - I*k0)^3)/64 + ((c - I*k0)*(3*c - I*k0)^5)/32 - (5*(3*c - I*k0)^7)/(128*(c - I*k0)) - (((c - I*k0)^5/(16*(3*c - I*k0)) - ((c - I*k0)^3*(3*c - I*k0))/16 - ((c - I*k0)*(3*c - I*k0)^3)/16 + (3*c - I*k0)^5/(16*(c - I*k0)))*k0^2)/2 - ((-(c - I*k0)^3/(8*(3*c - I*k0)) + ((c - I*k0)*(3*c - I*k0))/4 - (3*c - I*k0)^3/(8*(c - I*k0)))*k0^4)/8 - (((c - I*k0)/(2*(3*c - I*k0)) + (3*c - I*k0)/(2*(c - I*k0)))*k0^6)/16 - (5*k0^8)/(128*(c - I*k0)*(3*c - I*k0))) - 3*k0^2*((-5*(c - I*k0)^7)/(128*(3*c - I*k0)) + ((c - I*k0)^5*(3*c - I*k0))/32 + ((c - I*k0)^3*(3*c - I*k0)^3)/64 + ((c - I*k0)*(3*c - I*k0)^5)/32 - (5*(3*c - I*k0)^7)/(128*(c - I*k0)) - (((c - I*k0)^5/(16*(3*c - I*k0)) - ((c - I*k0)^3*(3*c - I*k0))/16 - ((c - I*k0)*(3*c - I*k0)^3)/16 + (3*c - I*k0)^5/(16*(c - I*k0)))*k0^2)/2 - ((-(c - I*k0)^3/(8*(3*c - I*k0)) + ((c - I*k0)*(3*c - I*k0))/4 - (3*c - I*k0)^3/(8*(c - I*k0)))*k0^4)/8 - (((c - I*k0)/(2*(3*c - I*k0)) + (3*c - I*k0)/(2*(c - I*k0)))*k0^6)/16 - (5*k0^8)/(128*(c - I*k0)*(3*c - I*k0))) - 18*c^2*((-5*(2*c - I*k0)^7)/(128*(3*c - I*k0)) + ((2*c - I*k0)^5*(3*c - I*k0))/32 + ((2*c - I*k0)^3*(3*c - I*k0)^3)/64 + ((2*c - I*k0)*(3*c - I*k0)^5)/32 - (5*(3*c - I*k0)^7)/(128*(2*c - I*k0)) - (((2*c - I*k0)^5/(16*(3*c - I*k0)) - ((2*c - I*k0)^3*(3*c - I*k0))/16 - ((2*c - I*k0)*(3*c - I*k0)^3)/16 + (3*c - I*k0)^5/(16*(2*c - I*k0)))*k0^2)/2 - ((-(2*c - I*k0)^3/(8*(3*c - I*k0)) + ((2*c - I*k0)*(3*c - I*k0))/4 - (3*c - I*k0)^3/(8*(2*c - I*k0)))*k0^4)/8 - (((2*c - I*k0)/(2*(3*c - I*k0)) + (3*c - I*k0)/(2*(2*c - I*k0)))*k0^6)/16 - (5*k0^8)/(128*(2*c - I*k0)*(3*c - I*k0))) + (15*I)*c*k0*((-5*(2*c - I*k0)^7)/(128*(3*c - I*k0)) + ((2*c - I*k0)^5*(3*c - I*k0))/32 + ((2*c - I*k0)^3*(3*c - I*k0)^3)/64 + ((2*c - I*k0)*(3*c - I*k0)^5)/32 - (5*(3*c - I*k0)^7)/(128*(2*c - I*k0)) - (((2*c - I*k0)^5/(16*(3*c - I*k0)) - ((2*c - I*k0)^3*(3*c - I*k0))/16 - ((2*c - I*k0)*(3*c - I*k0)^3)/16 + (3*c - I*k0)^5/(16*(2*c - I*k0)))*k0^2)/2 - ((-(2*c - I*k0)^3/(8*(3*c - I*k0)) + ((2*c - I*k0)*(3*c - I*k0))/4 - (3*c - I*k0)^3/(8*(2*c - I*k0)))*k0^4)/8 - (((2*c - I*k0)/(2*(3*c - I*k0)) + (3*c - I*k0)/(2*(2*c - I*k0)))*k0^6)/16 - (5*k0^8)/(128*(2*c - I*k0)*(3*c - I*k0))) + 3*k0^2*((-5*(2*c - I*k0)^7)/(128*(3*c - I*k0)) + ((2*c - I*k0)^5*(3*c - I*k0))/32 + ((2*c - I*k0)^3*(3*c - I*k0)^3)/64 + ((2*c - I*k0)*(3*c - I*k0)^5)/32 - (5*(3*c - I*k0)^7)/(128*(2*c - I*k0)) - (((2*c - I*k0)^5/(16*(3*c - I*k0)) - ((2*c - I*k0)^3*(3*c - I*k0))/16 - ((2*c - I*k0)*(3*c - I*k0)^3)/16 + (3*c - I*k0)^5/(16*(2*c - I*k0)))*k0^2)/2 - ((-(2*c - I*k0)^3/(8*(3*c - I*k0)) + ((2*c - I*k0)*(3*c - I*k0))/4 - (3*c - I*k0)^3/(8*(2*c - I*k0)))*k0^4)/8 - (((2*c - I*k0)/(2*(3*c - I*k0)) + (3*c - I*k0)/(2*(2*c - I*k0)))*k0^6)/16 - (5*k0^8)/(128*(2*c - I*k0)*(3*c - I*k0))))*(-((-((c - I*k0)^3*(2*c - I*k0))/(2*k^2) - ((c - I*k0)*(2*c - I*k0)^3)/(2*k^2))*(3*c - I*k0)^3)/(2*k) + ((((-((c - I*k0)^3*(2*c - I*k0))/(2*k^2) - ((c - I*k0)*(2*c - I*k0)^3)/(2*k^2))*(3*c - I*k0))/k - ((c - I*k0)*(2*c - I*k0)*(3*c - I*k0)^3)/(2*k^3))*k0^2)/2 + (3*(c - I*k0)*(2*c - I*k0)*(3*c - I*k0)*k0^4)/(8*k^3) + (3*(c - I*k0)*(2*c - I*k0)*(3*c - I*k0)^4*((3*c)/k - (I*k0)/k))/(8*k^2) + ((3*c - I*k0)*(((c - I*k0)^3*(2*c - I*k0)^3)/(4*k^2) + (3*(c - I*k0)^4*(2*c - I*k0)*(c/k - (I*k0)/k))/(8*k) + (3*(c - I*k0)*(2*c - I*k0)^4*((2*c)/k - (I*k0)/k))/(8*k)))/k) + (6*c^3*(((c - I*k0)^5/(16*(2*c - I*k0)) - ((c - I*k0)^3*(2*c - I*k0))/16 - ((c - I*k0)*(2*c - I*k0)^3)/16 + (2*c - I*k0)^5/(16*(c - I*k0)))/(3*c - I*k0) + ((-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)))*(3*c - I*k0))/2 - (((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*(3*c - I*k0)^3)/8 + (3*c - I*k0)^5/(16*(c - I*k0)*(2*c - I*k0))) - (11*I)*c^2*(((c - I*k0)^5/(16*(2*c - I*k0)) - ((c - I*k0)^3*(2*c - I*k0))/16 - ((c - I*k0)*(2*c - I*k0)^3)/16 + (2*c - I*k0)^5/(16*(c - I*k0)))/(3*c - I*k0) + ((-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)))*(3*c - I*k0))/2 - (((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*(3*c - I*k0)^3)/8 + (3*c - I*k0)^5/(16*(c - I*k0)*(2*c - I*k0)))*k0 - 6*c*(((c - I*k0)^5/(16*(2*c - I*k0)) - ((c - I*k0)^3*(2*c - I*k0))/16 - ((c - I*k0)*(2*c - I*k0)^3)/16 + (2*c - I*k0)^5/(16*(c - I*k0)))/(3*c - I*k0) + ((-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)))*(3*c - I*k0))/2 - (((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*(3*c - I*k0)^3)/8 + (3*c - I*k0)^5/(16*(c - I*k0)*(2*c - I*k0)))*k0^2 + I*(((c - I*k0)^5/(16*(2*c - I*k0)) - ((c - I*k0)^3*(2*c - I*k0))/16 - ((c - I*k0)*(2*c - I*k0)^3)/16 + (2*c - I*k0)^5/(16*(c - I*k0)))/(3*c - I*k0) + ((-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)))*(3*c - I*k0))/2 - (((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*(3*c - I*k0)^3)/8 + (3*c - I*k0)^5/(16*(c - I*k0)*(2*c - I*k0)))*k0^3 - 2*c^2*((c - I*k0)^5/(16*(2*c - I*k0)) - ((c - I*k0)^3*(2*c - I*k0))/16 - ((c - I*k0)*(2*c - I*k0)^3)/16 + (2*c - I*k0)^5/(16*(c - I*k0)) - ((-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)))*k0^2)/2 - (((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*k0^4)/8 - k0^6/(16*(c - I*k0)*(2*c - I*k0))) + (3*I)*c*k0*((c - I*k0)^5/(16*(2*c - I*k0)) - ((c - I*k0)^3*(2*c - I*k0))/16 - ((c - I*k0)*(2*c - I*k0)^3)/16 + (2*c - I*k0)^5/(16*(c - I*k0)) - ((-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)))*k0^2)/2 - (((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*k0^4)/8 - k0^6/(16*(c - I*k0)*(2*c - I*k0))) + k0^2*((c - I*k0)^5/(16*(2*c - I*k0)) - ((c - I*k0)^3*(2*c - I*k0))/16 - ((c - I*k0)*(2*c - I*k0)^3)/16 + (2*c - I*k0)^5/(16*(c - I*k0)) - ((-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)))*k0^2)/2 - (((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*k0^4)/8 - k0^6/(16*(c - I*k0)*(2*c - I*k0))) + 9*c^2*((c - I*k0)^5/(16*(3*c - I*k0)) - ((c - I*k0)^3*(3*c - I*k0))/16 - ((c - I*k0)*(3*c - I*k0)^3)/16 + (3*c - I*k0)^5/(16*(c - I*k0)) - ((-(c - I*k0)^3/(8*(3*c - I*k0)) + ((c - I*k0)*(3*c - I*k0))/4 - (3*c - I*k0)^3/(8*(c - I*k0)))*k0^2)/2 - (((c - I*k0)/(2*(3*c - I*k0)) + (3*c - I*k0)/(2*(c - I*k0)))*k0^4)/8 - k0^6/(16*(c - I*k0)*(3*c - I*k0))) - (12*I)*c*k0*((c - I*k0)^5/(16*(3*c - I*k0)) - ((c - I*k0)^3*(3*c - I*k0))/16 - ((c - I*k0)*(3*c - I*k0)^3)/16 + (3*c - I*k0)^5/(16*(c - I*k0)) - ((-(c - I*k0)^3/(8*(3*c - I*k0)) + ((c - I*k0)*(3*c - I*k0))/4 - (3*c - I*k0)^3/(8*(c - I*k0)))*k0^2)/2 - (((c - I*k0)/(2*(3*c - I*k0)) + (3*c - I*k0)/(2*(c - I*k0)))*k0^4)/8 - k0^6/(16*(c - I*k0)*(3*c - I*k0))) - 3*k0^2*((c - I*k0)^5/(16*(3*c - I*k0)) - ((c - I*k0)^3*(3*c - I*k0))/16 - ((c - I*k0)*(3*c - I*k0)^3)/16 + (3*c - I*k0)^5/(16*(c - I*k0)) - ((-(c - I*k0)^3/(8*(3*c - I*k0)) + ((c - I*k0)*(3*c - I*k0))/4 - (3*c - I*k0)^3/(8*(c - I*k0)))*k0^2)/2 - (((c - I*k0)/(2*(3*c - I*k0)) + (3*c - I*k0)/(2*(c - I*k0)))*k0^4)/8 - k0^6/(16*(c - I*k0)*(3*c - I*k0))) - 18*c^2*((2*c - I*k0)^5/(16*(3*c - I*k0)) - ((2*c - I*k0)^3*(3*c - I*k0))/16 - ((2*c - I*k0)*(3*c - I*k0)^3)/16 + (3*c - I*k0)^5/(16*(2*c - I*k0)) - ((-(2*c - I*k0)^3/(8*(3*c - I*k0)) + ((2*c - I*k0)*(3*c - I*k0))/4 - (3*c - I*k0)^3/(8*(2*c - I*k0)))*k0^2)/2 - (((2*c - I*k0)/(2*(3*c - I*k0)) + (3*c - I*k0)/(2*(2*c - I*k0)))*k0^4)/8 - k0^6/(16*(2*c - I*k0)*(3*c - I*k0))) + (15*I)*c*k0*((2*c - I*k0)^5/(16*(3*c - I*k0)) - ((2*c - I*k0)^3*(3*c - I*k0))/16 - ((2*c - I*k0)*(3*c - I*k0)^3)/16 + (3*c - I*k0)^5/(16*(2*c - I*k0)) - ((-(2*c - I*k0)^3/(8*(3*c - I*k0)) + ((2*c - I*k0)*(3*c - I*k0))/4 - (3*c - I*k0)^3/(8*(2*c - I*k0)))*k0^2)/2 - (((2*c - I*k0)/(2*(3*c - I*k0)) + (3*c - I*k0)/(2*(2*c - I*k0)))*k0^4)/8 - k0^6/(16*(2*c - I*k0)*(3*c - I*k0))) + 3*k0^2*((2*c - I*k0)^5/(16*(3*c - I*k0)) - ((2*c - I*k0)^3*(3*c - I*k0))/16 - ((2*c - I*k0)*(3*c - I*k0)^3)/16 + (3*c - I*k0)^5/(16*(2*c - I*k0)) - ((-(2*c - I*k0)^3/(8*(3*c - I*k0)) + ((2*c - I*k0)*(3*c - I*k0))/4 - (3*c - I*k0)^3/(8*(2*c - I*k0)))*k0^2)/2 - (((2*c - I*k0)/(2*(3*c - I*k0)) + (3*c - I*k0)/(2*(2*c - I*k0)))*k0^4)/8 - k0^6/(16*(2*c - I*k0)*(3*c - I*k0))))*((3*(((-((c - I*k0)^3*(2*c - I*k0))/(2*k^2) - ((c - I*k0)*(2*c - I*k0)^3)/(2*k^2))*(3*c - I*k0))/k - ((c - I*k0)*(2*c - I*k0)*(3*c - I*k0)^3)/(2*k^3))*k0^4)/8 + (5*(c - I*k0)*(2*c - I*k0)*(3*c - I*k0)*k0^6)/(16*k^3) + (3*(-((c - I*k0)^3*(2*c - I*k0))/(2*k^2) - ((c - I*k0)*(2*c - I*k0)^3)/(2*k^2))*(3*c - I*k0)^4*((3*c)/k - (I*k0)/k))/8 - (5*(c - I*k0)*(2*c - I*k0)*(3*c - I*k0)^6*((3*c)/k - (I*k0)/k))/(16*k^2) - ((3*c - I*k0)^3*(((c - I*k0)^3*(2*c - I*k0)^3)/(4*k^2) + (3*(c - I*k0)^4*(2*c - I*k0)*(c/k - (I*k0)/k))/(8*k) + (3*(c - I*k0)*(2*c - I*k0)^4*((2*c)/k - (I*k0)/k))/(8*k)))/(2*k) + ((3*c - I*k0)*((-5*(c - I*k0)^6*(2*c - I*k0)*(c/k - (I*k0)/k))/(16*k) - (3*(c - I*k0)^4*(2*c - I*k0)^3*(c/k - (I*k0)/k))/(16*k) - (3*(c - I*k0)^3*(2*c - I*k0)^4*((2*c)/k - (I*k0)/k))/(16*k) - (5*(c - I*k0)*(2*c - I*k0)^6*((2*c)/k - (I*k0)/k))/(16*k)))/k + (k0^2*(-((-((c - I*k0)^3*(2*c - I*k0))/(2*k^2) - ((c - I*k0)*(2*c - I*k0)^3)/(2*k^2))*(3*c - I*k0)^3)/(2*k) + (3*(c - I*k0)*(2*c - I*k0)*(3*c - I*k0)^4*((3*c)/k - (I*k0)/k))/(8*k^2) + ((3*c - I*k0)*(((c - I*k0)^3*(2*c - I*k0)^3)/(4*k^2) + (3*(c - I*k0)^4*(2*c - I*k0)*(c/k - (I*k0)/k))/(8*k) + (3*(c - I*k0)*(2*c - I*k0)^4*((2*c)/k - (I*k0)/k))/(8*k)))/k))/2) - (9*(3*c^4 - (2*I)*c^3*k0)*((5*(((-((c - I*k0)^3*(2*c - I*k0))/(2*k^2) - ((c - I*k0)*(2*c - I*k0)^3)/(2*k^2))*(3*c - I*k0))/k - ((c - I*k0)*(2*c - I*k0)*(3*c - I*k0)^3)/(2*k^3))*k0^6)/16 + (35*(c - I*k0)*(2*c - I*k0)*(3*c - I*k0)*k0^8)/(128*k^3) - (5*(-((c - I*k0)^3*(2*c - I*k0))/(2*k^2) - ((c - I*k0)*(2*c - I*k0)^3)/(2*k^2))*(3*c - I*k0)^6*((3*c)/k - (I*k0)/k))/16 + (35*(c - I*k0)*(2*c - I*k0)*(3*c - I*k0)^8*((3*c)/k - (I*k0)/k))/(128*k^2) + (3*(3*c - I*k0)^4*((3*c)/k - (I*k0)/k)*(((c - I*k0)^3*(2*c - I*k0)^3)/(4*k^2) + (3*(c - I*k0)^4*(2*c - I*k0)*(c/k - (I*k0)/k))/(8*k) + (3*(c - I*k0)*(2*c - I*k0)^4*((2*c)/k - (I*k0)/k))/(8*k)))/8 - ((3*c - I*k0)^3*((-5*(c - I*k0)^6*(2*c - I*k0)*(c/k - (I*k0)/k))/(16*k) - (3*(c - I*k0)^4*(2*c - I*k0)^3*(c/k - (I*k0)/k))/(16*k) - (3*(c - I*k0)^3*(2*c - I*k0)^4*((2*c)/k - (I*k0)/k))/(16*k) - (5*(c - I*k0)*(2*c - I*k0)^6*((2*c)/k - (I*k0)/k))/(16*k)))/(2*k) + ((3*c - I*k0)*((35*(c - I*k0)^8*(2*c - I*k0)*(c/k - (I*k0)/k))/(128*k) + (5*(c - I*k0)^6*(2*c - I*k0)^3*(c/k - (I*k0)/k))/(32*k) + (5*(c - I*k0)^3*(2*c - I*k0)^6*((2*c)/k - (I*k0)/k))/(32*k) + (35*(c - I*k0)*(2*c - I*k0)^8*((2*c)/k - (I*k0)/k))/(128*k) + (9*(c - I*k0)^4*(2*c - I*k0)^4*(c/k - (I*k0)/k)*((2*c)/k - (I*k0)/k))/64))/k + (3*k0^4*(-((-((c - I*k0)^3*(2*c - I*k0))/(2*k^2) - ((c - I*k0)*(2*c - I*k0)^3)/(2*k^2))*(3*c - I*k0)^3)/(2*k) + (3*(c - I*k0)*(2*c - I*k0)*(3*c - I*k0)^4*((3*c)/k - (I*k0)/k))/(8*k^2) + ((3*c - I*k0)*(((c - I*k0)^3*(2*c - I*k0)^3)/(4*k^2) + (3*(c - I*k0)^4*(2*c - I*k0)*(c/k - (I*k0)/k))/(8*k) + (3*(c - I*k0)*(2*c - I*k0)^4*((2*c)/k - (I*k0)/k))/(8*k)))/k))/8 + (k0^2*((3*(-((c - I*k0)^3*(2*c - I*k0))/(2*k^2) - ((c - I*k0)*(2*c - I*k0)^3)/(2*k^2))*(3*c - I*k0)^4*((3*c)/k - (I*k0)/k))/8 - (5*(c - I*k0)*(2*c - I*k0)*(3*c - I*k0)^6*((3*c)/k - (I*k0)/k))/(16*k^2) - ((3*c - I*k0)^3*(((c - I*k0)^3*(2*c - I*k0)^3)/(4*k^2) + (3*(c - I*k0)^4*(2*c - I*k0)*(c/k - (I*k0)/k))/(8*k) + (3*(c - I*k0)*(2*c - I*k0)^4*((2*c)/k - (I*k0)/k))/(8*k)))/(2*k) + ((3*c - I*k0)*((-5*(c - I*k0)^6*(2*c - I*k0)*(c/k - (I*k0)/k))/(16*k) - (3*(c - I*k0)^4*(2*c - I*k0)^3*(c/k - (I*k0)/k))/(16*k) - (3*(c - I*k0)^3*(2*c - I*k0)^4*((2*c)/k - (I*k0)/k))/(16*k) - (5*(c - I*k0)*(2*c - I*k0)^6*((2*c)/k - (I*k0)/k))/(16*k)))/k))/2))/2)/((c - I*k0)*(2*c - I*k0)*(3*c - I*k0)*k0)}, 2, 11, 1] diff --git a/besseltransforms/3-1-1 b/besseltransforms/3-1-1 deleted file mode 100644 index 2c31de2..0000000 --- a/besseltransforms/3-1-1 +++ /dev/null @@ -1,2 +0,0 @@ -(-k^(-1) - (3*(1 - 1/Sqrt[1 + k^2/(c - I*k0)^2]))/k + (3*(1 - 1/Sqrt[1 + k^2/(2*c - I*k0)^2]))/k + 1/(k*Sqrt[1 + k^2/(3*c - I*k0)^2]) + Sqrt[Pi]*((I*Piecewise[{{k0/(Sqrt[k^2 - k0^2]*Sqrt[Pi]), k0^2/k^2 < 1}}, 0])/k + Piecewise[{{(k0*(1 - k0/Sqrt[-k^2 + k0^2]))/(k*Sqrt[Pi]), k^2/k0^2 < 1}, {k0/(k*Sqrt[Pi]), k^2/k0^2 > 1}}, 0]/k0))/k0 -Piecewise[{{SeriesData[k, Infinity, {(-3*c^3)/(k^3*k0), 0, (-45*(-5*c^5 + (6*I)*c^4*k0 + 2*c^3*k0^2))/(4*k^3*k0), 0, (-105*(43*c^7 - (90*I)*c^6*k0 - 75*c^5*k0^2 + (30*I)*c^4*k0^3 + 5*c^3*k0^4))/(8*k^3*k0), 0, ((((-((c - I*k0)^3*(2*c - I*k0))/(2*k^2) - ((c - I*k0)*(2*c - I*k0)^3)/(2*k^2))*(3*c - I*k0))/k - ((c - I*k0)*(2*c - I*k0)*(3*c - I*k0)^3)/(2*k^3) + ((c - I*k0)*(2*c - I*k0)*(3*c - I*k0)*k0^2)/(2*k^3))*((c - I*k0)^5/(16*(2*c - I*k0)) - ((c - I*k0)^3*(2*c - I*k0))/16 - ((c - I*k0)*(2*c - I*k0)^3)/16 + (2*c - I*k0)^5/(16*(c - I*k0)) + I*(((c - I*k0)^5/(16*(2*c - I*k0)) - ((c - I*k0)^3*(2*c - I*k0))/16 - ((c - I*k0)*(2*c - I*k0)^3)/16 + (2*c - I*k0)^5/(16*(c - I*k0)))/(3*c - I*k0) + ((-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)))*(3*c - I*k0))/2 - (((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*(3*c - I*k0)^3)/8 + (3*c - I*k0)^5/(16*(c - I*k0)*(2*c - I*k0)))*k0 - ((-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)))*k0^2)/2 - (((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*k0^4)/8 - k0^6/(16*(c - I*k0)*(2*c - I*k0)) - 3*((c - I*k0)^5/(16*(3*c - I*k0)) - ((c - I*k0)^3*(3*c - I*k0))/16 - ((c - I*k0)*(3*c - I*k0)^3)/16 + (3*c - I*k0)^5/(16*(c - I*k0)) - ((-(c - I*k0)^3/(8*(3*c - I*k0)) + ((c - I*k0)*(3*c - I*k0))/4 - (3*c - I*k0)^3/(8*(c - I*k0)))*k0^2)/2 - (((c - I*k0)/(2*(3*c - I*k0)) + (3*c - I*k0)/(2*(c - I*k0)))*k0^4)/8 - k0^6/(16*(c - I*k0)*(3*c - I*k0))) + 3*((2*c - I*k0)^5/(16*(3*c - I*k0)) - ((2*c - I*k0)^3*(3*c - I*k0))/16 - ((2*c - I*k0)*(3*c - I*k0)^3)/16 + (3*c - I*k0)^5/(16*(2*c - I*k0)) - ((-(2*c - I*k0)^3/(8*(3*c - I*k0)) + ((2*c - I*k0)*(3*c - I*k0))/4 - (3*c - I*k0)^3/(8*(2*c - I*k0)))*k0^2)/2 - (((2*c - I*k0)/(2*(3*c - I*k0)) + (3*c - I*k0)/(2*(2*c - I*k0)))*k0^4)/8 - k0^6/(16*(2*c - I*k0)*(3*c - I*k0)))) + ((c - I*k0)*(2*c - I*k0)*(3*c - I*k0)*((-5*(c - I*k0)^7)/(128*(2*c - I*k0)) + ((c - I*k0)^5*(2*c - I*k0))/32 + ((c - I*k0)^3*(2*c - I*k0)^3)/64 + ((c - I*k0)*(2*c - I*k0)^5)/32 - (5*(2*c - I*k0)^7)/(128*(c - I*k0)) + I*(((-5*(c - I*k0)^7)/(128*(2*c - I*k0)) + ((c - I*k0)^5*(2*c - I*k0))/32 + ((c - I*k0)^3*(2*c - I*k0)^3)/64 + ((c - I*k0)*(2*c - I*k0)^5)/32 - (5*(2*c - I*k0)^7)/(128*(c - I*k0)))/(3*c - I*k0) + (((c - I*k0)^5/(16*(2*c - I*k0)) - ((c - I*k0)^3*(2*c - I*k0))/16 - ((c - I*k0)*(2*c - I*k0)^3)/16 + (2*c - I*k0)^5/(16*(c - I*k0)))*(3*c - I*k0))/2 - ((-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)))*(3*c - I*k0)^3)/8 + (((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*(3*c - I*k0)^5)/16 - (5*(3*c - I*k0)^7)/(128*(c - I*k0)*(2*c - I*k0)))*k0 - (((c - I*k0)^5/(16*(2*c - I*k0)) - ((c - I*k0)^3*(2*c - I*k0))/16 - ((c - I*k0)*(2*c - I*k0)^3)/16 + (2*c - I*k0)^5/(16*(c - I*k0)))*k0^2)/2 - ((-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)))*k0^4)/8 - (((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*k0^6)/16 - (5*k0^8)/(128*(c - I*k0)*(2*c - I*k0)) - 3*((-5*(c - I*k0)^7)/(128*(3*c - I*k0)) + ((c - I*k0)^5*(3*c - I*k0))/32 + ((c - I*k0)^3*(3*c - I*k0)^3)/64 + ((c - I*k0)*(3*c - I*k0)^5)/32 - (5*(3*c - I*k0)^7)/(128*(c - I*k0)) - (((c - I*k0)^5/(16*(3*c - I*k0)) - ((c - I*k0)^3*(3*c - I*k0))/16 - ((c - I*k0)*(3*c - I*k0)^3)/16 + (3*c - I*k0)^5/(16*(c - I*k0)))*k0^2)/2 - ((-(c - I*k0)^3/(8*(3*c - I*k0)) + ((c - I*k0)*(3*c - I*k0))/4 - (3*c - I*k0)^3/(8*(c - I*k0)))*k0^4)/8 - (((c - I*k0)/(2*(3*c - I*k0)) + (3*c - I*k0)/(2*(c - I*k0)))*k0^6)/16 - (5*k0^8)/(128*(c - I*k0)*(3*c - I*k0))) + 3*((-5*(2*c - I*k0)^7)/(128*(3*c - I*k0)) + ((2*c - I*k0)^5*(3*c - I*k0))/32 + ((2*c - I*k0)^3*(3*c - I*k0)^3)/64 + ((2*c - I*k0)*(3*c - I*k0)^5)/32 - (5*(3*c - I*k0)^7)/(128*(2*c - I*k0)) - (((2*c - I*k0)^5/(16*(3*c - I*k0)) - ((2*c - I*k0)^3*(3*c - I*k0))/16 - ((2*c - I*k0)*(3*c - I*k0)^3)/16 + (3*c - I*k0)^5/(16*(2*c - I*k0)))*k0^2)/2 - ((-(2*c - I*k0)^3/(8*(3*c - I*k0)) + ((2*c - I*k0)*(3*c - I*k0))/4 - (3*c - I*k0)^3/(8*(2*c - I*k0)))*k0^4)/8 - (((2*c - I*k0)/(2*(3*c - I*k0)) + (3*c - I*k0)/(2*(2*c - I*k0)))*k0^6)/16 - (5*k0^8)/(128*(2*c - I*k0)*(3*c - I*k0)))))/k^3 + (3*(47*c^5 - (66*I)*c^4*k0 - 22*c^3*k0^2)*(-((-((c - I*k0)^3*(2*c - I*k0))/(2*k^2) - ((c - I*k0)*(2*c - I*k0)^3)/(2*k^2))*(3*c - I*k0)^3)/(2*k) + ((((-((c - I*k0)^3*(2*c - I*k0))/(2*k^2) - ((c - I*k0)*(2*c - I*k0)^3)/(2*k^2))*(3*c - I*k0))/k - ((c - I*k0)*(2*c - I*k0)*(3*c - I*k0)^3)/(2*k^3))*k0^2)/2 + (3*(c - I*k0)*(2*c - I*k0)*(3*c - I*k0)*k0^4)/(8*k^3) + (3*(c - I*k0)*(2*c - I*k0)*(3*c - I*k0)^4*((3*c)/k - (I*k0)/k))/(8*k^2) + ((3*c - I*k0)*(((c - I*k0)^3*(2*c - I*k0)^3)/(4*k^2) + (3*(c - I*k0)^4*(2*c - I*k0)*(c/k - (I*k0)/k))/(8*k) + (3*(c - I*k0)*(2*c - I*k0)^4*((2*c)/k - (I*k0)/k))/(8*k)))/k))/(4*(c - I*k0)*(2*c - I*k0)*(3*c - I*k0)) - (3*c^3*((3*(((-((c - I*k0)^3*(2*c - I*k0))/(2*k^2) - ((c - I*k0)*(2*c - I*k0)^3)/(2*k^2))*(3*c - I*k0))/k - ((c - I*k0)*(2*c - I*k0)*(3*c - I*k0)^3)/(2*k^3))*k0^4)/8 + (5*(c - I*k0)*(2*c - I*k0)*(3*c - I*k0)*k0^6)/(16*k^3) + (3*(-((c - I*k0)^3*(2*c - I*k0))/(2*k^2) - ((c - I*k0)*(2*c - I*k0)^3)/(2*k^2))*(3*c - I*k0)^4*((3*c)/k - (I*k0)/k))/8 - (5*(c - I*k0)*(2*c - I*k0)*(3*c - I*k0)^6*((3*c)/k - (I*k0)/k))/(16*k^2) - ((3*c - I*k0)^3*(((c - I*k0)^3*(2*c - I*k0)^3)/(4*k^2) + (3*(c - I*k0)^4*(2*c - I*k0)*(c/k - (I*k0)/k))/(8*k) + (3*(c - I*k0)*(2*c - I*k0)^4*((2*c)/k - (I*k0)/k))/(8*k)))/(2*k) + ((3*c - I*k0)*((-5*(c - I*k0)^6*(2*c - I*k0)*(c/k - (I*k0)/k))/(16*k) - (3*(c - I*k0)^4*(2*c - I*k0)^3*(c/k - (I*k0)/k))/(16*k) - (3*(c - I*k0)^3*(2*c - I*k0)^4*((2*c)/k - (I*k0)/k))/(16*k) - (5*(c - I*k0)*(2*c - I*k0)^6*((2*c)/k - (I*k0)/k))/(16*k)))/k + (k0^2*(-((-((c - I*k0)^3*(2*c - I*k0))/(2*k^2) - ((c - I*k0)*(2*c - I*k0)^3)/(2*k^2))*(3*c - I*k0)^3)/(2*k) + (3*(c - I*k0)*(2*c - I*k0)*(3*c - I*k0)^4*((3*c)/k - (I*k0)/k))/(8*k^2) + ((3*c - I*k0)*(((c - I*k0)^3*(2*c - I*k0)^3)/(4*k^2) + (3*(c - I*k0)^4*(2*c - I*k0)*(c/k - (I*k0)/k))/(8*k) + (3*(c - I*k0)*(2*c - I*k0)^4*((2*c)/k - (I*k0)/k))/(8*k)))/k))/2))/((c - I*k0)*(2*c - I*k0)*(3*c - I*k0)))/k0, 0, ((((-((c - I*k0)^3*(2*c - I*k0))/(2*k^2) - ((c - I*k0)*(2*c - I*k0)^3)/(2*k^2))*(3*c - I*k0))/k - ((c - I*k0)*(2*c - I*k0)*(3*c - I*k0)^3)/(2*k^3) + ((c - I*k0)*(2*c - I*k0)*(3*c - I*k0)*k0^2)/(2*k^3))*((-5*(c - I*k0)^7)/(128*(2*c - I*k0)) + ((c - I*k0)^5*(2*c - I*k0))/32 + ((c - I*k0)^3*(2*c - I*k0)^3)/64 + ((c - I*k0)*(2*c - I*k0)^5)/32 - (5*(2*c - I*k0)^7)/(128*(c - I*k0)) + I*(((-5*(c - I*k0)^7)/(128*(2*c - I*k0)) + ((c - I*k0)^5*(2*c - I*k0))/32 + ((c - I*k0)^3*(2*c - I*k0)^3)/64 + ((c - I*k0)*(2*c - I*k0)^5)/32 - (5*(2*c - I*k0)^7)/(128*(c - I*k0)))/(3*c - I*k0) + (((c - I*k0)^5/(16*(2*c - I*k0)) - ((c - I*k0)^3*(2*c - I*k0))/16 - ((c - I*k0)*(2*c - I*k0)^3)/16 + (2*c - I*k0)^5/(16*(c - I*k0)))*(3*c - I*k0))/2 - ((-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)))*(3*c - I*k0)^3)/8 + (((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*(3*c - I*k0)^5)/16 - (5*(3*c - I*k0)^7)/(128*(c - I*k0)*(2*c - I*k0)))*k0 - (((c - I*k0)^5/(16*(2*c - I*k0)) - ((c - I*k0)^3*(2*c - I*k0))/16 - ((c - I*k0)*(2*c - I*k0)^3)/16 + (2*c - I*k0)^5/(16*(c - I*k0)))*k0^2)/2 - ((-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)))*k0^4)/8 - (((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*k0^6)/16 - (5*k0^8)/(128*(c - I*k0)*(2*c - I*k0)) - 3*((-5*(c - I*k0)^7)/(128*(3*c - I*k0)) + ((c - I*k0)^5*(3*c - I*k0))/32 + ((c - I*k0)^3*(3*c - I*k0)^3)/64 + ((c - I*k0)*(3*c - I*k0)^5)/32 - (5*(3*c - I*k0)^7)/(128*(c - I*k0)) - (((c - I*k0)^5/(16*(3*c - I*k0)) - ((c - I*k0)^3*(3*c - I*k0))/16 - ((c - I*k0)*(3*c - I*k0)^3)/16 + (3*c - I*k0)^5/(16*(c - I*k0)))*k0^2)/2 - ((-(c - I*k0)^3/(8*(3*c - I*k0)) + ((c - I*k0)*(3*c - I*k0))/4 - (3*c - I*k0)^3/(8*(c - I*k0)))*k0^4)/8 - (((c - I*k0)/(2*(3*c - I*k0)) + (3*c - I*k0)/(2*(c - I*k0)))*k0^6)/16 - (5*k0^8)/(128*(c - I*k0)*(3*c - I*k0))) + 3*((-5*(2*c - I*k0)^7)/(128*(3*c - I*k0)) + ((2*c - I*k0)^5*(3*c - I*k0))/32 + ((2*c - I*k0)^3*(3*c - I*k0)^3)/64 + ((2*c - I*k0)*(3*c - I*k0)^5)/32 - (5*(3*c - I*k0)^7)/(128*(2*c - I*k0)) - (((2*c - I*k0)^5/(16*(3*c - I*k0)) - ((2*c - I*k0)^3*(3*c - I*k0))/16 - ((2*c - I*k0)*(3*c - I*k0)^3)/16 + (3*c - I*k0)^5/(16*(2*c - I*k0)))*k0^2)/2 - ((-(2*c - I*k0)^3/(8*(3*c - I*k0)) + ((2*c - I*k0)*(3*c - I*k0))/4 - (3*c - I*k0)^3/(8*(2*c - I*k0)))*k0^4)/8 - (((2*c - I*k0)/(2*(3*c - I*k0)) + (3*c - I*k0)/(2*(2*c - I*k0)))*k0^6)/16 - (5*k0^8)/(128*(2*c - I*k0)*(3*c - I*k0)))) + ((c - I*k0)*(2*c - I*k0)*(3*c - I*k0)*((7*(c - I*k0)^9)/(256*(2*c - I*k0)) - (5*(c - I*k0)^7*(2*c - I*k0))/256 - ((c - I*k0)^5*(2*c - I*k0)^3)/128 - ((c - I*k0)^3*(2*c - I*k0)^5)/128 - (5*(c - I*k0)*(2*c - I*k0)^7)/256 + (7*(2*c - I*k0)^9)/(256*(c - I*k0)) + I*(((7*(c - I*k0)^9)/(256*(2*c - I*k0)) - (5*(c - I*k0)^7*(2*c - I*k0))/256 - ((c - I*k0)^5*(2*c - I*k0)^3)/128 - ((c - I*k0)^3*(2*c - I*k0)^5)/128 - (5*(c - I*k0)*(2*c - I*k0)^7)/256 + (7*(2*c - I*k0)^9)/(256*(c - I*k0)))/(3*c - I*k0) + (((-5*(c - I*k0)^7)/(128*(2*c - I*k0)) + ((c - I*k0)^5*(2*c - I*k0))/32 + ((c - I*k0)^3*(2*c - I*k0)^3)/64 + ((c - I*k0)*(2*c - I*k0)^5)/32 - (5*(2*c - I*k0)^7)/(128*(c - I*k0)))*(3*c - I*k0))/2 - (((c - I*k0)^5/(16*(2*c - I*k0)) - ((c - I*k0)^3*(2*c - I*k0))/16 - ((c - I*k0)*(2*c - I*k0)^3)/16 + (2*c - I*k0)^5/(16*(c - I*k0)))*(3*c - I*k0)^3)/8 + ((-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)))*(3*c - I*k0)^5)/16 - (5*((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*(3*c - I*k0)^7)/128 + (7*(3*c - I*k0)^9)/(256*(c - I*k0)*(2*c - I*k0)))*k0 - (((-5*(c - I*k0)^7)/(128*(2*c - I*k0)) + ((c - I*k0)^5*(2*c - I*k0))/32 + ((c - I*k0)^3*(2*c - I*k0)^3)/64 + ((c - I*k0)*(2*c - I*k0)^5)/32 - (5*(2*c - I*k0)^7)/(128*(c - I*k0)))*k0^2)/2 - (((c - I*k0)^5/(16*(2*c - I*k0)) - ((c - I*k0)^3*(2*c - I*k0))/16 - ((c - I*k0)*(2*c - I*k0)^3)/16 + (2*c - I*k0)^5/(16*(c - I*k0)))*k0^4)/8 - ((-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)))*k0^6)/16 - (5*((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*k0^8)/128 - (7*k0^10)/(256*(c - I*k0)*(2*c - I*k0)) - 3*((7*(c - I*k0)^9)/(256*(3*c - I*k0)) - (5*(c - I*k0)^7*(3*c - I*k0))/256 - ((c - I*k0)^5*(3*c - I*k0)^3)/128 - ((c - I*k0)^3*(3*c - I*k0)^5)/128 - (5*(c - I*k0)*(3*c - I*k0)^7)/256 + (7*(3*c - I*k0)^9)/(256*(c - I*k0)) - (((-5*(c - I*k0)^7)/(128*(3*c - I*k0)) + ((c - I*k0)^5*(3*c - I*k0))/32 + ((c - I*k0)^3*(3*c - I*k0)^3)/64 + ((c - I*k0)*(3*c - I*k0)^5)/32 - (5*(3*c - I*k0)^7)/(128*(c - I*k0)))*k0^2)/2 - (((c - I*k0)^5/(16*(3*c - I*k0)) - ((c - I*k0)^3*(3*c - I*k0))/16 - ((c - I*k0)*(3*c - I*k0)^3)/16 + (3*c - I*k0)^5/(16*(c - I*k0)))*k0^4)/8 - ((-(c - I*k0)^3/(8*(3*c - I*k0)) + ((c - I*k0)*(3*c - I*k0))/4 - (3*c - I*k0)^3/(8*(c - I*k0)))*k0^6)/16 - (5*((c - I*k0)/(2*(3*c - I*k0)) + (3*c - I*k0)/(2*(c - I*k0)))*k0^8)/128 - (7*k0^10)/(256*(c - I*k0)*(3*c - I*k0))) + 3*((7*(2*c - I*k0)^9)/(256*(3*c - I*k0)) - (5*(2*c - I*k0)^7*(3*c - I*k0))/256 - ((2*c - I*k0)^5*(3*c - I*k0)^3)/128 - ((2*c - I*k0)^3*(3*c - I*k0)^5)/128 - (5*(2*c - I*k0)*(3*c - I*k0)^7)/256 + (7*(3*c - I*k0)^9)/(256*(2*c - I*k0)) - (((-5*(2*c - I*k0)^7)/(128*(3*c - I*k0)) + ((2*c - I*k0)^5*(3*c - I*k0))/32 + ((2*c - I*k0)^3*(3*c - I*k0)^3)/64 + ((2*c - I*k0)*(3*c - I*k0)^5)/32 - (5*(3*c - I*k0)^7)/(128*(2*c - I*k0)))*k0^2)/2 - (((2*c - I*k0)^5/(16*(3*c - I*k0)) - ((2*c - I*k0)^3*(3*c - I*k0))/16 - ((2*c - I*k0)*(3*c - I*k0)^3)/16 + (3*c - I*k0)^5/(16*(2*c - I*k0)))*k0^4)/8 - ((-(2*c - I*k0)^3/(8*(3*c - I*k0)) + ((2*c - I*k0)*(3*c - I*k0))/4 - (3*c - I*k0)^3/(8*(2*c - I*k0)))*k0^6)/16 - (5*((2*c - I*k0)/(2*(3*c - I*k0)) + (3*c - I*k0)/(2*(2*c - I*k0)))*k0^8)/128 - (7*k0^10)/(256*(2*c - I*k0)*(3*c - I*k0)))))/k^3 + ((c - I*k0)^5/(16*(2*c - I*k0)) - ((c - I*k0)^3*(2*c - I*k0))/16 - ((c - I*k0)*(2*c - I*k0)^3)/16 + (2*c - I*k0)^5/(16*(c - I*k0)) + I*(((c - I*k0)^5/(16*(2*c - I*k0)) - ((c - I*k0)^3*(2*c - I*k0))/16 - ((c - I*k0)*(2*c - I*k0)^3)/16 + (2*c - I*k0)^5/(16*(c - I*k0)))/(3*c - I*k0) + ((-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)))*(3*c - I*k0))/2 - (((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*(3*c - I*k0)^3)/8 + (3*c - I*k0)^5/(16*(c - I*k0)*(2*c - I*k0)))*k0 - ((-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)))*k0^2)/2 - (((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*k0^4)/8 - k0^6/(16*(c - I*k0)*(2*c - I*k0)) - 3*((c - I*k0)^5/(16*(3*c - I*k0)) - ((c - I*k0)^3*(3*c - I*k0))/16 - ((c - I*k0)*(3*c - I*k0)^3)/16 + (3*c - I*k0)^5/(16*(c - I*k0)) - ((-(c - I*k0)^3/(8*(3*c - I*k0)) + ((c - I*k0)*(3*c - I*k0))/4 - (3*c - I*k0)^3/(8*(c - I*k0)))*k0^2)/2 - (((c - I*k0)/(2*(3*c - I*k0)) + (3*c - I*k0)/(2*(c - I*k0)))*k0^4)/8 - k0^6/(16*(c - I*k0)*(3*c - I*k0))) + 3*((2*c - I*k0)^5/(16*(3*c - I*k0)) - ((2*c - I*k0)^3*(3*c - I*k0))/16 - ((2*c - I*k0)*(3*c - I*k0)^3)/16 + (3*c - I*k0)^5/(16*(2*c - I*k0)) - ((-(2*c - I*k0)^3/(8*(3*c - I*k0)) + ((2*c - I*k0)*(3*c - I*k0))/4 - (3*c - I*k0)^3/(8*(2*c - I*k0)))*k0^2)/2 - (((2*c - I*k0)/(2*(3*c - I*k0)) + (3*c - I*k0)/(2*(2*c - I*k0)))*k0^4)/8 - k0^6/(16*(2*c - I*k0)*(3*c - I*k0))))*(-((-((c - I*k0)^3*(2*c - I*k0))/(2*k^2) - ((c - I*k0)*(2*c - I*k0)^3)/(2*k^2))*(3*c - I*k0)^3)/(2*k) + ((((-((c - I*k0)^3*(2*c - I*k0))/(2*k^2) - ((c - I*k0)*(2*c - I*k0)^3)/(2*k^2))*(3*c - I*k0))/k - ((c - I*k0)*(2*c - I*k0)*(3*c - I*k0)^3)/(2*k^3))*k0^2)/2 + (3*(c - I*k0)*(2*c - I*k0)*(3*c - I*k0)*k0^4)/(8*k^3) + (3*(c - I*k0)*(2*c - I*k0)*(3*c - I*k0)^4*((3*c)/k - (I*k0)/k))/(8*k^2) + ((3*c - I*k0)*(((c - I*k0)^3*(2*c - I*k0)^3)/(4*k^2) + (3*(c - I*k0)^4*(2*c - I*k0)*(c/k - (I*k0)/k))/(8*k) + (3*(c - I*k0)*(2*c - I*k0)^4*((2*c)/k - (I*k0)/k))/(8*k)))/k) + (3*(47*c^5 - (66*I)*c^4*k0 - 22*c^3*k0^2)*((3*(((-((c - I*k0)^3*(2*c - I*k0))/(2*k^2) - ((c - I*k0)*(2*c - I*k0)^3)/(2*k^2))*(3*c - I*k0))/k - ((c - I*k0)*(2*c - I*k0)*(3*c - I*k0)^3)/(2*k^3))*k0^4)/8 + (5*(c - I*k0)*(2*c - I*k0)*(3*c - I*k0)*k0^6)/(16*k^3) + (3*(-((c - I*k0)^3*(2*c - I*k0))/(2*k^2) - ((c - I*k0)*(2*c - I*k0)^3)/(2*k^2))*(3*c - I*k0)^4*((3*c)/k - (I*k0)/k))/8 - (5*(c - I*k0)*(2*c - I*k0)*(3*c - I*k0)^6*((3*c)/k - (I*k0)/k))/(16*k^2) - ((3*c - I*k0)^3*(((c - I*k0)^3*(2*c - I*k0)^3)/(4*k^2) + (3*(c - I*k0)^4*(2*c - I*k0)*(c/k - (I*k0)/k))/(8*k) + (3*(c - I*k0)*(2*c - I*k0)^4*((2*c)/k - (I*k0)/k))/(8*k)))/(2*k) + ((3*c - I*k0)*((-5*(c - I*k0)^6*(2*c - I*k0)*(c/k - (I*k0)/k))/(16*k) - (3*(c - I*k0)^4*(2*c - I*k0)^3*(c/k - (I*k0)/k))/(16*k) - (3*(c - I*k0)^3*(2*c - I*k0)^4*((2*c)/k - (I*k0)/k))/(16*k) - (5*(c - I*k0)*(2*c - I*k0)^6*((2*c)/k - (I*k0)/k))/(16*k)))/k + (k0^2*(-((-((c - I*k0)^3*(2*c - I*k0))/(2*k^2) - ((c - I*k0)*(2*c - I*k0)^3)/(2*k^2))*(3*c - I*k0)^3)/(2*k) + (3*(c - I*k0)*(2*c - I*k0)*(3*c - I*k0)^4*((3*c)/k - (I*k0)/k))/(8*k^2) + ((3*c - I*k0)*(((c - I*k0)^3*(2*c - I*k0)^3)/(4*k^2) + (3*(c - I*k0)^4*(2*c - I*k0)*(c/k - (I*k0)/k))/(8*k) + (3*(c - I*k0)*(2*c - I*k0)^4*((2*c)/k - (I*k0)/k))/(8*k)))/k))/2))/(4*(c - I*k0)*(2*c - I*k0)*(3*c - I*k0)) - (3*c^3*((5*(((-((c - I*k0)^3*(2*c - I*k0))/(2*k^2) - ((c - I*k0)*(2*c - I*k0)^3)/(2*k^2))*(3*c - I*k0))/k - ((c - I*k0)*(2*c - I*k0)*(3*c - I*k0)^3)/(2*k^3))*k0^6)/16 + (35*(c - I*k0)*(2*c - I*k0)*(3*c - I*k0)*k0^8)/(128*k^3) - (5*(-((c - I*k0)^3*(2*c - I*k0))/(2*k^2) - ((c - I*k0)*(2*c - I*k0)^3)/(2*k^2))*(3*c - I*k0)^6*((3*c)/k - (I*k0)/k))/16 + (35*(c - I*k0)*(2*c - I*k0)*(3*c - I*k0)^8*((3*c)/k - (I*k0)/k))/(128*k^2) + (3*(3*c - I*k0)^4*((3*c)/k - (I*k0)/k)*(((c - I*k0)^3*(2*c - I*k0)^3)/(4*k^2) + (3*(c - I*k0)^4*(2*c - I*k0)*(c/k - (I*k0)/k))/(8*k) + (3*(c - I*k0)*(2*c - I*k0)^4*((2*c)/k - (I*k0)/k))/(8*k)))/8 - ((3*c - I*k0)^3*((-5*(c - I*k0)^6*(2*c - I*k0)*(c/k - (I*k0)/k))/(16*k) - (3*(c - I*k0)^4*(2*c - I*k0)^3*(c/k - (I*k0)/k))/(16*k) - (3*(c - I*k0)^3*(2*c - I*k0)^4*((2*c)/k - (I*k0)/k))/(16*k) - (5*(c - I*k0)*(2*c - I*k0)^6*((2*c)/k - (I*k0)/k))/(16*k)))/(2*k) + ((3*c - I*k0)*((35*(c - I*k0)^8*(2*c - I*k0)*(c/k - (I*k0)/k))/(128*k) + (5*(c - I*k0)^6*(2*c - I*k0)^3*(c/k - (I*k0)/k))/(32*k) + (5*(c - I*k0)^3*(2*c - I*k0)^6*((2*c)/k - (I*k0)/k))/(32*k) + (35*(c - I*k0)*(2*c - I*k0)^8*((2*c)/k - (I*k0)/k))/(128*k) + (9*(c - I*k0)^4*(2*c - I*k0)^4*(c/k - (I*k0)/k)*((2*c)/k - (I*k0)/k))/64))/k + (3*k0^4*(-((-((c - I*k0)^3*(2*c - I*k0))/(2*k^2) - ((c - I*k0)*(2*c - I*k0)^3)/(2*k^2))*(3*c - I*k0)^3)/(2*k) + (3*(c - I*k0)*(2*c - I*k0)*(3*c - I*k0)^4*((3*c)/k - (I*k0)/k))/(8*k^2) + ((3*c - I*k0)*(((c - I*k0)^3*(2*c - I*k0)^3)/(4*k^2) + (3*(c - I*k0)^4*(2*c - I*k0)*(c/k - (I*k0)/k))/(8*k) + (3*(c - I*k0)*(2*c - I*k0)^4*((2*c)/k - (I*k0)/k))/(8*k)))/k))/8 + (k0^2*((3*(-((c - I*k0)^3*(2*c - I*k0))/(2*k^2) - ((c - I*k0)*(2*c - I*k0)^3)/(2*k^2))*(3*c - I*k0)^4*((3*c)/k - (I*k0)/k))/8 - (5*(c - I*k0)*(2*c - I*k0)*(3*c - I*k0)^6*((3*c)/k - (I*k0)/k))/(16*k^2) - ((3*c - I*k0)^3*(((c - I*k0)^3*(2*c - I*k0)^3)/(4*k^2) + (3*(c - I*k0)^4*(2*c - I*k0)*(c/k - (I*k0)/k))/(8*k) + (3*(c - I*k0)*(2*c - I*k0)^4*((2*c)/k - (I*k0)/k))/(8*k)))/(2*k) + ((3*c - I*k0)*((-5*(c - I*k0)^6*(2*c - I*k0)*(c/k - (I*k0)/k))/(16*k) - (3*(c - I*k0)^4*(2*c - I*k0)^3*(c/k - (I*k0)/k))/(16*k) - (3*(c - I*k0)^3*(2*c - I*k0)^4*((2*c)/k - (I*k0)/k))/(16*k) - (5*(c - I*k0)*(2*c - I*k0)^6*((2*c)/k - (I*k0)/k))/(16*k)))/k))/2))/((c - I*k0)*(2*c - I*k0)*(3*c - I*k0)))/k0}, 1, 11, 1], (k0 <= 0 && k^2/k0^2 > 1) || k0 > 0}}, SeriesData[k, Infinity, {I/k^3, 0, (I/2*((6*I)*c^3 + k0^3))/(k^3*k0), 0, (-((((3*I)*c^2 + 4*c*k0 - (2*I)*k0^2)*((-I/2*(c - I*k0)*(2*c - I*k0)*(3*c - I*k0)*k0^2)/k^3 - I*(((-((c - I*k0)^3*(2*c - I*k0))/(2*k^2) - ((c - I*k0)*(2*c - I*k0)^3)/(2*k^2))*(3*c - I*k0))/k - ((c - I*k0)*(2*c - I*k0)*(3*c - I*k0)^3)/(2*k^3) + ((c - I*k0)*(2*c - I*k0)*(3*c - I*k0)*k0^2)/(2*k^3))))/((2*c - I*k0)*(3*c - I*k0))) + (I*(c - I*k0)*(2*c - I*k0)*(3*c - I*k0)*((I/8*k0^4)/((c - I*k0)*(2*c - I*k0)) + I/2*k0^2*((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)) - k0^2/(2*(c - I*k0)*(2*c - I*k0))) - I*(-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)) - (((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*k0^2)/2 - k0^4/(8*(c - I*k0)*(2*c - I*k0))) + k0*((-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)))/(3*c - I*k0) + (((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*(3*c - I*k0))/2 - (3*c - I*k0)^3/(8*(c - I*k0)*(2*c - I*k0)) - ((((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))/(3*c - I*k0) + (3*c - I*k0)/(2*(c - I*k0)*(2*c - I*k0)))*k0^2)/2 - k0^4/(8*(c - I*k0)*(2*c - I*k0)*(3*c - I*k0))) - I*k0*(I*((-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)))/(3*c - I*k0) + (((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*(3*c - I*k0))/2 - (3*c - I*k0)^3/(8*(c - I*k0)*(2*c - I*k0))) - I/2*(((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))/(3*c - I*k0) + (3*c - I*k0)/(2*(c - I*k0)*(2*c - I*k0)))*k0^2 - (I/8*k0^4)/((c - I*k0)*(2*c - I*k0)*(3*c - I*k0))) + 3*((-I/8*k0^4)/((c - I*k0)*(3*c - I*k0)) - I/2*k0^2*((c - I*k0)/(2*(3*c - I*k0)) + (3*c - I*k0)/(2*(c - I*k0)) - k0^2/(2*(c - I*k0)*(3*c - I*k0))) + I*(-(c - I*k0)^3/(8*(3*c - I*k0)) + ((c - I*k0)*(3*c - I*k0))/4 - (3*c - I*k0)^3/(8*(c - I*k0)) - (((c - I*k0)/(2*(3*c - I*k0)) + (3*c - I*k0)/(2*(c - I*k0)))*k0^2)/2 - k0^4/(8*(c - I*k0)*(3*c - I*k0)))) - 3*((-I/8*k0^4)/((2*c - I*k0)*(3*c - I*k0)) - I/2*k0^2*((2*c - I*k0)/(2*(3*c - I*k0)) + (3*c - I*k0)/(2*(2*c - I*k0)) - k0^2/(2*(2*c - I*k0)*(3*c - I*k0))) + I*(-(2*c - I*k0)^3/(8*(3*c - I*k0)) + ((2*c - I*k0)*(3*c - I*k0))/4 - (3*c - I*k0)^3/(8*(2*c - I*k0)) - (((2*c - I*k0)/(2*(3*c - I*k0)) + (3*c - I*k0)/(2*(2*c - I*k0)))*k0^2)/2 - k0^4/(8*(2*c - I*k0)*(3*c - I*k0))))))/k^3 - (k0*(((-3*I)/8*(c - I*k0)*(2*c - I*k0)*(3*c - I*k0)*k0^4)/k^3 - I/2*k0^2*(((-((c - I*k0)^3*(2*c - I*k0))/(2*k^2) - ((c - I*k0)*(2*c - I*k0)^3)/(2*k^2))*(3*c - I*k0))/k - ((c - I*k0)*(2*c - I*k0)*(3*c - I*k0)^3)/(2*k^3) + ((c - I*k0)*(2*c - I*k0)*(3*c - I*k0)*k0^2)/(2*k^3)) - I*(-((-((c - I*k0)^3*(2*c - I*k0))/(2*k^2) - ((c - I*k0)*(2*c - I*k0)^3)/(2*k^2))*(3*c - I*k0)^3)/(2*k) + ((((-((c - I*k0)^3*(2*c - I*k0))/(2*k^2) - ((c - I*k0)*(2*c - I*k0)^3)/(2*k^2))*(3*c - I*k0))/k - ((c - I*k0)*(2*c - I*k0)*(3*c - I*k0)^3)/(2*k^3))*k0^2)/2 + (3*(c - I*k0)*(2*c - I*k0)*(3*c - I*k0)*k0^4)/(8*k^3) + (3*(c - I*k0)*(2*c - I*k0)*(3*c - I*k0)^4*((3*c)/k - (I*k0)/k))/(8*k^2) + ((3*c - I*k0)*(((c - I*k0)^3*(2*c - I*k0)^3)/(4*k^2) + (3*(c - I*k0)^4*(2*c - I*k0)*(c/k - (I*k0)/k))/(8*k) + (3*(c - I*k0)*(2*c - I*k0)^4*((2*c)/k - (I*k0)/k))/(8*k)))/k)))/((c - I*k0)*(2*c - I*k0)*(3*c - I*k0)))/k0, 0, (-(((-I/2*(c - I*k0)*(2*c - I*k0)*(3*c - I*k0)*k0^2)/k^3 - I*(((-((c - I*k0)^3*(2*c - I*k0))/(2*k^2) - ((c - I*k0)*(2*c - I*k0)^3)/(2*k^2))*(3*c - I*k0))/k - ((c - I*k0)*(2*c - I*k0)*(3*c - I*k0)^3)/(2*k^3) + ((c - I*k0)*(2*c - I*k0)*(3*c - I*k0)*k0^2)/(2*k^3)))*((I/8*k0^4)/((c - I*k0)*(2*c - I*k0)) + I/2*k0^2*((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)) - k0^2/(2*(c - I*k0)*(2*c - I*k0))) - I*(-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)) - (((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*k0^2)/2 - k0^4/(8*(c - I*k0)*(2*c - I*k0))) + k0*((-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)))/(3*c - I*k0) + (((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*(3*c - I*k0))/2 - (3*c - I*k0)^3/(8*(c - I*k0)*(2*c - I*k0)) - ((((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))/(3*c - I*k0) + (3*c - I*k0)/(2*(c - I*k0)*(2*c - I*k0)))*k0^2)/2 - k0^4/(8*(c - I*k0)*(2*c - I*k0)*(3*c - I*k0))) - I*k0*(I*((-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)))/(3*c - I*k0) + (((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*(3*c - I*k0))/2 - (3*c - I*k0)^3/(8*(c - I*k0)*(2*c - I*k0))) - I/2*(((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))/(3*c - I*k0) + (3*c - I*k0)/(2*(c - I*k0)*(2*c - I*k0)))*k0^2 - (I/8*k0^4)/((c - I*k0)*(2*c - I*k0)*(3*c - I*k0))) + 3*((-I/8*k0^4)/((c - I*k0)*(3*c - I*k0)) - I/2*k0^2*((c - I*k0)/(2*(3*c - I*k0)) + (3*c - I*k0)/(2*(c - I*k0)) - k0^2/(2*(c - I*k0)*(3*c - I*k0))) + I*(-(c - I*k0)^3/(8*(3*c - I*k0)) + ((c - I*k0)*(3*c - I*k0))/4 - (3*c - I*k0)^3/(8*(c - I*k0)) - (((c - I*k0)/(2*(3*c - I*k0)) + (3*c - I*k0)/(2*(c - I*k0)))*k0^2)/2 - k0^4/(8*(c - I*k0)*(3*c - I*k0)))) - 3*((-I/8*k0^4)/((2*c - I*k0)*(3*c - I*k0)) - I/2*k0^2*((2*c - I*k0)/(2*(3*c - I*k0)) + (3*c - I*k0)/(2*(2*c - I*k0)) - k0^2/(2*(2*c - I*k0)*(3*c - I*k0))) + I*(-(2*c - I*k0)^3/(8*(3*c - I*k0)) + ((2*c - I*k0)*(3*c - I*k0))/4 - (3*c - I*k0)^3/(8*(2*c - I*k0)) - (((2*c - I*k0)/(2*(3*c - I*k0)) + (3*c - I*k0)/(2*(2*c - I*k0)))*k0^2)/2 - k0^4/(8*(2*c - I*k0)*(3*c - I*k0)))))) + (I*(c - I*k0)*(2*c - I*k0)*(3*c - I*k0)*((I/16*k0^6)/((c - I*k0)*(2*c - I*k0)) + I/8*k0^4*((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)) - k0^2/(2*(c - I*k0)*(2*c - I*k0))) + I/2*k0^2*(-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)) - (((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*k0^2)/2 - k0^4/(8*(c - I*k0)*(2*c - I*k0))) - I*((c - I*k0)^5/(16*(2*c - I*k0)) - ((c - I*k0)^3*(2*c - I*k0))/16 - ((c - I*k0)*(2*c - I*k0)^3)/16 + (2*c - I*k0)^5/(16*(c - I*k0)) - ((-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)))*k0^2)/2 - (((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*k0^4)/8 - k0^6/(16*(c - I*k0)*(2*c - I*k0))) + k0*(((c - I*k0)^5/(16*(2*c - I*k0)) - ((c - I*k0)^3*(2*c - I*k0))/16 - ((c - I*k0)*(2*c - I*k0)^3)/16 + (2*c - I*k0)^5/(16*(c - I*k0)))/(3*c - I*k0) + ((-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)))*(3*c - I*k0))/2 - (((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*(3*c - I*k0)^3)/8 + (3*c - I*k0)^5/(16*(c - I*k0)*(2*c - I*k0)) - (((-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)))/(3*c - I*k0) + (((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*(3*c - I*k0))/2 - (3*c - I*k0)^3/(8*(c - I*k0)*(2*c - I*k0)))*k0^2)/2 - ((((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))/(3*c - I*k0) + (3*c - I*k0)/(2*(c - I*k0)*(2*c - I*k0)))*k0^4)/8 - k0^6/(16*(c - I*k0)*(2*c - I*k0)*(3*c - I*k0))) - I*k0*(I*(((c - I*k0)^5/(16*(2*c - I*k0)) - ((c - I*k0)^3*(2*c - I*k0))/16 - ((c - I*k0)*(2*c - I*k0)^3)/16 + (2*c - I*k0)^5/(16*(c - I*k0)))/(3*c - I*k0) + ((-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)))*(3*c - I*k0))/2 - (((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*(3*c - I*k0)^3)/8 + (3*c - I*k0)^5/(16*(c - I*k0)*(2*c - I*k0))) - I/2*((-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)))/(3*c - I*k0) + (((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*(3*c - I*k0))/2 - (3*c - I*k0)^3/(8*(c - I*k0)*(2*c - I*k0)))*k0^2 - I/8*(((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))/(3*c - I*k0) + (3*c - I*k0)/(2*(c - I*k0)*(2*c - I*k0)))*k0^4 - (I/16*k0^6)/((c - I*k0)*(2*c - I*k0)*(3*c - I*k0))) + 3*((-I/16*k0^6)/((c - I*k0)*(3*c - I*k0)) - I/8*k0^4*((c - I*k0)/(2*(3*c - I*k0)) + (3*c - I*k0)/(2*(c - I*k0)) - k0^2/(2*(c - I*k0)*(3*c - I*k0))) - I/2*k0^2*(-(c - I*k0)^3/(8*(3*c - I*k0)) + ((c - I*k0)*(3*c - I*k0))/4 - (3*c - I*k0)^3/(8*(c - I*k0)) - (((c - I*k0)/(2*(3*c - I*k0)) + (3*c - I*k0)/(2*(c - I*k0)))*k0^2)/2 - k0^4/(8*(c - I*k0)*(3*c - I*k0))) + I*((c - I*k0)^5/(16*(3*c - I*k0)) - ((c - I*k0)^3*(3*c - I*k0))/16 - ((c - I*k0)*(3*c - I*k0)^3)/16 + (3*c - I*k0)^5/(16*(c - I*k0)) - ((-(c - I*k0)^3/(8*(3*c - I*k0)) + ((c - I*k0)*(3*c - I*k0))/4 - (3*c - I*k0)^3/(8*(c - I*k0)))*k0^2)/2 - (((c - I*k0)/(2*(3*c - I*k0)) + (3*c - I*k0)/(2*(c - I*k0)))*k0^4)/8 - k0^6/(16*(c - I*k0)*(3*c - I*k0)))) - 3*((-I/16*k0^6)/((2*c - I*k0)*(3*c - I*k0)) - I/8*k0^4*((2*c - I*k0)/(2*(3*c - I*k0)) + (3*c - I*k0)/(2*(2*c - I*k0)) - k0^2/(2*(2*c - I*k0)*(3*c - I*k0))) - I/2*k0^2*(-(2*c - I*k0)^3/(8*(3*c - I*k0)) + ((2*c - I*k0)*(3*c - I*k0))/4 - (3*c - I*k0)^3/(8*(2*c - I*k0)) - (((2*c - I*k0)/(2*(3*c - I*k0)) + (3*c - I*k0)/(2*(2*c - I*k0)))*k0^2)/2 - k0^4/(8*(2*c - I*k0)*(3*c - I*k0))) + I*((2*c - I*k0)^5/(16*(3*c - I*k0)) - ((2*c - I*k0)^3*(3*c - I*k0))/16 - ((2*c - I*k0)*(3*c - I*k0)^3)/16 + (3*c - I*k0)^5/(16*(2*c - I*k0)) - ((-(2*c - I*k0)^3/(8*(3*c - I*k0)) + ((2*c - I*k0)*(3*c - I*k0))/4 - (3*c - I*k0)^3/(8*(2*c - I*k0)))*k0^2)/2 - (((2*c - I*k0)/(2*(3*c - I*k0)) + (3*c - I*k0)/(2*(2*c - I*k0)))*k0^4)/8 - k0^6/(16*(2*c - I*k0)*(3*c - I*k0))))))/k^3 - (((3*I)*c^2 + 4*c*k0 - (2*I)*k0^2)*(((-3*I)/8*(c - I*k0)*(2*c - I*k0)*(3*c - I*k0)*k0^4)/k^3 - I/2*k0^2*(((-((c - I*k0)^3*(2*c - I*k0))/(2*k^2) - ((c - I*k0)*(2*c - I*k0)^3)/(2*k^2))*(3*c - I*k0))/k - ((c - I*k0)*(2*c - I*k0)*(3*c - I*k0)^3)/(2*k^3) + ((c - I*k0)*(2*c - I*k0)*(3*c - I*k0)*k0^2)/(2*k^3)) - I*(-((-((c - I*k0)^3*(2*c - I*k0))/(2*k^2) - ((c - I*k0)*(2*c - I*k0)^3)/(2*k^2))*(3*c - I*k0)^3)/(2*k) + ((((-((c - I*k0)^3*(2*c - I*k0))/(2*k^2) - ((c - I*k0)*(2*c - I*k0)^3)/(2*k^2))*(3*c - I*k0))/k - ((c - I*k0)*(2*c - I*k0)*(3*c - I*k0)^3)/(2*k^3))*k0^2)/2 + (3*(c - I*k0)*(2*c - I*k0)*(3*c - I*k0)*k0^4)/(8*k^3) + (3*(c - I*k0)*(2*c - I*k0)*(3*c - I*k0)^4*((3*c)/k - (I*k0)/k))/(8*k^2) + ((3*c - I*k0)*(((c - I*k0)^3*(2*c - I*k0)^3)/(4*k^2) + (3*(c - I*k0)^4*(2*c - I*k0)*(c/k - (I*k0)/k))/(8*k) + (3*(c - I*k0)*(2*c - I*k0)^4*((2*c)/k - (I*k0)/k))/(8*k)))/k)))/((2*c - I*k0)*(3*c - I*k0)) - (k0*(((-5*I)/16*(c - I*k0)*(2*c - I*k0)*(3*c - I*k0)*k0^6)/k^3 - (3*I)/8*k0^4*(((-((c - I*k0)^3*(2*c - I*k0))/(2*k^2) - ((c - I*k0)*(2*c - I*k0)^3)/(2*k^2))*(3*c - I*k0))/k - ((c - I*k0)*(2*c - I*k0)*(3*c - I*k0)^3)/(2*k^3) + ((c - I*k0)*(2*c - I*k0)*(3*c - I*k0)*k0^2)/(2*k^3)) - I/2*k0^2*(-((-((c - I*k0)^3*(2*c - I*k0))/(2*k^2) - ((c - I*k0)*(2*c - I*k0)^3)/(2*k^2))*(3*c - I*k0)^3)/(2*k) + ((((-((c - I*k0)^3*(2*c - I*k0))/(2*k^2) - ((c - I*k0)*(2*c - I*k0)^3)/(2*k^2))*(3*c - I*k0))/k - ((c - I*k0)*(2*c - I*k0)*(3*c - I*k0)^3)/(2*k^3))*k0^2)/2 + (3*(c - I*k0)*(2*c - I*k0)*(3*c - I*k0)*k0^4)/(8*k^3) + (3*(c - I*k0)*(2*c - I*k0)*(3*c - I*k0)^4*((3*c)/k - (I*k0)/k))/(8*k^2) + ((3*c - I*k0)*(((c - I*k0)^3*(2*c - I*k0)^3)/(4*k^2) + (3*(c - I*k0)^4*(2*c - I*k0)*(c/k - (I*k0)/k))/(8*k) + (3*(c - I*k0)*(2*c - I*k0)^4*((2*c)/k - (I*k0)/k))/(8*k)))/k) - I*((3*(((-((c - I*k0)^3*(2*c - I*k0))/(2*k^2) - ((c - I*k0)*(2*c - I*k0)^3)/(2*k^2))*(3*c - I*k0))/k - ((c - I*k0)*(2*c - I*k0)*(3*c - I*k0)^3)/(2*k^3))*k0^4)/8 + (5*(c - I*k0)*(2*c - I*k0)*(3*c - I*k0)*k0^6)/(16*k^3) + (3*(-((c - I*k0)^3*(2*c - I*k0))/(2*k^2) - ((c - I*k0)*(2*c - I*k0)^3)/(2*k^2))*(3*c - I*k0)^4*((3*c)/k - (I*k0)/k))/8 - (5*(c - I*k0)*(2*c - I*k0)*(3*c - I*k0)^6*((3*c)/k - (I*k0)/k))/(16*k^2) - ((3*c - I*k0)^3*(((c - I*k0)^3*(2*c - I*k0)^3)/(4*k^2) + (3*(c - I*k0)^4*(2*c - I*k0)*(c/k - (I*k0)/k))/(8*k) + (3*(c - I*k0)*(2*c - I*k0)^4*((2*c)/k - (I*k0)/k))/(8*k)))/(2*k) + ((3*c - I*k0)*((-5*(c - I*k0)^6*(2*c - I*k0)*(c/k - (I*k0)/k))/(16*k) - (3*(c - I*k0)^4*(2*c - I*k0)^3*(c/k - (I*k0)/k))/(16*k) - (3*(c - I*k0)^3*(2*c - I*k0)^4*((2*c)/k - (I*k0)/k))/(16*k) - (5*(c - I*k0)*(2*c - I*k0)^6*((2*c)/k - (I*k0)/k))/(16*k)))/k + (k0^2*(-((-((c - I*k0)^3*(2*c - I*k0))/(2*k^2) - ((c - I*k0)*(2*c - I*k0)^3)/(2*k^2))*(3*c - I*k0)^3)/(2*k) + (3*(c - I*k0)*(2*c - I*k0)*(3*c - I*k0)^4*((3*c)/k - (I*k0)/k))/(8*k^2) + ((3*c - I*k0)*(((c - I*k0)^3*(2*c - I*k0)^3)/(4*k^2) + (3*(c - I*k0)^4*(2*c - I*k0)*(c/k - (I*k0)/k))/(8*k) + (3*(c - I*k0)*(2*c - I*k0)^4*((2*c)/k - (I*k0)/k))/(8*k)))/k))/2)))/((c - I*k0)*(2*c - I*k0)*(3*c - I*k0)))/k0, 0, (-(((-I/2*(c - I*k0)*(2*c - I*k0)*(3*c - I*k0)*k0^2)/k^3 - I*(((-((c - I*k0)^3*(2*c - I*k0))/(2*k^2) - ((c - I*k0)*(2*c - I*k0)^3)/(2*k^2))*(3*c - I*k0))/k - ((c - I*k0)*(2*c - I*k0)*(3*c - I*k0)^3)/(2*k^3) + ((c - I*k0)*(2*c - I*k0)*(3*c - I*k0)*k0^2)/(2*k^3)))*((I/16*k0^6)/((c - I*k0)*(2*c - I*k0)) + I/8*k0^4*((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)) - k0^2/(2*(c - I*k0)*(2*c - I*k0))) + I/2*k0^2*(-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)) - (((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*k0^2)/2 - k0^4/(8*(c - I*k0)*(2*c - I*k0))) - I*((c - I*k0)^5/(16*(2*c - I*k0)) - ((c - I*k0)^3*(2*c - I*k0))/16 - ((c - I*k0)*(2*c - I*k0)^3)/16 + (2*c - I*k0)^5/(16*(c - I*k0)) - ((-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)))*k0^2)/2 - (((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*k0^4)/8 - k0^6/(16*(c - I*k0)*(2*c - I*k0))) + k0*(((c - I*k0)^5/(16*(2*c - I*k0)) - ((c - I*k0)^3*(2*c - I*k0))/16 - ((c - I*k0)*(2*c - I*k0)^3)/16 + (2*c - I*k0)^5/(16*(c - I*k0)))/(3*c - I*k0) + ((-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)))*(3*c - I*k0))/2 - (((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*(3*c - I*k0)^3)/8 + (3*c - I*k0)^5/(16*(c - I*k0)*(2*c - I*k0)) - (((-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)))/(3*c - I*k0) + (((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*(3*c - I*k0))/2 - (3*c - I*k0)^3/(8*(c - I*k0)*(2*c - I*k0)))*k0^2)/2 - ((((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))/(3*c - I*k0) + (3*c - I*k0)/(2*(c - I*k0)*(2*c - I*k0)))*k0^4)/8 - k0^6/(16*(c - I*k0)*(2*c - I*k0)*(3*c - I*k0))) - I*k0*(I*(((c - I*k0)^5/(16*(2*c - I*k0)) - ((c - I*k0)^3*(2*c - I*k0))/16 - ((c - I*k0)*(2*c - I*k0)^3)/16 + (2*c - I*k0)^5/(16*(c - I*k0)))/(3*c - I*k0) + ((-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)))*(3*c - I*k0))/2 - (((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*(3*c - I*k0)^3)/8 + (3*c - I*k0)^5/(16*(c - I*k0)*(2*c - I*k0))) - I/2*((-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)))/(3*c - I*k0) + (((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*(3*c - I*k0))/2 - (3*c - I*k0)^3/(8*(c - I*k0)*(2*c - I*k0)))*k0^2 - I/8*(((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))/(3*c - I*k0) + (3*c - I*k0)/(2*(c - I*k0)*(2*c - I*k0)))*k0^4 - (I/16*k0^6)/((c - I*k0)*(2*c - I*k0)*(3*c - I*k0))) + 3*((-I/16*k0^6)/((c - I*k0)*(3*c - I*k0)) - I/8*k0^4*((c - I*k0)/(2*(3*c - I*k0)) + (3*c - I*k0)/(2*(c - I*k0)) - k0^2/(2*(c - I*k0)*(3*c - I*k0))) - I/2*k0^2*(-(c - I*k0)^3/(8*(3*c - I*k0)) + ((c - I*k0)*(3*c - I*k0))/4 - (3*c - I*k0)^3/(8*(c - I*k0)) - (((c - I*k0)/(2*(3*c - I*k0)) + (3*c - I*k0)/(2*(c - I*k0)))*k0^2)/2 - k0^4/(8*(c - I*k0)*(3*c - I*k0))) + I*((c - I*k0)^5/(16*(3*c - I*k0)) - ((c - I*k0)^3*(3*c - I*k0))/16 - ((c - I*k0)*(3*c - I*k0)^3)/16 + (3*c - I*k0)^5/(16*(c - I*k0)) - ((-(c - I*k0)^3/(8*(3*c - I*k0)) + ((c - I*k0)*(3*c - I*k0))/4 - (3*c - I*k0)^3/(8*(c - I*k0)))*k0^2)/2 - (((c - I*k0)/(2*(3*c - I*k0)) + (3*c - I*k0)/(2*(c - I*k0)))*k0^4)/8 - k0^6/(16*(c - I*k0)*(3*c - I*k0)))) - 3*((-I/16*k0^6)/((2*c - I*k0)*(3*c - I*k0)) - I/8*k0^4*((2*c - I*k0)/(2*(3*c - I*k0)) + (3*c - I*k0)/(2*(2*c - I*k0)) - k0^2/(2*(2*c - I*k0)*(3*c - I*k0))) - I/2*k0^2*(-(2*c - I*k0)^3/(8*(3*c - I*k0)) + ((2*c - I*k0)*(3*c - I*k0))/4 - (3*c - I*k0)^3/(8*(2*c - I*k0)) - (((2*c - I*k0)/(2*(3*c - I*k0)) + (3*c - I*k0)/(2*(2*c - I*k0)))*k0^2)/2 - k0^4/(8*(2*c - I*k0)*(3*c - I*k0))) + I*((2*c - I*k0)^5/(16*(3*c - I*k0)) - ((2*c - I*k0)^3*(3*c - I*k0))/16 - ((2*c - I*k0)*(3*c - I*k0)^3)/16 + (3*c - I*k0)^5/(16*(2*c - I*k0)) - ((-(2*c - I*k0)^3/(8*(3*c - I*k0)) + ((2*c - I*k0)*(3*c - I*k0))/4 - (3*c - I*k0)^3/(8*(2*c - I*k0)))*k0^2)/2 - (((2*c - I*k0)/(2*(3*c - I*k0)) + (3*c - I*k0)/(2*(2*c - I*k0)))*k0^4)/8 - k0^6/(16*(2*c - I*k0)*(3*c - I*k0)))))) + (I*(c - I*k0)*(2*c - I*k0)*(3*c - I*k0)*(((5*I)/128*k0^8)/((c - I*k0)*(2*c - I*k0)) + I/16*k0^6*((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)) - k0^2/(2*(c - I*k0)*(2*c - I*k0))) + I/8*k0^4*(-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)) - (((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*k0^2)/2 - k0^4/(8*(c - I*k0)*(2*c - I*k0))) + I/2*k0^2*((c - I*k0)^5/(16*(2*c - I*k0)) - ((c - I*k0)^3*(2*c - I*k0))/16 - ((c - I*k0)*(2*c - I*k0)^3)/16 + (2*c - I*k0)^5/(16*(c - I*k0)) - ((-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)))*k0^2)/2 - (((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*k0^4)/8 - k0^6/(16*(c - I*k0)*(2*c - I*k0))) - I*((-5*(c - I*k0)^7)/(128*(2*c - I*k0)) + ((c - I*k0)^5*(2*c - I*k0))/32 + ((c - I*k0)^3*(2*c - I*k0)^3)/64 + ((c - I*k0)*(2*c - I*k0)^5)/32 - (5*(2*c - I*k0)^7)/(128*(c - I*k0)) - (((c - I*k0)^5/(16*(2*c - I*k0)) - ((c - I*k0)^3*(2*c - I*k0))/16 - ((c - I*k0)*(2*c - I*k0)^3)/16 + (2*c - I*k0)^5/(16*(c - I*k0)))*k0^2)/2 - ((-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)))*k0^4)/8 - (((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*k0^6)/16 - (5*k0^8)/(128*(c - I*k0)*(2*c - I*k0))) + k0*(((-5*(c - I*k0)^7)/(128*(2*c - I*k0)) + ((c - I*k0)^5*(2*c - I*k0))/32 + ((c - I*k0)^3*(2*c - I*k0)^3)/64 + ((c - I*k0)*(2*c - I*k0)^5)/32 - (5*(2*c - I*k0)^7)/(128*(c - I*k0)))/(3*c - I*k0) + (((c - I*k0)^5/(16*(2*c - I*k0)) - ((c - I*k0)^3*(2*c - I*k0))/16 - ((c - I*k0)*(2*c - I*k0)^3)/16 + (2*c - I*k0)^5/(16*(c - I*k0)))*(3*c - I*k0))/2 - ((-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)))*(3*c - I*k0)^3)/8 + (((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*(3*c - I*k0)^5)/16 - (5*(3*c - I*k0)^7)/(128*(c - I*k0)*(2*c - I*k0)) - ((((c - I*k0)^5/(16*(2*c - I*k0)) - ((c - I*k0)^3*(2*c - I*k0))/16 - ((c - I*k0)*(2*c - I*k0)^3)/16 + (2*c - I*k0)^5/(16*(c - I*k0)))/(3*c - I*k0) + ((-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)))*(3*c - I*k0))/2 - (((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*(3*c - I*k0)^3)/8 + (3*c - I*k0)^5/(16*(c - I*k0)*(2*c - I*k0)))*k0^2)/2 - (((-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)))/(3*c - I*k0) + (((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*(3*c - I*k0))/2 - (3*c - I*k0)^3/(8*(c - I*k0)*(2*c - I*k0)))*k0^4)/8 - ((((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))/(3*c - I*k0) + (3*c - I*k0)/(2*(c - I*k0)*(2*c - I*k0)))*k0^6)/16 - (5*k0^8)/(128*(c - I*k0)*(2*c - I*k0)*(3*c - I*k0))) - I*k0*(I*(((-5*(c - I*k0)^7)/(128*(2*c - I*k0)) + ((c - I*k0)^5*(2*c - I*k0))/32 + ((c - I*k0)^3*(2*c - I*k0)^3)/64 + ((c - I*k0)*(2*c - I*k0)^5)/32 - (5*(2*c - I*k0)^7)/(128*(c - I*k0)))/(3*c - I*k0) + (((c - I*k0)^5/(16*(2*c - I*k0)) - ((c - I*k0)^3*(2*c - I*k0))/16 - ((c - I*k0)*(2*c - I*k0)^3)/16 + (2*c - I*k0)^5/(16*(c - I*k0)))*(3*c - I*k0))/2 - ((-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)))*(3*c - I*k0)^3)/8 + (((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*(3*c - I*k0)^5)/16 - (5*(3*c - I*k0)^7)/(128*(c - I*k0)*(2*c - I*k0))) - I/2*(((c - I*k0)^5/(16*(2*c - I*k0)) - ((c - I*k0)^3*(2*c - I*k0))/16 - ((c - I*k0)*(2*c - I*k0)^3)/16 + (2*c - I*k0)^5/(16*(c - I*k0)))/(3*c - I*k0) + ((-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)))*(3*c - I*k0))/2 - (((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*(3*c - I*k0)^3)/8 + (3*c - I*k0)^5/(16*(c - I*k0)*(2*c - I*k0)))*k0^2 - I/8*((-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)))/(3*c - I*k0) + (((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*(3*c - I*k0))/2 - (3*c - I*k0)^3/(8*(c - I*k0)*(2*c - I*k0)))*k0^4 - I/16*(((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))/(3*c - I*k0) + (3*c - I*k0)/(2*(c - I*k0)*(2*c - I*k0)))*k0^6 - ((5*I)/128*k0^8)/((c - I*k0)*(2*c - I*k0)*(3*c - I*k0))) + 3*(((-5*I)/128*k0^8)/((c - I*k0)*(3*c - I*k0)) - I/16*k0^6*((c - I*k0)/(2*(3*c - I*k0)) + (3*c - I*k0)/(2*(c - I*k0)) - k0^2/(2*(c - I*k0)*(3*c - I*k0))) - I/8*k0^4*(-(c - I*k0)^3/(8*(3*c - I*k0)) + ((c - I*k0)*(3*c - I*k0))/4 - (3*c - I*k0)^3/(8*(c - I*k0)) - (((c - I*k0)/(2*(3*c - I*k0)) + (3*c - I*k0)/(2*(c - I*k0)))*k0^2)/2 - k0^4/(8*(c - I*k0)*(3*c - I*k0))) - I/2*k0^2*((c - I*k0)^5/(16*(3*c - I*k0)) - ((c - I*k0)^3*(3*c - I*k0))/16 - ((c - I*k0)*(3*c - I*k0)^3)/16 + (3*c - I*k0)^5/(16*(c - I*k0)) - ((-(c - I*k0)^3/(8*(3*c - I*k0)) + ((c - I*k0)*(3*c - I*k0))/4 - (3*c - I*k0)^3/(8*(c - I*k0)))*k0^2)/2 - (((c - I*k0)/(2*(3*c - I*k0)) + (3*c - I*k0)/(2*(c - I*k0)))*k0^4)/8 - k0^6/(16*(c - I*k0)*(3*c - I*k0))) + I*((-5*(c - I*k0)^7)/(128*(3*c - I*k0)) + ((c - I*k0)^5*(3*c - I*k0))/32 + ((c - I*k0)^3*(3*c - I*k0)^3)/64 + ((c - I*k0)*(3*c - I*k0)^5)/32 - (5*(3*c - I*k0)^7)/(128*(c - I*k0)) - (((c - I*k0)^5/(16*(3*c - I*k0)) - ((c - I*k0)^3*(3*c - I*k0))/16 - ((c - I*k0)*(3*c - I*k0)^3)/16 + (3*c - I*k0)^5/(16*(c - I*k0)))*k0^2)/2 - ((-(c - I*k0)^3/(8*(3*c - I*k0)) + ((c - I*k0)*(3*c - I*k0))/4 - (3*c - I*k0)^3/(8*(c - I*k0)))*k0^4)/8 - (((c - I*k0)/(2*(3*c - I*k0)) + (3*c - I*k0)/(2*(c - I*k0)))*k0^6)/16 - (5*k0^8)/(128*(c - I*k0)*(3*c - I*k0)))) - 3*(((-5*I)/128*k0^8)/((2*c - I*k0)*(3*c - I*k0)) - I/16*k0^6*((2*c - I*k0)/(2*(3*c - I*k0)) + (3*c - I*k0)/(2*(2*c - I*k0)) - k0^2/(2*(2*c - I*k0)*(3*c - I*k0))) - I/8*k0^4*(-(2*c - I*k0)^3/(8*(3*c - I*k0)) + ((2*c - I*k0)*(3*c - I*k0))/4 - (3*c - I*k0)^3/(8*(2*c - I*k0)) - (((2*c - I*k0)/(2*(3*c - I*k0)) + (3*c - I*k0)/(2*(2*c - I*k0)))*k0^2)/2 - k0^4/(8*(2*c - I*k0)*(3*c - I*k0))) - I/2*k0^2*((2*c - I*k0)^5/(16*(3*c - I*k0)) - ((2*c - I*k0)^3*(3*c - I*k0))/16 - ((2*c - I*k0)*(3*c - I*k0)^3)/16 + (3*c - I*k0)^5/(16*(2*c - I*k0)) - ((-(2*c - I*k0)^3/(8*(3*c - I*k0)) + ((2*c - I*k0)*(3*c - I*k0))/4 - (3*c - I*k0)^3/(8*(2*c - I*k0)))*k0^2)/2 - (((2*c - I*k0)/(2*(3*c - I*k0)) + (3*c - I*k0)/(2*(2*c - I*k0)))*k0^4)/8 - k0^6/(16*(2*c - I*k0)*(3*c - I*k0))) + I*((-5*(2*c - I*k0)^7)/(128*(3*c - I*k0)) + ((2*c - I*k0)^5*(3*c - I*k0))/32 + ((2*c - I*k0)^3*(3*c - I*k0)^3)/64 + ((2*c - I*k0)*(3*c - I*k0)^5)/32 - (5*(3*c - I*k0)^7)/(128*(2*c - I*k0)) - (((2*c - I*k0)^5/(16*(3*c - I*k0)) - ((2*c - I*k0)^3*(3*c - I*k0))/16 - ((2*c - I*k0)*(3*c - I*k0)^3)/16 + (3*c - I*k0)^5/(16*(2*c - I*k0)))*k0^2)/2 - ((-(2*c - I*k0)^3/(8*(3*c - I*k0)) + ((2*c - I*k0)*(3*c - I*k0))/4 - (3*c - I*k0)^3/(8*(2*c - I*k0)))*k0^4)/8 - (((2*c - I*k0)/(2*(3*c - I*k0)) + (3*c - I*k0)/(2*(2*c - I*k0)))*k0^6)/16 - (5*k0^8)/(128*(2*c - I*k0)*(3*c - I*k0))))))/k^3 - ((I/8*k0^4)/((c - I*k0)*(2*c - I*k0)) + I/2*k0^2*((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)) - k0^2/(2*(c - I*k0)*(2*c - I*k0))) - I*(-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)) - (((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*k0^2)/2 - k0^4/(8*(c - I*k0)*(2*c - I*k0))) + k0*((-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)))/(3*c - I*k0) + (((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*(3*c - I*k0))/2 - (3*c - I*k0)^3/(8*(c - I*k0)*(2*c - I*k0)) - ((((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))/(3*c - I*k0) + (3*c - I*k0)/(2*(c - I*k0)*(2*c - I*k0)))*k0^2)/2 - k0^4/(8*(c - I*k0)*(2*c - I*k0)*(3*c - I*k0))) - I*k0*(I*((-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)))/(3*c - I*k0) + (((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*(3*c - I*k0))/2 - (3*c - I*k0)^3/(8*(c - I*k0)*(2*c - I*k0))) - I/2*(((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))/(3*c - I*k0) + (3*c - I*k0)/(2*(c - I*k0)*(2*c - I*k0)))*k0^2 - (I/8*k0^4)/((c - I*k0)*(2*c - I*k0)*(3*c - I*k0))) + 3*((-I/8*k0^4)/((c - I*k0)*(3*c - I*k0)) - I/2*k0^2*((c - I*k0)/(2*(3*c - I*k0)) + (3*c - I*k0)/(2*(c - I*k0)) - k0^2/(2*(c - I*k0)*(3*c - I*k0))) + I*(-(c - I*k0)^3/(8*(3*c - I*k0)) + ((c - I*k0)*(3*c - I*k0))/4 - (3*c - I*k0)^3/(8*(c - I*k0)) - (((c - I*k0)/(2*(3*c - I*k0)) + (3*c - I*k0)/(2*(c - I*k0)))*k0^2)/2 - k0^4/(8*(c - I*k0)*(3*c - I*k0)))) - 3*((-I/8*k0^4)/((2*c - I*k0)*(3*c - I*k0)) - I/2*k0^2*((2*c - I*k0)/(2*(3*c - I*k0)) + (3*c - I*k0)/(2*(2*c - I*k0)) - k0^2/(2*(2*c - I*k0)*(3*c - I*k0))) + I*(-(2*c - I*k0)^3/(8*(3*c - I*k0)) + ((2*c - I*k0)*(3*c - I*k0))/4 - (3*c - I*k0)^3/(8*(2*c - I*k0)) - (((2*c - I*k0)/(2*(3*c - I*k0)) + (3*c - I*k0)/(2*(2*c - I*k0)))*k0^2)/2 - k0^4/(8*(2*c - I*k0)*(3*c - I*k0)))))*(((-3*I)/8*(c - I*k0)*(2*c - I*k0)*(3*c - I*k0)*k0^4)/k^3 - I/2*k0^2*(((-((c - I*k0)^3*(2*c - I*k0))/(2*k^2) - ((c - I*k0)*(2*c - I*k0)^3)/(2*k^2))*(3*c - I*k0))/k - ((c - I*k0)*(2*c - I*k0)*(3*c - I*k0)^3)/(2*k^3) + ((c - I*k0)*(2*c - I*k0)*(3*c - I*k0)*k0^2)/(2*k^3)) - I*(-((-((c - I*k0)^3*(2*c - I*k0))/(2*k^2) - ((c - I*k0)*(2*c - I*k0)^3)/(2*k^2))*(3*c - I*k0)^3)/(2*k) + ((((-((c - I*k0)^3*(2*c - I*k0))/(2*k^2) - ((c - I*k0)*(2*c - I*k0)^3)/(2*k^2))*(3*c - I*k0))/k - ((c - I*k0)*(2*c - I*k0)*(3*c - I*k0)^3)/(2*k^3))*k0^2)/2 + (3*(c - I*k0)*(2*c - I*k0)*(3*c - I*k0)*k0^4)/(8*k^3) + (3*(c - I*k0)*(2*c - I*k0)*(3*c - I*k0)^4*((3*c)/k - (I*k0)/k))/(8*k^2) + ((3*c - I*k0)*(((c - I*k0)^3*(2*c - I*k0)^3)/(4*k^2) + (3*(c - I*k0)^4*(2*c - I*k0)*(c/k - (I*k0)/k))/(8*k) + (3*(c - I*k0)*(2*c - I*k0)^4*((2*c)/k - (I*k0)/k))/(8*k)))/k)) - (((3*I)*c^2 + 4*c*k0 - (2*I)*k0^2)*(((-5*I)/16*(c - I*k0)*(2*c - I*k0)*(3*c - I*k0)*k0^6)/k^3 - (3*I)/8*k0^4*(((-((c - I*k0)^3*(2*c - I*k0))/(2*k^2) - ((c - I*k0)*(2*c - I*k0)^3)/(2*k^2))*(3*c - I*k0))/k - ((c - I*k0)*(2*c - I*k0)*(3*c - I*k0)^3)/(2*k^3) + ((c - I*k0)*(2*c - I*k0)*(3*c - I*k0)*k0^2)/(2*k^3)) - I/2*k0^2*(-((-((c - I*k0)^3*(2*c - I*k0))/(2*k^2) - ((c - I*k0)*(2*c - I*k0)^3)/(2*k^2))*(3*c - I*k0)^3)/(2*k) + ((((-((c - I*k0)^3*(2*c - I*k0))/(2*k^2) - ((c - I*k0)*(2*c - I*k0)^3)/(2*k^2))*(3*c - I*k0))/k - ((c - I*k0)*(2*c - I*k0)*(3*c - I*k0)^3)/(2*k^3))*k0^2)/2 + (3*(c - I*k0)*(2*c - I*k0)*(3*c - I*k0)*k0^4)/(8*k^3) + (3*(c - I*k0)*(2*c - I*k0)*(3*c - I*k0)^4*((3*c)/k - (I*k0)/k))/(8*k^2) + ((3*c - I*k0)*(((c - I*k0)^3*(2*c - I*k0)^3)/(4*k^2) + (3*(c - I*k0)^4*(2*c - I*k0)*(c/k - (I*k0)/k))/(8*k) + (3*(c - I*k0)*(2*c - I*k0)^4*((2*c)/k - (I*k0)/k))/(8*k)))/k) - I*((3*(((-((c - I*k0)^3*(2*c - I*k0))/(2*k^2) - ((c - I*k0)*(2*c - I*k0)^3)/(2*k^2))*(3*c - I*k0))/k - ((c - I*k0)*(2*c - I*k0)*(3*c - I*k0)^3)/(2*k^3))*k0^4)/8 + (5*(c - I*k0)*(2*c - I*k0)*(3*c - I*k0)*k0^6)/(16*k^3) + (3*(-((c - I*k0)^3*(2*c - I*k0))/(2*k^2) - ((c - I*k0)*(2*c - I*k0)^3)/(2*k^2))*(3*c - I*k0)^4*((3*c)/k - (I*k0)/k))/8 - (5*(c - I*k0)*(2*c - I*k0)*(3*c - I*k0)^6*((3*c)/k - (I*k0)/k))/(16*k^2) - ((3*c - I*k0)^3*(((c - I*k0)^3*(2*c - I*k0)^3)/(4*k^2) + (3*(c - I*k0)^4*(2*c - I*k0)*(c/k - (I*k0)/k))/(8*k) + (3*(c - I*k0)*(2*c - I*k0)^4*((2*c)/k - (I*k0)/k))/(8*k)))/(2*k) + ((3*c - I*k0)*((-5*(c - I*k0)^6*(2*c - I*k0)*(c/k - (I*k0)/k))/(16*k) - (3*(c - I*k0)^4*(2*c - I*k0)^3*(c/k - (I*k0)/k))/(16*k) - (3*(c - I*k0)^3*(2*c - I*k0)^4*((2*c)/k - (I*k0)/k))/(16*k) - (5*(c - I*k0)*(2*c - I*k0)^6*((2*c)/k - (I*k0)/k))/(16*k)))/k + (k0^2*(-((-((c - I*k0)^3*(2*c - I*k0))/(2*k^2) - ((c - I*k0)*(2*c - I*k0)^3)/(2*k^2))*(3*c - I*k0)^3)/(2*k) + (3*(c - I*k0)*(2*c - I*k0)*(3*c - I*k0)^4*((3*c)/k - (I*k0)/k))/(8*k^2) + ((3*c - I*k0)*(((c - I*k0)^3*(2*c - I*k0)^3)/(4*k^2) + (3*(c - I*k0)^4*(2*c - I*k0)*(c/k - (I*k0)/k))/(8*k) + (3*(c - I*k0)*(2*c - I*k0)^4*((2*c)/k - (I*k0)/k))/(8*k)))/k))/2)))/((2*c - I*k0)*(3*c - I*k0)) - (k0*(((-35*I)/128*(c - I*k0)*(2*c - I*k0)*(3*c - I*k0)*k0^8)/k^3 - (5*I)/16*k0^6*(((-((c - I*k0)^3*(2*c - I*k0))/(2*k^2) - ((c - I*k0)*(2*c - I*k0)^3)/(2*k^2))*(3*c - I*k0))/k - ((c - I*k0)*(2*c - I*k0)*(3*c - I*k0)^3)/(2*k^3) + ((c - I*k0)*(2*c - I*k0)*(3*c - I*k0)*k0^2)/(2*k^3)) - (3*I)/8*k0^4*(-((-((c - I*k0)^3*(2*c - I*k0))/(2*k^2) - ((c - I*k0)*(2*c - I*k0)^3)/(2*k^2))*(3*c - I*k0)^3)/(2*k) + ((((-((c - I*k0)^3*(2*c - I*k0))/(2*k^2) - ((c - I*k0)*(2*c - I*k0)^3)/(2*k^2))*(3*c - I*k0))/k - ((c - I*k0)*(2*c - I*k0)*(3*c - I*k0)^3)/(2*k^3))*k0^2)/2 + (3*(c - I*k0)*(2*c - I*k0)*(3*c - I*k0)*k0^4)/(8*k^3) + (3*(c - I*k0)*(2*c - I*k0)*(3*c - I*k0)^4*((3*c)/k - (I*k0)/k))/(8*k^2) + ((3*c - I*k0)*(((c - I*k0)^3*(2*c - I*k0)^3)/(4*k^2) + (3*(c - I*k0)^4*(2*c - I*k0)*(c/k - (I*k0)/k))/(8*k) + (3*(c - I*k0)*(2*c - I*k0)^4*((2*c)/k - (I*k0)/k))/(8*k)))/k) - I/2*k0^2*((3*(((-((c - I*k0)^3*(2*c - I*k0))/(2*k^2) - ((c - I*k0)*(2*c - I*k0)^3)/(2*k^2))*(3*c - I*k0))/k - ((c - I*k0)*(2*c - I*k0)*(3*c - I*k0)^3)/(2*k^3))*k0^4)/8 + (5*(c - I*k0)*(2*c - I*k0)*(3*c - I*k0)*k0^6)/(16*k^3) + (3*(-((c - I*k0)^3*(2*c - I*k0))/(2*k^2) - ((c - I*k0)*(2*c - I*k0)^3)/(2*k^2))*(3*c - I*k0)^4*((3*c)/k - (I*k0)/k))/8 - (5*(c - I*k0)*(2*c - I*k0)*(3*c - I*k0)^6*((3*c)/k - (I*k0)/k))/(16*k^2) - ((3*c - I*k0)^3*(((c - I*k0)^3*(2*c - I*k0)^3)/(4*k^2) + (3*(c - I*k0)^4*(2*c - I*k0)*(c/k - (I*k0)/k))/(8*k) + (3*(c - I*k0)*(2*c - I*k0)^4*((2*c)/k - (I*k0)/k))/(8*k)))/(2*k) + ((3*c - I*k0)*((-5*(c - I*k0)^6*(2*c - I*k0)*(c/k - (I*k0)/k))/(16*k) - (3*(c - I*k0)^4*(2*c - I*k0)^3*(c/k - (I*k0)/k))/(16*k) - (3*(c - I*k0)^3*(2*c - I*k0)^4*((2*c)/k - (I*k0)/k))/(16*k) - (5*(c - I*k0)*(2*c - I*k0)^6*((2*c)/k - (I*k0)/k))/(16*k)))/k + (k0^2*(-((-((c - I*k0)^3*(2*c - I*k0))/(2*k^2) - ((c - I*k0)*(2*c - I*k0)^3)/(2*k^2))*(3*c - I*k0)^3)/(2*k) + (3*(c - I*k0)*(2*c - I*k0)*(3*c - I*k0)^4*((3*c)/k - (I*k0)/k))/(8*k^2) + ((3*c - I*k0)*(((c - I*k0)^3*(2*c - I*k0)^3)/(4*k^2) + (3*(c - I*k0)^4*(2*c - I*k0)*(c/k - (I*k0)/k))/(8*k) + (3*(c - I*k0)*(2*c - I*k0)^4*((2*c)/k - (I*k0)/k))/(8*k)))/k))/2) - I*((5*(((-((c - I*k0)^3*(2*c - I*k0))/(2*k^2) - ((c - I*k0)*(2*c - I*k0)^3)/(2*k^2))*(3*c - I*k0))/k - ((c - I*k0)*(2*c - I*k0)*(3*c - I*k0)^3)/(2*k^3))*k0^6)/16 + (35*(c - I*k0)*(2*c - I*k0)*(3*c - I*k0)*k0^8)/(128*k^3) - (5*(-((c - I*k0)^3*(2*c - I*k0))/(2*k^2) - ((c - I*k0)*(2*c - I*k0)^3)/(2*k^2))*(3*c - I*k0)^6*((3*c)/k - (I*k0)/k))/16 + (35*(c - I*k0)*(2*c - I*k0)*(3*c - I*k0)^8*((3*c)/k - (I*k0)/k))/(128*k^2) + (3*(3*c - I*k0)^4*((3*c)/k - (I*k0)/k)*(((c - I*k0)^3*(2*c - I*k0)^3)/(4*k^2) + (3*(c - I*k0)^4*(2*c - I*k0)*(c/k - (I*k0)/k))/(8*k) + (3*(c - I*k0)*(2*c - I*k0)^4*((2*c)/k - (I*k0)/k))/(8*k)))/8 - ((3*c - I*k0)^3*((-5*(c - I*k0)^6*(2*c - I*k0)*(c/k - (I*k0)/k))/(16*k) - (3*(c - I*k0)^4*(2*c - I*k0)^3*(c/k - (I*k0)/k))/(16*k) - (3*(c - I*k0)^3*(2*c - I*k0)^4*((2*c)/k - (I*k0)/k))/(16*k) - (5*(c - I*k0)*(2*c - I*k0)^6*((2*c)/k - (I*k0)/k))/(16*k)))/(2*k) + ((3*c - I*k0)*((35*(c - I*k0)^8*(2*c - I*k0)*(c/k - (I*k0)/k))/(128*k) + (5*(c - I*k0)^6*(2*c - I*k0)^3*(c/k - (I*k0)/k))/(32*k) + (5*(c - I*k0)^3*(2*c - I*k0)^6*((2*c)/k - (I*k0)/k))/(32*k) + (35*(c - I*k0)*(2*c - I*k0)^8*((2*c)/k - (I*k0)/k))/(128*k) + (9*(c - I*k0)^4*(2*c - I*k0)^4*(c/k - (I*k0)/k)*((2*c)/k - (I*k0)/k))/64))/k + (3*k0^4*(-((-((c - I*k0)^3*(2*c - I*k0))/(2*k^2) - ((c - I*k0)*(2*c - I*k0)^3)/(2*k^2))*(3*c - I*k0)^3)/(2*k) + (3*(c - I*k0)*(2*c - I*k0)*(3*c - I*k0)^4*((3*c)/k - (I*k0)/k))/(8*k^2) + ((3*c - I*k0)*(((c - I*k0)^3*(2*c - I*k0)^3)/(4*k^2) + (3*(c - I*k0)^4*(2*c - I*k0)*(c/k - (I*k0)/k))/(8*k) + (3*(c - I*k0)*(2*c - I*k0)^4*((2*c)/k - (I*k0)/k))/(8*k)))/k))/8 + (k0^2*((3*(-((c - I*k0)^3*(2*c - I*k0))/(2*k^2) - ((c - I*k0)*(2*c - I*k0)^3)/(2*k^2))*(3*c - I*k0)^4*((3*c)/k - (I*k0)/k))/8 - (5*(c - I*k0)*(2*c - I*k0)*(3*c - I*k0)^6*((3*c)/k - (I*k0)/k))/(16*k^2) - ((3*c - I*k0)^3*(((c - I*k0)^3*(2*c - I*k0)^3)/(4*k^2) + (3*(c - I*k0)^4*(2*c - I*k0)*(c/k - (I*k0)/k))/(8*k) + (3*(c - I*k0)*(2*c - I*k0)^4*((2*c)/k - (I*k0)/k))/(8*k)))/(2*k) + ((3*c - I*k0)*((-5*(c - I*k0)^6*(2*c - I*k0)*(c/k - (I*k0)/k))/(16*k) - (3*(c - I*k0)^4*(2*c - I*k0)^3*(c/k - (I*k0)/k))/(16*k) - (3*(c - I*k0)^3*(2*c - I*k0)^4*((2*c)/k - (I*k0)/k))/(16*k) - (5*(c - I*k0)*(2*c - I*k0)^6*((2*c)/k - (I*k0)/k))/(16*k)))/k))/2)))/((c - I*k0)*(2*c - I*k0)*(3*c - I*k0)))/k0, 0, (-(((-I/2*(c - I*k0)*(2*c - I*k0)*(3*c - I*k0)*k0^2)/k^3 - I*(((-((c - I*k0)^3*(2*c - I*k0))/(2*k^2) - ((c - I*k0)*(2*c - I*k0)^3)/(2*k^2))*(3*c - I*k0))/k - ((c - I*k0)*(2*c - I*k0)*(3*c - I*k0)^3)/(2*k^3) + ((c - I*k0)*(2*c - I*k0)*(3*c - I*k0)*k0^2)/(2*k^3)))*(((5*I)/128*k0^8)/((c - I*k0)*(2*c - I*k0)) + I/16*k0^6*((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)) - k0^2/(2*(c - I*k0)*(2*c - I*k0))) + I/8*k0^4*(-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)) - (((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*k0^2)/2 - k0^4/(8*(c - I*k0)*(2*c - I*k0))) + I/2*k0^2*((c - I*k0)^5/(16*(2*c - I*k0)) - ((c - I*k0)^3*(2*c - I*k0))/16 - ((c - I*k0)*(2*c - I*k0)^3)/16 + (2*c - I*k0)^5/(16*(c - I*k0)) - ((-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)))*k0^2)/2 - (((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*k0^4)/8 - k0^6/(16*(c - I*k0)*(2*c - I*k0))) - I*((-5*(c - I*k0)^7)/(128*(2*c - I*k0)) + ((c - I*k0)^5*(2*c - I*k0))/32 + ((c - I*k0)^3*(2*c - I*k0)^3)/64 + ((c - I*k0)*(2*c - I*k0)^5)/32 - (5*(2*c - I*k0)^7)/(128*(c - I*k0)) - (((c - I*k0)^5/(16*(2*c - I*k0)) - ((c - I*k0)^3*(2*c - I*k0))/16 - ((c - I*k0)*(2*c - I*k0)^3)/16 + (2*c - I*k0)^5/(16*(c - I*k0)))*k0^2)/2 - ((-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)))*k0^4)/8 - (((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*k0^6)/16 - (5*k0^8)/(128*(c - I*k0)*(2*c - I*k0))) + k0*(((-5*(c - I*k0)^7)/(128*(2*c - I*k0)) + ((c - I*k0)^5*(2*c - I*k0))/32 + ((c - I*k0)^3*(2*c - I*k0)^3)/64 + ((c - I*k0)*(2*c - I*k0)^5)/32 - (5*(2*c - I*k0)^7)/(128*(c - I*k0)))/(3*c - I*k0) + (((c - I*k0)^5/(16*(2*c - I*k0)) - ((c - I*k0)^3*(2*c - I*k0))/16 - ((c - I*k0)*(2*c - I*k0)^3)/16 + (2*c - I*k0)^5/(16*(c - I*k0)))*(3*c - I*k0))/2 - ((-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)))*(3*c - I*k0)^3)/8 + (((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*(3*c - I*k0)^5)/16 - (5*(3*c - I*k0)^7)/(128*(c - I*k0)*(2*c - I*k0)) - ((((c - I*k0)^5/(16*(2*c - I*k0)) - ((c - I*k0)^3*(2*c - I*k0))/16 - ((c - I*k0)*(2*c - I*k0)^3)/16 + (2*c - I*k0)^5/(16*(c - I*k0)))/(3*c - I*k0) + ((-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)))*(3*c - I*k0))/2 - (((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*(3*c - I*k0)^3)/8 + (3*c - I*k0)^5/(16*(c - I*k0)*(2*c - I*k0)))*k0^2)/2 - (((-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)))/(3*c - I*k0) + (((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*(3*c - I*k0))/2 - (3*c - I*k0)^3/(8*(c - I*k0)*(2*c - I*k0)))*k0^4)/8 - ((((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))/(3*c - I*k0) + (3*c - I*k0)/(2*(c - I*k0)*(2*c - I*k0)))*k0^6)/16 - (5*k0^8)/(128*(c - I*k0)*(2*c - I*k0)*(3*c - I*k0))) - I*k0*(I*(((-5*(c - I*k0)^7)/(128*(2*c - I*k0)) + ((c - I*k0)^5*(2*c - I*k0))/32 + ((c - I*k0)^3*(2*c - I*k0)^3)/64 + ((c - I*k0)*(2*c - I*k0)^5)/32 - (5*(2*c - I*k0)^7)/(128*(c - I*k0)))/(3*c - I*k0) + (((c - I*k0)^5/(16*(2*c - I*k0)) - ((c - I*k0)^3*(2*c - I*k0))/16 - ((c - I*k0)*(2*c - I*k0)^3)/16 + (2*c - I*k0)^5/(16*(c - I*k0)))*(3*c - I*k0))/2 - ((-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)))*(3*c - I*k0)^3)/8 + (((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*(3*c - I*k0)^5)/16 - (5*(3*c - I*k0)^7)/(128*(c - I*k0)*(2*c - I*k0))) - I/2*(((c - I*k0)^5/(16*(2*c - I*k0)) - ((c - I*k0)^3*(2*c - I*k0))/16 - ((c - I*k0)*(2*c - I*k0)^3)/16 + (2*c - I*k0)^5/(16*(c - I*k0)))/(3*c - I*k0) + ((-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)))*(3*c - I*k0))/2 - (((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*(3*c - I*k0)^3)/8 + (3*c - I*k0)^5/(16*(c - I*k0)*(2*c - I*k0)))*k0^2 - I/8*((-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)))/(3*c - I*k0) + (((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*(3*c - I*k0))/2 - (3*c - I*k0)^3/(8*(c - I*k0)*(2*c - I*k0)))*k0^4 - I/16*(((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))/(3*c - I*k0) + (3*c - I*k0)/(2*(c - I*k0)*(2*c - I*k0)))*k0^6 - ((5*I)/128*k0^8)/((c - I*k0)*(2*c - I*k0)*(3*c - I*k0))) + 3*(((-5*I)/128*k0^8)/((c - I*k0)*(3*c - I*k0)) - I/16*k0^6*((c - I*k0)/(2*(3*c - I*k0)) + (3*c - I*k0)/(2*(c - I*k0)) - k0^2/(2*(c - I*k0)*(3*c - I*k0))) - I/8*k0^4*(-(c - I*k0)^3/(8*(3*c - I*k0)) + ((c - I*k0)*(3*c - I*k0))/4 - (3*c - I*k0)^3/(8*(c - I*k0)) - (((c - I*k0)/(2*(3*c - I*k0)) + (3*c - I*k0)/(2*(c - I*k0)))*k0^2)/2 - k0^4/(8*(c - I*k0)*(3*c - I*k0))) - I/2*k0^2*((c - I*k0)^5/(16*(3*c - I*k0)) - ((c - I*k0)^3*(3*c - I*k0))/16 - ((c - I*k0)*(3*c - I*k0)^3)/16 + (3*c - I*k0)^5/(16*(c - I*k0)) - ((-(c - I*k0)^3/(8*(3*c - I*k0)) + ((c - I*k0)*(3*c - I*k0))/4 - (3*c - I*k0)^3/(8*(c - I*k0)))*k0^2)/2 - (((c - I*k0)/(2*(3*c - I*k0)) + (3*c - I*k0)/(2*(c - I*k0)))*k0^4)/8 - k0^6/(16*(c - I*k0)*(3*c - I*k0))) + I*((-5*(c - I*k0)^7)/(128*(3*c - I*k0)) + ((c - I*k0)^5*(3*c - I*k0))/32 + ((c - I*k0)^3*(3*c - I*k0)^3)/64 + ((c - I*k0)*(3*c - I*k0)^5)/32 - (5*(3*c - I*k0)^7)/(128*(c - I*k0)) - (((c - I*k0)^5/(16*(3*c - I*k0)) - ((c - I*k0)^3*(3*c - I*k0))/16 - ((c - I*k0)*(3*c - I*k0)^3)/16 + (3*c - I*k0)^5/(16*(c - I*k0)))*k0^2)/2 - ((-(c - I*k0)^3/(8*(3*c - I*k0)) + ((c - I*k0)*(3*c - I*k0))/4 - (3*c - I*k0)^3/(8*(c - I*k0)))*k0^4)/8 - (((c - I*k0)/(2*(3*c - I*k0)) + (3*c - I*k0)/(2*(c - I*k0)))*k0^6)/16 - (5*k0^8)/(128*(c - I*k0)*(3*c - I*k0)))) - 3*(((-5*I)/128*k0^8)/((2*c - I*k0)*(3*c - I*k0)) - I/16*k0^6*((2*c - I*k0)/(2*(3*c - I*k0)) + (3*c - I*k0)/(2*(2*c - I*k0)) - k0^2/(2*(2*c - I*k0)*(3*c - I*k0))) - I/8*k0^4*(-(2*c - I*k0)^3/(8*(3*c - I*k0)) + ((2*c - I*k0)*(3*c - I*k0))/4 - (3*c - I*k0)^3/(8*(2*c - I*k0)) - (((2*c - I*k0)/(2*(3*c - I*k0)) + (3*c - I*k0)/(2*(2*c - I*k0)))*k0^2)/2 - k0^4/(8*(2*c - I*k0)*(3*c - I*k0))) - I/2*k0^2*((2*c - I*k0)^5/(16*(3*c - I*k0)) - ((2*c - I*k0)^3*(3*c - I*k0))/16 - ((2*c - I*k0)*(3*c - I*k0)^3)/16 + (3*c - I*k0)^5/(16*(2*c - I*k0)) - ((-(2*c - I*k0)^3/(8*(3*c - I*k0)) + ((2*c - I*k0)*(3*c - I*k0))/4 - (3*c - I*k0)^3/(8*(2*c - I*k0)))*k0^2)/2 - (((2*c - I*k0)/(2*(3*c - I*k0)) + (3*c - I*k0)/(2*(2*c - I*k0)))*k0^4)/8 - k0^6/(16*(2*c - I*k0)*(3*c - I*k0))) + I*((-5*(2*c - I*k0)^7)/(128*(3*c - I*k0)) + ((2*c - I*k0)^5*(3*c - I*k0))/32 + ((2*c - I*k0)^3*(3*c - I*k0)^3)/64 + ((2*c - I*k0)*(3*c - I*k0)^5)/32 - (5*(3*c - I*k0)^7)/(128*(2*c - I*k0)) - (((2*c - I*k0)^5/(16*(3*c - I*k0)) - ((2*c - I*k0)^3*(3*c - I*k0))/16 - ((2*c - I*k0)*(3*c - I*k0)^3)/16 + (3*c - I*k0)^5/(16*(2*c - I*k0)))*k0^2)/2 - ((-(2*c - I*k0)^3/(8*(3*c - I*k0)) + ((2*c - I*k0)*(3*c - I*k0))/4 - (3*c - I*k0)^3/(8*(2*c - I*k0)))*k0^4)/8 - (((2*c - I*k0)/(2*(3*c - I*k0)) + (3*c - I*k0)/(2*(2*c - I*k0)))*k0^6)/16 - (5*k0^8)/(128*(2*c - I*k0)*(3*c - I*k0)))))) + (I*(c - I*k0)*(2*c - I*k0)*(3*c - I*k0)*(((7*I)/256*k0^10)/((c - I*k0)*(2*c - I*k0)) + (5*I)/128*k0^8*((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)) - k0^2/(2*(c - I*k0)*(2*c - I*k0))) + I/16*k0^6*(-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)) - (((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*k0^2)/2 - k0^4/(8*(c - I*k0)*(2*c - I*k0))) + I/8*k0^4*((c - I*k0)^5/(16*(2*c - I*k0)) - ((c - I*k0)^3*(2*c - I*k0))/16 - ((c - I*k0)*(2*c - I*k0)^3)/16 + (2*c - I*k0)^5/(16*(c - I*k0)) - ((-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)))*k0^2)/2 - (((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*k0^4)/8 - k0^6/(16*(c - I*k0)*(2*c - I*k0))) + I/2*k0^2*((-5*(c - I*k0)^7)/(128*(2*c - I*k0)) + ((c - I*k0)^5*(2*c - I*k0))/32 + ((c - I*k0)^3*(2*c - I*k0)^3)/64 + ((c - I*k0)*(2*c - I*k0)^5)/32 - (5*(2*c - I*k0)^7)/(128*(c - I*k0)) - (((c - I*k0)^5/(16*(2*c - I*k0)) - ((c - I*k0)^3*(2*c - I*k0))/16 - ((c - I*k0)*(2*c - I*k0)^3)/16 + (2*c - I*k0)^5/(16*(c - I*k0)))*k0^2)/2 - ((-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)))*k0^4)/8 - (((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*k0^6)/16 - (5*k0^8)/(128*(c - I*k0)*(2*c - I*k0))) - I*((7*(c - I*k0)^9)/(256*(2*c - I*k0)) - (5*(c - I*k0)^7*(2*c - I*k0))/256 - ((c - I*k0)^5*(2*c - I*k0)^3)/128 - ((c - I*k0)^3*(2*c - I*k0)^5)/128 - (5*(c - I*k0)*(2*c - I*k0)^7)/256 + (7*(2*c - I*k0)^9)/(256*(c - I*k0)) - (((-5*(c - I*k0)^7)/(128*(2*c - I*k0)) + ((c - I*k0)^5*(2*c - I*k0))/32 + ((c - I*k0)^3*(2*c - I*k0)^3)/64 + ((c - I*k0)*(2*c - I*k0)^5)/32 - (5*(2*c - I*k0)^7)/(128*(c - I*k0)))*k0^2)/2 - (((c - I*k0)^5/(16*(2*c - I*k0)) - ((c - I*k0)^3*(2*c - I*k0))/16 - ((c - I*k0)*(2*c - I*k0)^3)/16 + (2*c - I*k0)^5/(16*(c - I*k0)))*k0^4)/8 - ((-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)))*k0^6)/16 - (5*((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*k0^8)/128 - (7*k0^10)/(256*(c - I*k0)*(2*c - I*k0))) + k0*(((7*(c - I*k0)^9)/(256*(2*c - I*k0)) - (5*(c - I*k0)^7*(2*c - I*k0))/256 - ((c - I*k0)^5*(2*c - I*k0)^3)/128 - ((c - I*k0)^3*(2*c - I*k0)^5)/128 - (5*(c - I*k0)*(2*c - I*k0)^7)/256 + (7*(2*c - I*k0)^9)/(256*(c - I*k0)))/(3*c - I*k0) + (((-5*(c - I*k0)^7)/(128*(2*c - I*k0)) + ((c - I*k0)^5*(2*c - I*k0))/32 + ((c - I*k0)^3*(2*c - I*k0)^3)/64 + ((c - I*k0)*(2*c - I*k0)^5)/32 - (5*(2*c - I*k0)^7)/(128*(c - I*k0)))*(3*c - I*k0))/2 - (((c - I*k0)^5/(16*(2*c - I*k0)) - ((c - I*k0)^3*(2*c - I*k0))/16 - ((c - I*k0)*(2*c - I*k0)^3)/16 + (2*c - I*k0)^5/(16*(c - I*k0)))*(3*c - I*k0)^3)/8 + ((-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)))*(3*c - I*k0)^5)/16 - (5*((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*(3*c - I*k0)^7)/128 + (7*(3*c - I*k0)^9)/(256*(c - I*k0)*(2*c - I*k0)) - ((((-5*(c - I*k0)^7)/(128*(2*c - I*k0)) + ((c - I*k0)^5*(2*c - I*k0))/32 + ((c - I*k0)^3*(2*c - I*k0)^3)/64 + ((c - I*k0)*(2*c - I*k0)^5)/32 - (5*(2*c - I*k0)^7)/(128*(c - I*k0)))/(3*c - I*k0) + (((c - I*k0)^5/(16*(2*c - I*k0)) - ((c - I*k0)^3*(2*c - I*k0))/16 - ((c - I*k0)*(2*c - I*k0)^3)/16 + (2*c - I*k0)^5/(16*(c - I*k0)))*(3*c - I*k0))/2 - ((-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)))*(3*c - I*k0)^3)/8 + (((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*(3*c - I*k0)^5)/16 - (5*(3*c - I*k0)^7)/(128*(c - I*k0)*(2*c - I*k0)))*k0^2)/2 - ((((c - I*k0)^5/(16*(2*c - I*k0)) - ((c - I*k0)^3*(2*c - I*k0))/16 - ((c - I*k0)*(2*c - I*k0)^3)/16 + (2*c - I*k0)^5/(16*(c - I*k0)))/(3*c - I*k0) + ((-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)))*(3*c - I*k0))/2 - (((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*(3*c - I*k0)^3)/8 + (3*c - I*k0)^5/(16*(c - I*k0)*(2*c - I*k0)))*k0^4)/8 - (((-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)))/(3*c - I*k0) + (((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*(3*c - I*k0))/2 - (3*c - I*k0)^3/(8*(c - I*k0)*(2*c - I*k0)))*k0^6)/16 - (5*(((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))/(3*c - I*k0) + (3*c - I*k0)/(2*(c - I*k0)*(2*c - I*k0)))*k0^8)/128 - (7*k0^10)/(256*(c - I*k0)*(2*c - I*k0)*(3*c - I*k0))) - I*k0*(I*(((7*(c - I*k0)^9)/(256*(2*c - I*k0)) - (5*(c - I*k0)^7*(2*c - I*k0))/256 - ((c - I*k0)^5*(2*c - I*k0)^3)/128 - ((c - I*k0)^3*(2*c - I*k0)^5)/128 - (5*(c - I*k0)*(2*c - I*k0)^7)/256 + (7*(2*c - I*k0)^9)/(256*(c - I*k0)))/(3*c - I*k0) + (((-5*(c - I*k0)^7)/(128*(2*c - I*k0)) + ((c - I*k0)^5*(2*c - I*k0))/32 + ((c - I*k0)^3*(2*c - I*k0)^3)/64 + ((c - I*k0)*(2*c - I*k0)^5)/32 - (5*(2*c - I*k0)^7)/(128*(c - I*k0)))*(3*c - I*k0))/2 - (((c - I*k0)^5/(16*(2*c - I*k0)) - ((c - I*k0)^3*(2*c - I*k0))/16 - ((c - I*k0)*(2*c - I*k0)^3)/16 + (2*c - I*k0)^5/(16*(c - I*k0)))*(3*c - I*k0)^3)/8 + ((-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)))*(3*c - I*k0)^5)/16 - (5*((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*(3*c - I*k0)^7)/128 + (7*(3*c - I*k0)^9)/(256*(c - I*k0)*(2*c - I*k0))) - I/2*(((-5*(c - I*k0)^7)/(128*(2*c - I*k0)) + ((c - I*k0)^5*(2*c - I*k0))/32 + ((c - I*k0)^3*(2*c - I*k0)^3)/64 + ((c - I*k0)*(2*c - I*k0)^5)/32 - (5*(2*c - I*k0)^7)/(128*(c - I*k0)))/(3*c - I*k0) + (((c - I*k0)^5/(16*(2*c - I*k0)) - ((c - I*k0)^3*(2*c - I*k0))/16 - ((c - I*k0)*(2*c - I*k0)^3)/16 + (2*c - I*k0)^5/(16*(c - I*k0)))*(3*c - I*k0))/2 - ((-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)))*(3*c - I*k0)^3)/8 + (((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*(3*c - I*k0)^5)/16 - (5*(3*c - I*k0)^7)/(128*(c - I*k0)*(2*c - I*k0)))*k0^2 - I/8*(((c - I*k0)^5/(16*(2*c - I*k0)) - ((c - I*k0)^3*(2*c - I*k0))/16 - ((c - I*k0)*(2*c - I*k0)^3)/16 + (2*c - I*k0)^5/(16*(c - I*k0)))/(3*c - I*k0) + ((-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)))*(3*c - I*k0))/2 - (((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*(3*c - I*k0)^3)/8 + (3*c - I*k0)^5/(16*(c - I*k0)*(2*c - I*k0)))*k0^4 - I/16*((-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)))/(3*c - I*k0) + (((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*(3*c - I*k0))/2 - (3*c - I*k0)^3/(8*(c - I*k0)*(2*c - I*k0)))*k0^6 - (5*I)/128*(((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))/(3*c - I*k0) + (3*c - I*k0)/(2*(c - I*k0)*(2*c - I*k0)))*k0^8 - ((7*I)/256*k0^10)/((c - I*k0)*(2*c - I*k0)*(3*c - I*k0))) + 3*(((-7*I)/256*k0^10)/((c - I*k0)*(3*c - I*k0)) - (5*I)/128*k0^8*((c - I*k0)/(2*(3*c - I*k0)) + (3*c - I*k0)/(2*(c - I*k0)) - k0^2/(2*(c - I*k0)*(3*c - I*k0))) - I/16*k0^6*(-(c - I*k0)^3/(8*(3*c - I*k0)) + ((c - I*k0)*(3*c - I*k0))/4 - (3*c - I*k0)^3/(8*(c - I*k0)) - (((c - I*k0)/(2*(3*c - I*k0)) + (3*c - I*k0)/(2*(c - I*k0)))*k0^2)/2 - k0^4/(8*(c - I*k0)*(3*c - I*k0))) - I/8*k0^4*((c - I*k0)^5/(16*(3*c - I*k0)) - ((c - I*k0)^3*(3*c - I*k0))/16 - ((c - I*k0)*(3*c - I*k0)^3)/16 + (3*c - I*k0)^5/(16*(c - I*k0)) - ((-(c - I*k0)^3/(8*(3*c - I*k0)) + ((c - I*k0)*(3*c - I*k0))/4 - (3*c - I*k0)^3/(8*(c - I*k0)))*k0^2)/2 - (((c - I*k0)/(2*(3*c - I*k0)) + (3*c - I*k0)/(2*(c - I*k0)))*k0^4)/8 - k0^6/(16*(c - I*k0)*(3*c - I*k0))) - I/2*k0^2*((-5*(c - I*k0)^7)/(128*(3*c - I*k0)) + ((c - I*k0)^5*(3*c - I*k0))/32 + ((c - I*k0)^3*(3*c - I*k0)^3)/64 + ((c - I*k0)*(3*c - I*k0)^5)/32 - (5*(3*c - I*k0)^7)/(128*(c - I*k0)) - (((c - I*k0)^5/(16*(3*c - I*k0)) - ((c - I*k0)^3*(3*c - I*k0))/16 - ((c - I*k0)*(3*c - I*k0)^3)/16 + (3*c - I*k0)^5/(16*(c - I*k0)))*k0^2)/2 - ((-(c - I*k0)^3/(8*(3*c - I*k0)) + ((c - I*k0)*(3*c - I*k0))/4 - (3*c - I*k0)^3/(8*(c - I*k0)))*k0^4)/8 - (((c - I*k0)/(2*(3*c - I*k0)) + (3*c - I*k0)/(2*(c - I*k0)))*k0^6)/16 - (5*k0^8)/(128*(c - I*k0)*(3*c - I*k0))) + I*((7*(c - I*k0)^9)/(256*(3*c - I*k0)) - (5*(c - I*k0)^7*(3*c - I*k0))/256 - ((c - I*k0)^5*(3*c - I*k0)^3)/128 - ((c - I*k0)^3*(3*c - I*k0)^5)/128 - (5*(c - I*k0)*(3*c - I*k0)^7)/256 + (7*(3*c - I*k0)^9)/(256*(c - I*k0)) - (((-5*(c - I*k0)^7)/(128*(3*c - I*k0)) + ((c - I*k0)^5*(3*c - I*k0))/32 + ((c - I*k0)^3*(3*c - I*k0)^3)/64 + ((c - I*k0)*(3*c - I*k0)^5)/32 - (5*(3*c - I*k0)^7)/(128*(c - I*k0)))*k0^2)/2 - (((c - I*k0)^5/(16*(3*c - I*k0)) - ((c - I*k0)^3*(3*c - I*k0))/16 - ((c - I*k0)*(3*c - I*k0)^3)/16 + (3*c - I*k0)^5/(16*(c - I*k0)))*k0^4)/8 - ((-(c - I*k0)^3/(8*(3*c - I*k0)) + ((c - I*k0)*(3*c - I*k0))/4 - (3*c - I*k0)^3/(8*(c - I*k0)))*k0^6)/16 - (5*((c - I*k0)/(2*(3*c - I*k0)) + (3*c - I*k0)/(2*(c - I*k0)))*k0^8)/128 - (7*k0^10)/(256*(c - I*k0)*(3*c - I*k0)))) - 3*(((-7*I)/256*k0^10)/((2*c - I*k0)*(3*c - I*k0)) - (5*I)/128*k0^8*((2*c - I*k0)/(2*(3*c - I*k0)) + (3*c - I*k0)/(2*(2*c - I*k0)) - k0^2/(2*(2*c - I*k0)*(3*c - I*k0))) - I/16*k0^6*(-(2*c - I*k0)^3/(8*(3*c - I*k0)) + ((2*c - I*k0)*(3*c - I*k0))/4 - (3*c - I*k0)^3/(8*(2*c - I*k0)) - (((2*c - I*k0)/(2*(3*c - I*k0)) + (3*c - I*k0)/(2*(2*c - I*k0)))*k0^2)/2 - k0^4/(8*(2*c - I*k0)*(3*c - I*k0))) - I/8*k0^4*((2*c - I*k0)^5/(16*(3*c - I*k0)) - ((2*c - I*k0)^3*(3*c - I*k0))/16 - ((2*c - I*k0)*(3*c - I*k0)^3)/16 + (3*c - I*k0)^5/(16*(2*c - I*k0)) - ((-(2*c - I*k0)^3/(8*(3*c - I*k0)) + ((2*c - I*k0)*(3*c - I*k0))/4 - (3*c - I*k0)^3/(8*(2*c - I*k0)))*k0^2)/2 - (((2*c - I*k0)/(2*(3*c - I*k0)) + (3*c - I*k0)/(2*(2*c - I*k0)))*k0^4)/8 - k0^6/(16*(2*c - I*k0)*(3*c - I*k0))) - I/2*k0^2*((-5*(2*c - I*k0)^7)/(128*(3*c - I*k0)) + ((2*c - I*k0)^5*(3*c - I*k0))/32 + ((2*c - I*k0)^3*(3*c - I*k0)^3)/64 + ((2*c - I*k0)*(3*c - I*k0)^5)/32 - (5*(3*c - I*k0)^7)/(128*(2*c - I*k0)) - (((2*c - I*k0)^5/(16*(3*c - I*k0)) - ((2*c - I*k0)^3*(3*c - I*k0))/16 - ((2*c - I*k0)*(3*c - I*k0)^3)/16 + (3*c - I*k0)^5/(16*(2*c - I*k0)))*k0^2)/2 - ((-(2*c - I*k0)^3/(8*(3*c - I*k0)) + ((2*c - I*k0)*(3*c - I*k0))/4 - (3*c - I*k0)^3/(8*(2*c - I*k0)))*k0^4)/8 - (((2*c - I*k0)/(2*(3*c - I*k0)) + (3*c - I*k0)/(2*(2*c - I*k0)))*k0^6)/16 - (5*k0^8)/(128*(2*c - I*k0)*(3*c - I*k0))) + I*((7*(2*c - I*k0)^9)/(256*(3*c - I*k0)) - (5*(2*c - I*k0)^7*(3*c - I*k0))/256 - ((2*c - I*k0)^5*(3*c - I*k0)^3)/128 - ((2*c - I*k0)^3*(3*c - I*k0)^5)/128 - (5*(2*c - I*k0)*(3*c - I*k0)^7)/256 + (7*(3*c - I*k0)^9)/(256*(2*c - I*k0)) - (((-5*(2*c - I*k0)^7)/(128*(3*c - I*k0)) + ((2*c - I*k0)^5*(3*c - I*k0))/32 + ((2*c - I*k0)^3*(3*c - I*k0)^3)/64 + ((2*c - I*k0)*(3*c - I*k0)^5)/32 - (5*(3*c - I*k0)^7)/(128*(2*c - I*k0)))*k0^2)/2 - (((2*c - I*k0)^5/(16*(3*c - I*k0)) - ((2*c - I*k0)^3*(3*c - I*k0))/16 - ((2*c - I*k0)*(3*c - I*k0)^3)/16 + (3*c - I*k0)^5/(16*(2*c - I*k0)))*k0^4)/8 - ((-(2*c - I*k0)^3/(8*(3*c - I*k0)) + ((2*c - I*k0)*(3*c - I*k0))/4 - (3*c - I*k0)^3/(8*(2*c - I*k0)))*k0^6)/16 - (5*((2*c - I*k0)/(2*(3*c - I*k0)) + (3*c - I*k0)/(2*(2*c - I*k0)))*k0^8)/128 - (7*k0^10)/(256*(2*c - I*k0)*(3*c - I*k0))))))/k^3 - ((I/16*k0^6)/((c - I*k0)*(2*c - I*k0)) + I/8*k0^4*((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)) - k0^2/(2*(c - I*k0)*(2*c - I*k0))) + I/2*k0^2*(-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)) - (((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*k0^2)/2 - k0^4/(8*(c - I*k0)*(2*c - I*k0))) - I*((c - I*k0)^5/(16*(2*c - I*k0)) - ((c - I*k0)^3*(2*c - I*k0))/16 - ((c - I*k0)*(2*c - I*k0)^3)/16 + (2*c - I*k0)^5/(16*(c - I*k0)) - ((-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)))*k0^2)/2 - (((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*k0^4)/8 - k0^6/(16*(c - I*k0)*(2*c - I*k0))) + k0*(((c - I*k0)^5/(16*(2*c - I*k0)) - ((c - I*k0)^3*(2*c - I*k0))/16 - ((c - I*k0)*(2*c - I*k0)^3)/16 + (2*c - I*k0)^5/(16*(c - I*k0)))/(3*c - I*k0) + ((-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)))*(3*c - I*k0))/2 - (((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*(3*c - I*k0)^3)/8 + (3*c - I*k0)^5/(16*(c - I*k0)*(2*c - I*k0)) - (((-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)))/(3*c - I*k0) + (((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*(3*c - I*k0))/2 - (3*c - I*k0)^3/(8*(c - I*k0)*(2*c - I*k0)))*k0^2)/2 - ((((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))/(3*c - I*k0) + (3*c - I*k0)/(2*(c - I*k0)*(2*c - I*k0)))*k0^4)/8 - k0^6/(16*(c - I*k0)*(2*c - I*k0)*(3*c - I*k0))) - I*k0*(I*(((c - I*k0)^5/(16*(2*c - I*k0)) - ((c - I*k0)^3*(2*c - I*k0))/16 - ((c - I*k0)*(2*c - I*k0)^3)/16 + (2*c - I*k0)^5/(16*(c - I*k0)))/(3*c - I*k0) + ((-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)))*(3*c - I*k0))/2 - (((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*(3*c - I*k0)^3)/8 + (3*c - I*k0)^5/(16*(c - I*k0)*(2*c - I*k0))) - I/2*((-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)))/(3*c - I*k0) + (((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*(3*c - I*k0))/2 - (3*c - I*k0)^3/(8*(c - I*k0)*(2*c - I*k0)))*k0^2 - I/8*(((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))/(3*c - I*k0) + (3*c - I*k0)/(2*(c - I*k0)*(2*c - I*k0)))*k0^4 - (I/16*k0^6)/((c - I*k0)*(2*c - I*k0)*(3*c - I*k0))) + 3*((-I/16*k0^6)/((c - I*k0)*(3*c - I*k0)) - I/8*k0^4*((c - I*k0)/(2*(3*c - I*k0)) + (3*c - I*k0)/(2*(c - I*k0)) - k0^2/(2*(c - I*k0)*(3*c - I*k0))) - I/2*k0^2*(-(c - I*k0)^3/(8*(3*c - I*k0)) + ((c - I*k0)*(3*c - I*k0))/4 - (3*c - I*k0)^3/(8*(c - I*k0)) - (((c - I*k0)/(2*(3*c - I*k0)) + (3*c - I*k0)/(2*(c - I*k0)))*k0^2)/2 - k0^4/(8*(c - I*k0)*(3*c - I*k0))) + I*((c - I*k0)^5/(16*(3*c - I*k0)) - ((c - I*k0)^3*(3*c - I*k0))/16 - ((c - I*k0)*(3*c - I*k0)^3)/16 + (3*c - I*k0)^5/(16*(c - I*k0)) - ((-(c - I*k0)^3/(8*(3*c - I*k0)) + ((c - I*k0)*(3*c - I*k0))/4 - (3*c - I*k0)^3/(8*(c - I*k0)))*k0^2)/2 - (((c - I*k0)/(2*(3*c - I*k0)) + (3*c - I*k0)/(2*(c - I*k0)))*k0^4)/8 - k0^6/(16*(c - I*k0)*(3*c - I*k0)))) - 3*((-I/16*k0^6)/((2*c - I*k0)*(3*c - I*k0)) - I/8*k0^4*((2*c - I*k0)/(2*(3*c - I*k0)) + (3*c - I*k0)/(2*(2*c - I*k0)) - k0^2/(2*(2*c - I*k0)*(3*c - I*k0))) - I/2*k0^2*(-(2*c - I*k0)^3/(8*(3*c - I*k0)) + ((2*c - I*k0)*(3*c - I*k0))/4 - (3*c - I*k0)^3/(8*(2*c - I*k0)) - (((2*c - I*k0)/(2*(3*c - I*k0)) + (3*c - I*k0)/(2*(2*c - I*k0)))*k0^2)/2 - k0^4/(8*(2*c - I*k0)*(3*c - I*k0))) + I*((2*c - I*k0)^5/(16*(3*c - I*k0)) - ((2*c - I*k0)^3*(3*c - I*k0))/16 - ((2*c - I*k0)*(3*c - I*k0)^3)/16 + (3*c - I*k0)^5/(16*(2*c - I*k0)) - ((-(2*c - I*k0)^3/(8*(3*c - I*k0)) + ((2*c - I*k0)*(3*c - I*k0))/4 - (3*c - I*k0)^3/(8*(2*c - I*k0)))*k0^2)/2 - (((2*c - I*k0)/(2*(3*c - I*k0)) + (3*c - I*k0)/(2*(2*c - I*k0)))*k0^4)/8 - k0^6/(16*(2*c - I*k0)*(3*c - I*k0)))))*(((-3*I)/8*(c - I*k0)*(2*c - I*k0)*(3*c - I*k0)*k0^4)/k^3 - I/2*k0^2*(((-((c - I*k0)^3*(2*c - I*k0))/(2*k^2) - ((c - I*k0)*(2*c - I*k0)^3)/(2*k^2))*(3*c - I*k0))/k - ((c - I*k0)*(2*c - I*k0)*(3*c - I*k0)^3)/(2*k^3) + ((c - I*k0)*(2*c - I*k0)*(3*c - I*k0)*k0^2)/(2*k^3)) - I*(-((-((c - I*k0)^3*(2*c - I*k0))/(2*k^2) - ((c - I*k0)*(2*c - I*k0)^3)/(2*k^2))*(3*c - I*k0)^3)/(2*k) + ((((-((c - I*k0)^3*(2*c - I*k0))/(2*k^2) - ((c - I*k0)*(2*c - I*k0)^3)/(2*k^2))*(3*c - I*k0))/k - ((c - I*k0)*(2*c - I*k0)*(3*c - I*k0)^3)/(2*k^3))*k0^2)/2 + (3*(c - I*k0)*(2*c - I*k0)*(3*c - I*k0)*k0^4)/(8*k^3) + (3*(c - I*k0)*(2*c - I*k0)*(3*c - I*k0)^4*((3*c)/k - (I*k0)/k))/(8*k^2) + ((3*c - I*k0)*(((c - I*k0)^3*(2*c - I*k0)^3)/(4*k^2) + (3*(c - I*k0)^4*(2*c - I*k0)*(c/k - (I*k0)/k))/(8*k) + (3*(c - I*k0)*(2*c - I*k0)^4*((2*c)/k - (I*k0)/k))/(8*k)))/k)) - ((I/8*k0^4)/((c - I*k0)*(2*c - I*k0)) + I/2*k0^2*((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)) - k0^2/(2*(c - I*k0)*(2*c - I*k0))) - I*(-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)) - (((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*k0^2)/2 - k0^4/(8*(c - I*k0)*(2*c - I*k0))) + k0*((-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)))/(3*c - I*k0) + (((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*(3*c - I*k0))/2 - (3*c - I*k0)^3/(8*(c - I*k0)*(2*c - I*k0)) - ((((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))/(3*c - I*k0) + (3*c - I*k0)/(2*(c - I*k0)*(2*c - I*k0)))*k0^2)/2 - k0^4/(8*(c - I*k0)*(2*c - I*k0)*(3*c - I*k0))) - I*k0*(I*((-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)))/(3*c - I*k0) + (((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*(3*c - I*k0))/2 - (3*c - I*k0)^3/(8*(c - I*k0)*(2*c - I*k0))) - I/2*(((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))/(3*c - I*k0) + (3*c - I*k0)/(2*(c - I*k0)*(2*c - I*k0)))*k0^2 - (I/8*k0^4)/((c - I*k0)*(2*c - I*k0)*(3*c - I*k0))) + 3*((-I/8*k0^4)/((c - I*k0)*(3*c - I*k0)) - I/2*k0^2*((c - I*k0)/(2*(3*c - I*k0)) + (3*c - I*k0)/(2*(c - I*k0)) - k0^2/(2*(c - I*k0)*(3*c - I*k0))) + I*(-(c - I*k0)^3/(8*(3*c - I*k0)) + ((c - I*k0)*(3*c - I*k0))/4 - (3*c - I*k0)^3/(8*(c - I*k0)) - (((c - I*k0)/(2*(3*c - I*k0)) + (3*c - I*k0)/(2*(c - I*k0)))*k0^2)/2 - k0^4/(8*(c - I*k0)*(3*c - I*k0)))) - 3*((-I/8*k0^4)/((2*c - I*k0)*(3*c - I*k0)) - I/2*k0^2*((2*c - I*k0)/(2*(3*c - I*k0)) + (3*c - I*k0)/(2*(2*c - I*k0)) - k0^2/(2*(2*c - I*k0)*(3*c - I*k0))) + I*(-(2*c - I*k0)^3/(8*(3*c - I*k0)) + ((2*c - I*k0)*(3*c - I*k0))/4 - (3*c - I*k0)^3/(8*(2*c - I*k0)) - (((2*c - I*k0)/(2*(3*c - I*k0)) + (3*c - I*k0)/(2*(2*c - I*k0)))*k0^2)/2 - k0^4/(8*(2*c - I*k0)*(3*c - I*k0)))))*(((-5*I)/16*(c - I*k0)*(2*c - I*k0)*(3*c - I*k0)*k0^6)/k^3 - (3*I)/8*k0^4*(((-((c - I*k0)^3*(2*c - I*k0))/(2*k^2) - ((c - I*k0)*(2*c - I*k0)^3)/(2*k^2))*(3*c - I*k0))/k - ((c - I*k0)*(2*c - I*k0)*(3*c - I*k0)^3)/(2*k^3) + ((c - I*k0)*(2*c - I*k0)*(3*c - I*k0)*k0^2)/(2*k^3)) - I/2*k0^2*(-((-((c - I*k0)^3*(2*c - I*k0))/(2*k^2) - ((c - I*k0)*(2*c - I*k0)^3)/(2*k^2))*(3*c - I*k0)^3)/(2*k) + ((((-((c - I*k0)^3*(2*c - I*k0))/(2*k^2) - ((c - I*k0)*(2*c - I*k0)^3)/(2*k^2))*(3*c - I*k0))/k - ((c - I*k0)*(2*c - I*k0)*(3*c - I*k0)^3)/(2*k^3))*k0^2)/2 + (3*(c - I*k0)*(2*c - I*k0)*(3*c - I*k0)*k0^4)/(8*k^3) + (3*(c - I*k0)*(2*c - I*k0)*(3*c - I*k0)^4*((3*c)/k - (I*k0)/k))/(8*k^2) + ((3*c - I*k0)*(((c - I*k0)^3*(2*c - I*k0)^3)/(4*k^2) + (3*(c - I*k0)^4*(2*c - I*k0)*(c/k - (I*k0)/k))/(8*k) + (3*(c - I*k0)*(2*c - I*k0)^4*((2*c)/k - (I*k0)/k))/(8*k)))/k) - I*((3*(((-((c - I*k0)^3*(2*c - I*k0))/(2*k^2) - ((c - I*k0)*(2*c - I*k0)^3)/(2*k^2))*(3*c - I*k0))/k - ((c - I*k0)*(2*c - I*k0)*(3*c - I*k0)^3)/(2*k^3))*k0^4)/8 + (5*(c - I*k0)*(2*c - I*k0)*(3*c - I*k0)*k0^6)/(16*k^3) + (3*(-((c - I*k0)^3*(2*c - I*k0))/(2*k^2) - ((c - I*k0)*(2*c - I*k0)^3)/(2*k^2))*(3*c - I*k0)^4*((3*c)/k - (I*k0)/k))/8 - (5*(c - I*k0)*(2*c - I*k0)*(3*c - I*k0)^6*((3*c)/k - (I*k0)/k))/(16*k^2) - ((3*c - I*k0)^3*(((c - I*k0)^3*(2*c - I*k0)^3)/(4*k^2) + (3*(c - I*k0)^4*(2*c - I*k0)*(c/k - (I*k0)/k))/(8*k) + (3*(c - I*k0)*(2*c - I*k0)^4*((2*c)/k - (I*k0)/k))/(8*k)))/(2*k) + ((3*c - I*k0)*((-5*(c - I*k0)^6*(2*c - I*k0)*(c/k - (I*k0)/k))/(16*k) - (3*(c - I*k0)^4*(2*c - I*k0)^3*(c/k - (I*k0)/k))/(16*k) - (3*(c - I*k0)^3*(2*c - I*k0)^4*((2*c)/k - (I*k0)/k))/(16*k) - (5*(c - I*k0)*(2*c - I*k0)^6*((2*c)/k - (I*k0)/k))/(16*k)))/k + (k0^2*(-((-((c - I*k0)^3*(2*c - I*k0))/(2*k^2) - ((c - I*k0)*(2*c - I*k0)^3)/(2*k^2))*(3*c - I*k0)^3)/(2*k) + (3*(c - I*k0)*(2*c - I*k0)*(3*c - I*k0)^4*((3*c)/k - (I*k0)/k))/(8*k^2) + ((3*c - I*k0)*(((c - I*k0)^3*(2*c - I*k0)^3)/(4*k^2) + (3*(c - I*k0)^4*(2*c - I*k0)*(c/k - (I*k0)/k))/(8*k) + (3*(c - I*k0)*(2*c - I*k0)^4*((2*c)/k - (I*k0)/k))/(8*k)))/k))/2)) - (((3*I)*c^2 + 4*c*k0 - (2*I)*k0^2)*(((-35*I)/128*(c - I*k0)*(2*c - I*k0)*(3*c - I*k0)*k0^8)/k^3 - (5*I)/16*k0^6*(((-((c - I*k0)^3*(2*c - I*k0))/(2*k^2) - ((c - I*k0)*(2*c - I*k0)^3)/(2*k^2))*(3*c - I*k0))/k - ((c - I*k0)*(2*c - I*k0)*(3*c - I*k0)^3)/(2*k^3) + ((c - I*k0)*(2*c - I*k0)*(3*c - I*k0)*k0^2)/(2*k^3)) - (3*I)/8*k0^4*(-((-((c - I*k0)^3*(2*c - I*k0))/(2*k^2) - ((c - I*k0)*(2*c - I*k0)^3)/(2*k^2))*(3*c - I*k0)^3)/(2*k) + ((((-((c - I*k0)^3*(2*c - I*k0))/(2*k^2) - ((c - I*k0)*(2*c - I*k0)^3)/(2*k^2))*(3*c - I*k0))/k - ((c - I*k0)*(2*c - I*k0)*(3*c - I*k0)^3)/(2*k^3))*k0^2)/2 + (3*(c - I*k0)*(2*c - I*k0)*(3*c - I*k0)*k0^4)/(8*k^3) + (3*(c - I*k0)*(2*c - I*k0)*(3*c - I*k0)^4*((3*c)/k - (I*k0)/k))/(8*k^2) + ((3*c - I*k0)*(((c - I*k0)^3*(2*c - I*k0)^3)/(4*k^2) + (3*(c - I*k0)^4*(2*c - I*k0)*(c/k - (I*k0)/k))/(8*k) + (3*(c - I*k0)*(2*c - I*k0)^4*((2*c)/k - (I*k0)/k))/(8*k)))/k) - I/2*k0^2*((3*(((-((c - I*k0)^3*(2*c - I*k0))/(2*k^2) - ((c - I*k0)*(2*c - I*k0)^3)/(2*k^2))*(3*c - I*k0))/k - ((c - I*k0)*(2*c - I*k0)*(3*c - I*k0)^3)/(2*k^3))*k0^4)/8 + (5*(c - I*k0)*(2*c - I*k0)*(3*c - I*k0)*k0^6)/(16*k^3) + (3*(-((c - I*k0)^3*(2*c - I*k0))/(2*k^2) - ((c - I*k0)*(2*c - I*k0)^3)/(2*k^2))*(3*c - I*k0)^4*((3*c)/k - (I*k0)/k))/8 - (5*(c - I*k0)*(2*c - I*k0)*(3*c - I*k0)^6*((3*c)/k - (I*k0)/k))/(16*k^2) - ((3*c - I*k0)^3*(((c - I*k0)^3*(2*c - I*k0)^3)/(4*k^2) + (3*(c - I*k0)^4*(2*c - I*k0)*(c/k - (I*k0)/k))/(8*k) + (3*(c - I*k0)*(2*c - I*k0)^4*((2*c)/k - (I*k0)/k))/(8*k)))/(2*k) + ((3*c - I*k0)*((-5*(c - I*k0)^6*(2*c - I*k0)*(c/k - (I*k0)/k))/(16*k) - (3*(c - I*k0)^4*(2*c - I*k0)^3*(c/k - (I*k0)/k))/(16*k) - (3*(c - I*k0)^3*(2*c - I*k0)^4*((2*c)/k - (I*k0)/k))/(16*k) - (5*(c - I*k0)*(2*c - I*k0)^6*((2*c)/k - (I*k0)/k))/(16*k)))/k + (k0^2*(-((-((c - I*k0)^3*(2*c - I*k0))/(2*k^2) - ((c - I*k0)*(2*c - I*k0)^3)/(2*k^2))*(3*c - I*k0)^3)/(2*k) + (3*(c - I*k0)*(2*c - I*k0)*(3*c - I*k0)^4*((3*c)/k - (I*k0)/k))/(8*k^2) + ((3*c - I*k0)*(((c - I*k0)^3*(2*c - I*k0)^3)/(4*k^2) + (3*(c - I*k0)^4*(2*c - I*k0)*(c/k - (I*k0)/k))/(8*k) + (3*(c - I*k0)*(2*c - I*k0)^4*((2*c)/k - (I*k0)/k))/(8*k)))/k))/2) - I*((5*(((-((c - I*k0)^3*(2*c - I*k0))/(2*k^2) - ((c - I*k0)*(2*c - I*k0)^3)/(2*k^2))*(3*c - I*k0))/k - ((c - I*k0)*(2*c - I*k0)*(3*c - I*k0)^3)/(2*k^3))*k0^6)/16 + (35*(c - I*k0)*(2*c - I*k0)*(3*c - I*k0)*k0^8)/(128*k^3) - (5*(-((c - I*k0)^3*(2*c - I*k0))/(2*k^2) - ((c - I*k0)*(2*c - I*k0)^3)/(2*k^2))*(3*c - I*k0)^6*((3*c)/k - (I*k0)/k))/16 + (35*(c - I*k0)*(2*c - I*k0)*(3*c - I*k0)^8*((3*c)/k - (I*k0)/k))/(128*k^2) + (3*(3*c - I*k0)^4*((3*c)/k - (I*k0)/k)*(((c - I*k0)^3*(2*c - I*k0)^3)/(4*k^2) + (3*(c - I*k0)^4*(2*c - I*k0)*(c/k - (I*k0)/k))/(8*k) + (3*(c - I*k0)*(2*c - I*k0)^4*((2*c)/k - (I*k0)/k))/(8*k)))/8 - ((3*c - I*k0)^3*((-5*(c - I*k0)^6*(2*c - I*k0)*(c/k - (I*k0)/k))/(16*k) - (3*(c - I*k0)^4*(2*c - I*k0)^3*(c/k - (I*k0)/k))/(16*k) - (3*(c - I*k0)^3*(2*c - I*k0)^4*((2*c)/k - (I*k0)/k))/(16*k) - (5*(c - I*k0)*(2*c - I*k0)^6*((2*c)/k - (I*k0)/k))/(16*k)))/(2*k) + ((3*c - I*k0)*((35*(c - I*k0)^8*(2*c - I*k0)*(c/k - (I*k0)/k))/(128*k) + (5*(c - I*k0)^6*(2*c - I*k0)^3*(c/k - (I*k0)/k))/(32*k) + (5*(c - I*k0)^3*(2*c - I*k0)^6*((2*c)/k - (I*k0)/k))/(32*k) + (35*(c - I*k0)*(2*c - I*k0)^8*((2*c)/k - (I*k0)/k))/(128*k) + (9*(c - I*k0)^4*(2*c - I*k0)^4*(c/k - (I*k0)/k)*((2*c)/k - (I*k0)/k))/64))/k + (3*k0^4*(-((-((c - I*k0)^3*(2*c - I*k0))/(2*k^2) - ((c - I*k0)*(2*c - I*k0)^3)/(2*k^2))*(3*c - I*k0)^3)/(2*k) + (3*(c - I*k0)*(2*c - I*k0)*(3*c - I*k0)^4*((3*c)/k - (I*k0)/k))/(8*k^2) + ((3*c - I*k0)*(((c - I*k0)^3*(2*c - I*k0)^3)/(4*k^2) + (3*(c - I*k0)^4*(2*c - I*k0)*(c/k - (I*k0)/k))/(8*k) + (3*(c - I*k0)*(2*c - I*k0)^4*((2*c)/k - (I*k0)/k))/(8*k)))/k))/8 + (k0^2*((3*(-((c - I*k0)^3*(2*c - I*k0))/(2*k^2) - ((c - I*k0)*(2*c - I*k0)^3)/(2*k^2))*(3*c - I*k0)^4*((3*c)/k - (I*k0)/k))/8 - (5*(c - I*k0)*(2*c - I*k0)*(3*c - I*k0)^6*((3*c)/k - (I*k0)/k))/(16*k^2) - ((3*c - I*k0)^3*(((c - I*k0)^3*(2*c - I*k0)^3)/(4*k^2) + (3*(c - I*k0)^4*(2*c - I*k0)*(c/k - (I*k0)/k))/(8*k) + (3*(c - I*k0)*(2*c - I*k0)^4*((2*c)/k - (I*k0)/k))/(8*k)))/(2*k) + ((3*c - I*k0)*((-5*(c - I*k0)^6*(2*c - I*k0)*(c/k - (I*k0)/k))/(16*k) - (3*(c - I*k0)^4*(2*c - I*k0)^3*(c/k - (I*k0)/k))/(16*k) - (3*(c - I*k0)^3*(2*c - I*k0)^4*((2*c)/k - (I*k0)/k))/(16*k) - (5*(c - I*k0)*(2*c - I*k0)^6*((2*c)/k - (I*k0)/k))/(16*k)))/k))/2)))/((2*c - I*k0)*(3*c - I*k0)) - (k0*(((-63*I)/256*(c - I*k0)*(2*c - I*k0)*(3*c - I*k0)*k0^10)/k^3 - (35*I)/128*k0^8*(((-((c - I*k0)^3*(2*c - I*k0))/(2*k^2) - ((c - I*k0)*(2*c - I*k0)^3)/(2*k^2))*(3*c - I*k0))/k - ((c - I*k0)*(2*c - I*k0)*(3*c - I*k0)^3)/(2*k^3) + ((c - I*k0)*(2*c - I*k0)*(3*c - I*k0)*k0^2)/(2*k^3)) - (5*I)/16*k0^6*(-((-((c - I*k0)^3*(2*c - I*k0))/(2*k^2) - ((c - I*k0)*(2*c - I*k0)^3)/(2*k^2))*(3*c - I*k0)^3)/(2*k) + ((((-((c - I*k0)^3*(2*c - I*k0))/(2*k^2) - ((c - I*k0)*(2*c - I*k0)^3)/(2*k^2))*(3*c - I*k0))/k - ((c - I*k0)*(2*c - I*k0)*(3*c - I*k0)^3)/(2*k^3))*k0^2)/2 + (3*(c - I*k0)*(2*c - I*k0)*(3*c - I*k0)*k0^4)/(8*k^3) + (3*(c - I*k0)*(2*c - I*k0)*(3*c - I*k0)^4*((3*c)/k - (I*k0)/k))/(8*k^2) + ((3*c - I*k0)*(((c - I*k0)^3*(2*c - I*k0)^3)/(4*k^2) + (3*(c - I*k0)^4*(2*c - I*k0)*(c/k - (I*k0)/k))/(8*k) + (3*(c - I*k0)*(2*c - I*k0)^4*((2*c)/k - (I*k0)/k))/(8*k)))/k) - (3*I)/8*k0^4*((3*(((-((c - I*k0)^3*(2*c - I*k0))/(2*k^2) - ((c - I*k0)*(2*c - I*k0)^3)/(2*k^2))*(3*c - I*k0))/k - ((c - I*k0)*(2*c - I*k0)*(3*c - I*k0)^3)/(2*k^3))*k0^4)/8 + (5*(c - I*k0)*(2*c - I*k0)*(3*c - I*k0)*k0^6)/(16*k^3) + (3*(-((c - I*k0)^3*(2*c - I*k0))/(2*k^2) - ((c - I*k0)*(2*c - I*k0)^3)/(2*k^2))*(3*c - I*k0)^4*((3*c)/k - (I*k0)/k))/8 - (5*(c - I*k0)*(2*c - I*k0)*(3*c - I*k0)^6*((3*c)/k - (I*k0)/k))/(16*k^2) - ((3*c - I*k0)^3*(((c - I*k0)^3*(2*c - I*k0)^3)/(4*k^2) + (3*(c - I*k0)^4*(2*c - I*k0)*(c/k - (I*k0)/k))/(8*k) + (3*(c - I*k0)*(2*c - I*k0)^4*((2*c)/k - (I*k0)/k))/(8*k)))/(2*k) + ((3*c - I*k0)*((-5*(c - I*k0)^6*(2*c - I*k0)*(c/k - (I*k0)/k))/(16*k) - (3*(c - I*k0)^4*(2*c - I*k0)^3*(c/k - (I*k0)/k))/(16*k) - (3*(c - I*k0)^3*(2*c - I*k0)^4*((2*c)/k - (I*k0)/k))/(16*k) - (5*(c - I*k0)*(2*c - I*k0)^6*((2*c)/k - (I*k0)/k))/(16*k)))/k + (k0^2*(-((-((c - I*k0)^3*(2*c - I*k0))/(2*k^2) - ((c - I*k0)*(2*c - I*k0)^3)/(2*k^2))*(3*c - I*k0)^3)/(2*k) + (3*(c - I*k0)*(2*c - I*k0)*(3*c - I*k0)^4*((3*c)/k - (I*k0)/k))/(8*k^2) + ((3*c - I*k0)*(((c - I*k0)^3*(2*c - I*k0)^3)/(4*k^2) + (3*(c - I*k0)^4*(2*c - I*k0)*(c/k - (I*k0)/k))/(8*k) + (3*(c - I*k0)*(2*c - I*k0)^4*((2*c)/k - (I*k0)/k))/(8*k)))/k))/2) - I/2*k0^2*((5*(((-((c - I*k0)^3*(2*c - I*k0))/(2*k^2) - ((c - I*k0)*(2*c - I*k0)^3)/(2*k^2))*(3*c - I*k0))/k - ((c - I*k0)*(2*c - I*k0)*(3*c - I*k0)^3)/(2*k^3))*k0^6)/16 + (35*(c - I*k0)*(2*c - I*k0)*(3*c - I*k0)*k0^8)/(128*k^3) - (5*(-((c - I*k0)^3*(2*c - I*k0))/(2*k^2) - ((c - I*k0)*(2*c - I*k0)^3)/(2*k^2))*(3*c - I*k0)^6*((3*c)/k - (I*k0)/k))/16 + (35*(c - I*k0)*(2*c - I*k0)*(3*c - I*k0)^8*((3*c)/k - (I*k0)/k))/(128*k^2) + (3*(3*c - I*k0)^4*((3*c)/k - (I*k0)/k)*(((c - I*k0)^3*(2*c - I*k0)^3)/(4*k^2) + (3*(c - I*k0)^4*(2*c - I*k0)*(c/k - (I*k0)/k))/(8*k) + (3*(c - I*k0)*(2*c - I*k0)^4*((2*c)/k - (I*k0)/k))/(8*k)))/8 - ((3*c - I*k0)^3*((-5*(c - I*k0)^6*(2*c - I*k0)*(c/k - (I*k0)/k))/(16*k) - (3*(c - I*k0)^4*(2*c - I*k0)^3*(c/k - (I*k0)/k))/(16*k) - (3*(c - I*k0)^3*(2*c - I*k0)^4*((2*c)/k - (I*k0)/k))/(16*k) - (5*(c - I*k0)*(2*c - I*k0)^6*((2*c)/k - (I*k0)/k))/(16*k)))/(2*k) + ((3*c - I*k0)*((35*(c - I*k0)^8*(2*c - I*k0)*(c/k - (I*k0)/k))/(128*k) + (5*(c - I*k0)^6*(2*c - I*k0)^3*(c/k - (I*k0)/k))/(32*k) + (5*(c - I*k0)^3*(2*c - I*k0)^6*((2*c)/k - (I*k0)/k))/(32*k) + (35*(c - I*k0)*(2*c - I*k0)^8*((2*c)/k - (I*k0)/k))/(128*k) + (9*(c - I*k0)^4*(2*c - I*k0)^4*(c/k - (I*k0)/k)*((2*c)/k - (I*k0)/k))/64))/k + (3*k0^4*(-((-((c - I*k0)^3*(2*c - I*k0))/(2*k^2) - ((c - I*k0)*(2*c - I*k0)^3)/(2*k^2))*(3*c - I*k0)^3)/(2*k) + (3*(c - I*k0)*(2*c - I*k0)*(3*c - I*k0)^4*((3*c)/k - (I*k0)/k))/(8*k^2) + ((3*c - I*k0)*(((c - I*k0)^3*(2*c - I*k0)^3)/(4*k^2) + (3*(c - I*k0)^4*(2*c - I*k0)*(c/k - (I*k0)/k))/(8*k) + (3*(c - I*k0)*(2*c - I*k0)^4*((2*c)/k - (I*k0)/k))/(8*k)))/k))/8 + (k0^2*((3*(-((c - I*k0)^3*(2*c - I*k0))/(2*k^2) - ((c - I*k0)*(2*c - I*k0)^3)/(2*k^2))*(3*c - I*k0)^4*((3*c)/k - (I*k0)/k))/8 - (5*(c - I*k0)*(2*c - I*k0)*(3*c - I*k0)^6*((3*c)/k - (I*k0)/k))/(16*k^2) - ((3*c - I*k0)^3*(((c - I*k0)^3*(2*c - I*k0)^3)/(4*k^2) + (3*(c - I*k0)^4*(2*c - I*k0)*(c/k - (I*k0)/k))/(8*k) + (3*(c - I*k0)*(2*c - I*k0)^4*((2*c)/k - (I*k0)/k))/(8*k)))/(2*k) + ((3*c - I*k0)*((-5*(c - I*k0)^6*(2*c - I*k0)*(c/k - (I*k0)/k))/(16*k) - (3*(c - I*k0)^4*(2*c - I*k0)^3*(c/k - (I*k0)/k))/(16*k) - (3*(c - I*k0)^3*(2*c - I*k0)^4*((2*c)/k - (I*k0)/k))/(16*k) - (5*(c - I*k0)*(2*c - I*k0)^6*((2*c)/k - (I*k0)/k))/(16*k)))/k))/2) - I*((35*(((-((c - I*k0)^3*(2*c - I*k0))/(2*k^2) - ((c - I*k0)*(2*c - I*k0)^3)/(2*k^2))*(3*c - I*k0))/k - ((c - I*k0)*(2*c - I*k0)*(3*c - I*k0)^3)/(2*k^3))*k0^8)/128 + (63*(c - I*k0)*(2*c - I*k0)*(3*c - I*k0)*k0^10)/(256*k^3) + (35*(-((c - I*k0)^3*(2*c - I*k0))/(2*k^2) - ((c - I*k0)*(2*c - I*k0)^3)/(2*k^2))*(3*c - I*k0)^8*((3*c)/k - (I*k0)/k))/128 - (63*(c - I*k0)*(2*c - I*k0)*(3*c - I*k0)^10*((3*c)/k - (I*k0)/k))/(256*k^2) - (5*(3*c - I*k0)^6*((3*c)/k - (I*k0)/k)*(((c - I*k0)^3*(2*c - I*k0)^3)/(4*k^2) + (3*(c - I*k0)^4*(2*c - I*k0)*(c/k - (I*k0)/k))/(8*k) + (3*(c - I*k0)*(2*c - I*k0)^4*((2*c)/k - (I*k0)/k))/(8*k)))/16 + (3*(3*c - I*k0)^4*((3*c)/k - (I*k0)/k)*((-5*(c - I*k0)^6*(2*c - I*k0)*(c/k - (I*k0)/k))/(16*k) - (3*(c - I*k0)^4*(2*c - I*k0)^3*(c/k - (I*k0)/k))/(16*k) - (3*(c - I*k0)^3*(2*c - I*k0)^4*((2*c)/k - (I*k0)/k))/(16*k) - (5*(c - I*k0)*(2*c - I*k0)^6*((2*c)/k - (I*k0)/k))/(16*k)))/8 - ((3*c - I*k0)^3*((35*(c - I*k0)^8*(2*c - I*k0)*(c/k - (I*k0)/k))/(128*k) + (5*(c - I*k0)^6*(2*c - I*k0)^3*(c/k - (I*k0)/k))/(32*k) + (5*(c - I*k0)^3*(2*c - I*k0)^6*((2*c)/k - (I*k0)/k))/(32*k) + (35*(c - I*k0)*(2*c - I*k0)^8*((2*c)/k - (I*k0)/k))/(128*k) + (9*(c - I*k0)^4*(2*c - I*k0)^4*(c/k - (I*k0)/k)*((2*c)/k - (I*k0)/k))/64))/(2*k) + ((3*c - I*k0)*((-63*(c - I*k0)^10*(2*c - I*k0)*(c/k - (I*k0)/k))/(256*k) - (35*(c - I*k0)^8*(2*c - I*k0)^3*(c/k - (I*k0)/k))/(256*k) - (35*(c - I*k0)^3*(2*c - I*k0)^8*((2*c)/k - (I*k0)/k))/(256*k) - (63*(c - I*k0)*(2*c - I*k0)^10*((2*c)/k - (I*k0)/k))/(256*k) - (15*(c - I*k0)^6*(2*c - I*k0)^4*(c/k - (I*k0)/k)*((2*c)/k - (I*k0)/k))/128 - (15*(c - I*k0)^4*(2*c - I*k0)^6*(c/k - (I*k0)/k)*((2*c)/k - (I*k0)/k))/128))/k + (5*k0^6*(-((-((c - I*k0)^3*(2*c - I*k0))/(2*k^2) - ((c - I*k0)*(2*c - I*k0)^3)/(2*k^2))*(3*c - I*k0)^3)/(2*k) + (3*(c - I*k0)*(2*c - I*k0)*(3*c - I*k0)^4*((3*c)/k - (I*k0)/k))/(8*k^2) + ((3*c - I*k0)*(((c - I*k0)^3*(2*c - I*k0)^3)/(4*k^2) + (3*(c - I*k0)^4*(2*c - I*k0)*(c/k - (I*k0)/k))/(8*k) + (3*(c - I*k0)*(2*c - I*k0)^4*((2*c)/k - (I*k0)/k))/(8*k)))/k))/16 + (3*k0^4*((3*(-((c - I*k0)^3*(2*c - I*k0))/(2*k^2) - ((c - I*k0)*(2*c - I*k0)^3)/(2*k^2))*(3*c - I*k0)^4*((3*c)/k - (I*k0)/k))/8 - (5*(c - I*k0)*(2*c - I*k0)*(3*c - I*k0)^6*((3*c)/k - (I*k0)/k))/(16*k^2) - ((3*c - I*k0)^3*(((c - I*k0)^3*(2*c - I*k0)^3)/(4*k^2) + (3*(c - I*k0)^4*(2*c - I*k0)*(c/k - (I*k0)/k))/(8*k) + (3*(c - I*k0)*(2*c - I*k0)^4*((2*c)/k - (I*k0)/k))/(8*k)))/(2*k) + ((3*c - I*k0)*((-5*(c - I*k0)^6*(2*c - I*k0)*(c/k - (I*k0)/k))/(16*k) - (3*(c - I*k0)^4*(2*c - I*k0)^3*(c/k - (I*k0)/k))/(16*k) - (3*(c - I*k0)^3*(2*c - I*k0)^4*((2*c)/k - (I*k0)/k))/(16*k) - (5*(c - I*k0)*(2*c - I*k0)^6*((2*c)/k - (I*k0)/k))/(16*k)))/k))/8 + (k0^2*((-5*(-((c - I*k0)^3*(2*c - I*k0))/(2*k^2) - ((c - I*k0)*(2*c - I*k0)^3)/(2*k^2))*(3*c - I*k0)^6*((3*c)/k - (I*k0)/k))/16 + (35*(c - I*k0)*(2*c - I*k0)*(3*c - I*k0)^8*((3*c)/k - (I*k0)/k))/(128*k^2) + (3*(3*c - I*k0)^4*((3*c)/k - (I*k0)/k)*(((c - I*k0)^3*(2*c - I*k0)^3)/(4*k^2) + (3*(c - I*k0)^4*(2*c - I*k0)*(c/k - (I*k0)/k))/(8*k) + (3*(c - I*k0)*(2*c - I*k0)^4*((2*c)/k - (I*k0)/k))/(8*k)))/8 - ((3*c - I*k0)^3*((-5*(c - I*k0)^6*(2*c - I*k0)*(c/k - (I*k0)/k))/(16*k) - (3*(c - I*k0)^4*(2*c - I*k0)^3*(c/k - (I*k0)/k))/(16*k) - (3*(c - I*k0)^3*(2*c - I*k0)^4*((2*c)/k - (I*k0)/k))/(16*k) - (5*(c - I*k0)*(2*c - I*k0)^6*((2*c)/k - (I*k0)/k))/(16*k)))/(2*k) + ((3*c - I*k0)*((35*(c - I*k0)^8*(2*c - I*k0)*(c/k - (I*k0)/k))/(128*k) + (5*(c - I*k0)^6*(2*c - I*k0)^3*(c/k - (I*k0)/k))/(32*k) + (5*(c - I*k0)^3*(2*c - I*k0)^6*((2*c)/k - (I*k0)/k))/(32*k) + (35*(c - I*k0)*(2*c - I*k0)^8*((2*c)/k - (I*k0)/k))/(128*k) + (9*(c - I*k0)^4*(2*c - I*k0)^4*(c/k - (I*k0)/k)*((2*c)/k - (I*k0)/k))/64))/k))/2)))/((c - I*k0)*(2*c - I*k0)*(3*c - I*k0)))/k0}, -1, 11, 1]] diff --git a/besseltransforms/3-1-2.REMOVED.git-id b/besseltransforms/3-1-2.REMOVED.git-id deleted file mode 100644 index 0550948..0000000 --- a/besseltransforms/3-1-2.REMOVED.git-id +++ /dev/null @@ -1 +0,0 @@ -9a2ec0ef6771d8a7db72ddc960cbd1172c4c24e2 \ No newline at end of file diff --git a/besseltransforms/3-2-0 b/besseltransforms/3-2-0 deleted file mode 100644 index e69de29..0000000 diff --git a/besseltransforms/3-2-1 b/besseltransforms/3-2-1 deleted file mode 100644 index d3994f1..0000000 --- a/besseltransforms/3-2-1 +++ /dev/null @@ -1,2 +0,0 @@ -(-6*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0) + 6*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0) - 2*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0) + k*Sqrt[Pi]*(Piecewise[{{0, k^2/k0^2 <= 1}}, (2*Sqrt[k^2 - k0^2])/(k*Sqrt[Pi])] + I*Piecewise[{{(2*k0)/(k*Sqrt[Pi]), k0^2/k^2 < 1}, {(2*(k0 - Sqrt[-k^2 + k0^2]))/(k*Sqrt[Pi]), k0^2/k^2 > 1}}, 0]))/(2*k*k0^2) -Piecewise[{{SeriesData[k, Infinity, {(9*c^4)/(2*k0^2) - ((3*I)*c^3)/k0, 0, (-15*(9*c^6 - (15*I)*c^5*k0 - 9*c^4*k0^2 + (2*I)*c^3*k0^3))/(4*k0^2), 0, (105*(69*c^8 - (172*I)*c^7*k0 - 180*c^6*k0^2 + (100*I)*c^5*k0^3 + 30*c^4*k0^4 - (4*I)*c^3*k0^5))/(32*k0^2), 0, (-105*(933*c^10 - (3025*I)*c^9*k0 - 4347*c^8*k0^2 + (3612*I)*c^7*k0^3 + 1890*c^6*k0^4 - (630*I)*c^5*k0^5 - 126*c^4*k0^6 + (12*I)*c^3*k0^7))/(64*k0^2)}, 4, 11, 1], (k0 <= 0 && k^2/k0^2 > 1) || k0 > 0}}, SeriesData[k, Infinity, {-k0^(-2), 0, 1/2, 0, ((3*c*(c - I*k0)^3)/8 - (3*c*(2*c - I*k0)^3)/4 + (3*c*(3*c - I*k0)^3)/8 - (3*I)/8*(c - I*k0)^3*k0 + (3*I)/8*(2*c - I*k0)^3*k0 - I/8*(3*c - I*k0)^3*k0)/k0^2, 0, ((-3*c*(c - I*k0)^5)/16 + (3*c*(2*c - I*k0)^5)/8 - (3*c*(3*c - I*k0)^5)/16 + (3*I)/16*(c - I*k0)^5*k0 - (3*I)/16*(2*c - I*k0)^5*k0 + I/16*(3*c - I*k0)^5*k0)/k0^2, 0, ((15*c*(c - I*k0)^7)/128 - (15*c*(2*c - I*k0)^7)/64 + (15*c*(3*c - I*k0)^7)/128 - (15*I)/128*(c - I*k0)^7*k0 + (15*I)/128*(2*c - I*k0)^7*k0 - (5*I)/128*(3*c - I*k0)^7*k0)/k0^2, 0, ((-21*c*(c - I*k0)^9)/256 + (21*c*(2*c - I*k0)^9)/128 - (21*c*(3*c - I*k0)^9)/256 + (21*I)/256*(c - I*k0)^9*k0 - (21*I)/256*(2*c - I*k0)^9*k0 + (7*I)/256*(3*c - I*k0)^9*k0)/k0^2}, 0, 11, 1]] diff --git a/besseltransforms/3-2-2 b/besseltransforms/3-2-2 deleted file mode 100644 index fbfe2c8..0000000 --- a/besseltransforms/3-2-2 +++ /dev/null @@ -1,2 +0,0 @@ -(-1 + (6*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^2)/k^2 - (6*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^2)/k^2 + (2*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^2)/k^2 + Sqrt[Pi]*(I*Piecewise[{{0, k^2/k0^2 <= 1}}, (2*k0*Sqrt[k^2 - k0^2])/(k^2*Sqrt[Pi])] + Piecewise[{{(k^2 + 2*k0*(-k0 + Sqrt[-k^2 + k0^2]))/(k^2*Sqrt[Pi]), k^2/k0^2 < 1}, {(1 - (2*k0^2)/k^2)/Sqrt[Pi], k^2/k0^2 > 1}}, 0]))/(2*k0^2) -SeriesData[k, Infinity, {(3*c^3)/k0^2, 0, (-15*(5*c^5 - (6*I)*c^4*k0 - 2*c^3*k0^2))/(4*k0^2), 0, (21*(43*c^7 - (90*I)*c^6*k0 - 75*c^5*k0^2 + (30*I)*c^4*k0^3 + 5*c^3*k0^4))/(8*k0^2), 0, (-15*(3025*c^9 - (8694*I)*c^8*k0 - 10836*c^7*k0^2 + (7560*I)*c^6*k0^3 + 3150*c^5*k0^4 - (756*I)*c^4*k0^5 - 84*c^3*k0^6))/(64*k0^2)}, 3, 11, 1] diff --git a/besseltransforms/3-3-0 b/besseltransforms/3-3-0 deleted file mode 100644 index e69de29..0000000 diff --git a/besseltransforms/3-3-1 b/besseltransforms/3-3-1 deleted file mode 100644 index 1c42766..0000000 --- a/besseltransforms/3-3-1 +++ /dev/null @@ -1,9 +0,0 @@ -Integrate[(E^(I*k0*x)*(1 - E^(-(c*x)))^3*BesselJ[1, k*x])/(k0^3*x^2), {x, 0, Infinity}, Assumptions -> n == 1 && q == 3 && κ == 3] - - -3 c x + I k0 x c x 3 2 2 4 4 6 6 8 8 Pi 2 2 4 4 6 6 8 8 Pi - -(E (-1 + E ) (8 k x (-14783093325 + 1452971520 k x - 309657600 k x + 251658240 k x + 2147483648 k x ) Cos[-- + k x] - 3 (156043762875 - 11416204800 k x + 1589575680 k x - 587202560 k x + 2147483648 k x ) Sin[-- + k x])) - 4 4 -Integrate::idiv: Integral of ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ does not converge on {0, Infinity}. - 19/2 3 23/2 - 8589934592 k k0 Sqrt[2 Pi] x -Series[Integrate[(E^(I*k0*x)*(1 - E^(-(c*x)))^3*BesselJ[1, k*x])/(k0^3*x^2), {x, 0, Infinity}, Assumptions -> n == 1 && q == 3 && κ == 3], {k, Infinity, 10}] diff --git a/besseltransforms/3-3-2 b/besseltransforms/3-3-2 deleted file mode 100644 index 799bd6d..0000000 --- a/besseltransforms/3-3-2 +++ /dev/null @@ -1,2 +0,0 @@ -(6*(3 - 2*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0) - (12*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^3)/k^2 + 6*(-3 + 2*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0) + (12*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^3)/k^2 + 2*(3 - 2*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0) - (4*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^3)/k^2 + 3*k0*Sqrt[Pi]*(Piecewise[{{0, k^2/k0^2 <= 1}}, (4*(k^2 - k0^2)^(3/2))/(3*k^2*k0*Sqrt[Pi])] + I*Piecewise[{{(-2*(2*k0*(k0 - Sqrt[-k^2 + k0^2]) + k^2*(-3 + (2*Sqrt[-k^2 + k0^2])/k0)))/(3*k^2*Sqrt[Pi]), k^2/k0^2 < 1}, {(2*(1 - (2*k0^2)/(3*k^2)))/Sqrt[Pi], k^2/k0^2 > 1}}, 0]))/(12*k0^3) -SeriesData[k, Infinity, {(2*c^3)/k0^3, (-9*c^4)/(2*k0^3) + ((3*I)*c^3)/k0^2, 0, (5*(9*c^6 - (15*I)*c^5*k0 - 9*c^4*k0^2 + (2*I)*c^3*k0^3))/(4*k0^3), 0, (-21*(69*c^8 - (172*I)*c^7*k0 - 180*c^6*k0^2 + (100*I)*c^5*k0^3 + 30*c^4*k0^4 - (4*I)*c^3*k0^5))/(32*k0^3), 0, (15*(933*c^10 - (3025*I)*c^9*k0 - 4347*c^8*k0^2 + (3612*I)*c^7*k0^3 + 1890*c^6*k0^4 - (630*I)*c^5*k0^5 - 126*c^4*k0^6 + (12*I)*c^3*k0^7))/(64*k0^3)}, 2, 11, 1] diff --git a/besseltransforms/3-3-3 b/besseltransforms/3-3-3 deleted file mode 100644 index 481d01d..0000000 --- a/besseltransforms/3-3-3 +++ /dev/null @@ -1,2 +0,0 @@ -(k^2*(3 - 2*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^2 - 2*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^4 + 3*k^2*(-3 + 2*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^2 + 6*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^4 + 3*k^2*(3 - 2*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^2 - 6*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^4 + k^2*(-3 + 2*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^2 + 2*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^4)/(6*k^3*k0^3) -SeriesData[k, Infinity, {(3*c^3)/k0^3, (-20*c^4)/k0^3 + ((8*I)*c^3)/k0^2, (15*(13*c^5 - (10*I)*c^4*k0 - 2*c^3*k0^2))/(4*k0^3), 0, (-7*(243*c^7 - (350*I)*c^6*k0 - 195*c^5*k0^2 + (50*I)*c^4*k0^3 + 5*c^3*k0^4))/(8*k0^3), 0, (3*(34105*c^9 - (69930*I)*c^8*k0 - 61236*c^7*k0^2 + (29400*I)*c^6*k0^3 + 8190*c^5*k0^4 - (1260*I)*c^4*k0^5 - 84*c^3*k0^6))/(64*k0^3), 0, (-33*(55591*c^11 - (145750*I)*c^10*k0 - 170525*c^9*k0^2 + (116550*I)*c^8*k0^3 + 51030*c^7*k0^4 - (14700*I)*c^6*k0^5 - 2730*c^5*k0^6 + (300*I)*c^4*k0^7 + 15*c^3*k0^8))/(128*k0^3)}, 2, 11, 1] diff --git a/besseltransforms/3-3-4 b/besseltransforms/3-3-4 deleted file mode 100644 index eab2da8..0000000 --- a/besseltransforms/3-3-4 +++ /dev/null @@ -1,2 +0,0 @@ -(-3*(k^4*(-15 + 4*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0) + 4*k^2*(-10 + 7*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^3 + 24*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^5) + 3*(k^4*(-15 + 4*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0) + 4*k^2*(-10 + 7*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^3 + 24*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^5) + k^4*(-15 + 4*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0) + 4*k^2*(-10 + 7*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^3 + 24*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^5 - k^4*(-15 + 4*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0) - 4*k^2*(-10 + 7*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^3 - 24*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^5)/(60*k^4*k0^3) -SeriesData[k, Infinity, {(4*c^3)/k0^3, (-75*c^4)/(2*k0^3) + ((15*I)*c^3)/k0^2, (156*c^5)/k0^3 - ((120*I)*c^4)/k0^2 - (24*c^3)/k0, (-35*(35*c^6 - (39*I)*c^5*k0 - 15*c^4*k0^2 + (2*I)*c^3*k0^3))/(4*k0^3), 0, (63*(555*c^8 - (972*I)*c^7*k0 - 700*c^6*k0^2 + (260*I)*c^5*k0^3 + 50*c^4*k0^4 - (4*I)*c^3*k0^5))/(32*k0^3), 0, (-33*(14575*c^10 - (34105*I)*c^9*k0 - 34965*c^8*k0^2 + (20412*I)*c^7*k0^3 + 7350*c^6*k0^4 - (1638*I)*c^5*k0^5 - 210*c^4*k0^6 + (12*I)*c^3*k0^7))/(64*k0^3)}, 2, 11, 1] diff --git a/besseltransforms/3-3-5 b/besseltransforms/3-3-5 deleted file mode 100644 index a508a6b..0000000 --- a/besseltransforms/3-3-5 +++ /dev/null @@ -1,2 +0,0 @@ -(3*k^4*(5 - 2*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^2 + 2*k^2*(15 - 11*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^4 - 16*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^6 + 9*k^4*(-5 + 2*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^2 + 6*k^2*(-15 + 11*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^4 + 48*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^6 + 9*k^4*(5 - 2*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^2 + 6*k^2*(15 - 11*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^4 - 48*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^6 + 3*k^4*(-5 + 2*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^2 + 2*k^2*(-15 + 11*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^4 + 16*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^6)/(30*k^5*k0^3) -SeriesData[k, Infinity, {(5*c^3)/k0^3, (-12*(5*c^4 - (2*I)*c^3*k0))/k0^3, (105*(13*c^5 - (10*I)*c^4*k0 - 2*c^3*k0^2))/(4*k0^3), (-32*(35*c^6 - (39*I)*c^5*k0 - 15*c^4*k0^2 + (2*I)*c^3*k0^3))/k0^3, (63*(243*c^7 - (350*I)*c^6*k0 - 195*c^5*k0^2 + (50*I)*c^4*k0^3 + 5*c^3*k0^4))/(8*k0^3), 0, (-11*(34105*c^9 - (69930*I)*c^8*k0 - 61236*c^7*k0^2 + (29400*I)*c^6*k0^3 + 8190*c^5*k0^4 - (1260*I)*c^4*k0^5 - 84*c^3*k0^6))/(64*k0^3), 0, ((-39*(c - I*k0)^11)/128 + (117*(2*c - I*k0)^11)/128 - (117*(3*c - I*k0)^11)/128 + (39*(4*c - I*k0)^11)/128)/(30*k0^3)}, 2, 11, 1] diff --git a/besseltransforms/3-3-6 b/besseltransforms/3-3-6 deleted file mode 100644 index eb3a4ac..0000000 --- a/besseltransforms/3-3-6 +++ /dev/null @@ -1,2 +0,0 @@ -(-3*(k^6*(-35 + 6*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0) + 6*k^4*(-35 + 17*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^3 + 16*k^2*(-21 + 16*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^5 + 160*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^7) + 3*(k^6*(-35 + 6*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0) + 6*k^4*(-35 + 17*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^3 + 16*k^2*(-21 + 16*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^5 + 160*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^7) + k^6*(-35 + 6*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0) + 6*k^4*(-35 + 17*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^3 + 16*k^2*(-21 + 16*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^5 + 160*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^7 - k^6*(-35 + 6*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0) - 6*k^4*(-35 + 17*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^3 - 16*k^2*(-21 + 16*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^5 - 160*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^7)/(210*k^6*k0^3) -SeriesData[k, Infinity, {(6*c^3)/k0^3, (-35*(5*c^4 - (2*I)*c^3*k0))/(2*k0^3), (48*(13*c^5 - (10*I)*c^4*k0 - 2*c^3*k0^2))/k0^3, (-315*(35*c^6 - (39*I)*c^5*k0 - 15*c^4*k0^2 + (2*I)*c^3*k0^3))/(4*k0^3), (32*(243*c^7 - (350*I)*c^6*k0 - 195*c^5*k0^2 + (50*I)*c^4*k0^3 + 5*c^3*k0^4))/k0^3, (-693*(555*c^8 - (972*I)*c^7*k0 - 700*c^6*k0^2 + (260*I)*c^5*k0^3 + 50*c^4*k0^4 - (4*I)*c^3*k0^5))/(32*k0^3), 0, ((-1001*(c - I*k0)^10)/128 + (3003*(2*c - I*k0)^10)/128 - (3003*(3*c - I*k0)^10)/128 + (1001*(4*c - I*k0)^10)/128)/(210*k0^3)}, 2, 11, 1] diff --git a/besseltransforms/3-3-7 b/besseltransforms/3-3-7 deleted file mode 100644 index 73e7bdb..0000000 --- a/besseltransforms/3-3-7 +++ /dev/null @@ -1,2 +0,0 @@ -((7*k^8 + 24*k^6*(7 - 2*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^2 + 16*k^4*(42 - 23*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^4 + 64*k^2*(14 - 11*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^6 - 384*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^8)/(336*k^7) - (7*k^8 + 24*k^6*(7 - 2*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^2 + 16*k^4*(42 - 23*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^4 + 64*k^2*(14 - 11*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^6 - 384*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^8)/(112*k^7) + (7*k^8 + 24*k^6*(7 - 2*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^2 + 16*k^4*(42 - 23*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^4 + 64*k^2*(14 - 11*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^6 - 384*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^8)/(112*k^7) - (7*k^8 + 24*k^6*(7 - 2*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^2 + 16*k^4*(42 - 23*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^4 + 64*k^2*(14 - 11*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^6 - 384*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^8)/(336*k^7))/k0^3 -SeriesData[k, Infinity, {(7*c^3)/k0^3, (-24*(5*c^4 - (2*I)*c^3*k0))/k0^3, (315*(13*c^5 - (10*I)*c^4*k0 - 2*c^3*k0^2))/(4*k0^3), (-160*(35*c^6 - (39*I)*c^5*k0 - 15*c^4*k0^2 + (2*I)*c^3*k0^3))/k0^3, (693*(243*c^7 - (350*I)*c^6*k0 - 195*c^5*k0^2 + (50*I)*c^4*k0^3 + 5*c^3*k0^4))/(8*k0^3), (-96*(555*c^8 - (972*I)*c^7*k0 - 700*c^6*k0^2 + (260*I)*c^5*k0^3 + 50*c^4*k0^4 - (4*I)*c^3*k0^5))/k0^3, ((-143*(c - I*k0)^9)/384 + (143*(2*c - I*k0)^9)/128 - (143*(3*c - I*k0)^9)/128 + (143*(4*c - I*k0)^9)/384)/k0^3, 0, ((13*(c - I*k0)^11)/256 - (39*(2*c - I*k0)^11)/256 + (39*(3*c - I*k0)^11)/256 - (13*(4*c - I*k0)^11)/256)/k0^3}, 2, 11, 1] diff --git a/besseltransforms/4-1-0.REMOVED.git-id b/besseltransforms/4-1-0.REMOVED.git-id deleted file mode 100644 index f886e48..0000000 --- a/besseltransforms/4-1-0.REMOVED.git-id +++ /dev/null @@ -1 +0,0 @@ -bee84490a2f9b473adccfa023c6611be883a01a7 \ No newline at end of file diff --git a/besseltransforms/4-1-1.REMOVED.git-id b/besseltransforms/4-1-1.REMOVED.git-id deleted file mode 100644 index 0bdd7c6..0000000 --- a/besseltransforms/4-1-1.REMOVED.git-id +++ /dev/null @@ -1 +0,0 @@ -a9ad81536da843935e33ae577308937e51c35ca7 \ No newline at end of file diff --git a/besseltransforms/4-1-2.REMOVED.git-id b/besseltransforms/4-1-2.REMOVED.git-id deleted file mode 100644 index 45ce22a..0000000 --- a/besseltransforms/4-1-2.REMOVED.git-id +++ /dev/null @@ -1 +0,0 @@ -8640f89aa7c80f216e563672dd2763f2c7becbce \ No newline at end of file diff --git a/besseltransforms/4-1-3 b/besseltransforms/4-1-3 deleted file mode 100644 index 3bbfe99..0000000 --- a/besseltransforms/4-1-3 +++ /dev/null @@ -1,2 +0,0 @@ -((k^2*(-3 + Sqrt[1 + k^2/(c - I*k0)^2]) + 4*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^2)/(k^3*Sqrt[1 + k^2/(c - I*k0)^2]) - (4*(k^2*(-3 + Sqrt[1 + k^2/(2*c - I*k0)^2]) + 4*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^2))/(k^3*Sqrt[1 + k^2/(2*c - I*k0)^2]) + (6*(k^2*(-3 + Sqrt[1 + k^2/(3*c - I*k0)^2]) + 4*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^2))/(k^3*Sqrt[1 + k^2/(3*c - I*k0)^2]) - (4*(k^2*(-3 + Sqrt[1 + k^2/(4*c - I*k0)^2]) + 4*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^2))/(k^3*Sqrt[1 + k^2/(4*c - I*k0)^2]) + (k^2*(-3 + Sqrt[1 + k^2/(5*c - I*k0)^2]) + 4*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^2)/(k^3*Sqrt[1 + k^2/(5*c - I*k0)^2]))/k0 -SeriesData[k, Infinity, {((-105*I)*c^4)/k + (315*c^5)/(k*k0), 0, (-945*(30*c^7 - (28*I)*c^6*k0 - 9*c^5*k0^2 + I*c^4*k0^3))/(2*k*k0), 0, (3465*(2025*c^9 - (2979*I)*c^8*k0 - 1800*c^7*k0^2 + (560*I)*c^6*k0^3 + 90*c^5*k0^4 - (6*I)*c^4*k0^5))/(16*k*k0)}, 5, 11, 1] diff --git a/besseltransforms/4-1-4 b/besseltransforms/4-1-4 deleted file mode 100644 index ff93fca..0000000 --- a/besseltransforms/4-1-4 +++ /dev/null @@ -1,2 +0,0 @@ -((k^4 - 4*k^2*(-2 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^2 - 8*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^4)/(k^4*Sqrt[1 + k^2/(c - I*k0)^2]*(c - I*k0)) - (4*(k^4 - 4*k^2*(-2 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^2 - 8*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^4))/(k^4*Sqrt[1 + k^2/(2*c - I*k0)^2]*(2*c - I*k0)) + (6*(k^4 - 4*k^2*(-2 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^2 - 8*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^4))/(k^4*Sqrt[1 + k^2/(3*c - I*k0)^2]*(3*c - I*k0)) - (4*(k^4 - 4*k^2*(-2 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^2 - 8*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^4))/(k^4*Sqrt[1 + k^2/(4*c - I*k0)^2]*(4*c - I*k0)) + (k^4 - 4*k^2*(-2 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^2 - 8*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^4)/(k^4*Sqrt[1 + k^2/(5*c - I*k0)^2]*(5*c - I*k0)))/k0 -SeriesData[k, Infinity, {(105*c^4)/(k*k0), 0, (-315*(28*c^6 - (18*I)*c^5*k0 - 3*c^4*k0^2))/(2*k*k0), 0, (2079*(993*c^8 - (1200*I)*c^7*k0 - 560*c^6*k0^2 + (120*I)*c^5*k0^3 + 10*c^4*k0^4))/(16*k*k0), 0, (-2145*(49346*c^10 - (85050*I)*c^9*k0 - 62559*c^8*k0^2 + (25200*I)*c^7*k0^3 + 5880*c^6*k0^4 - (756*I)*c^5*k0^5 - 42*c^4*k0^6))/(32*k*k0)}, 4, 11, 1] diff --git a/besseltransforms/4-1-5 b/besseltransforms/4-1-5 deleted file mode 100644 index dba2345..0000000 --- a/besseltransforms/4-1-5 +++ /dev/null @@ -1,2 +0,0 @@ -((k^4*(-5 + Sqrt[1 + k^2/(c - I*k0)^2]) + 4*k^2*(-5 + 3*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^2 + 16*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^4)/(k^5*Sqrt[1 + k^2/(c - I*k0)^2]) - (4*(k^4*(-5 + Sqrt[1 + k^2/(2*c - I*k0)^2]) + 4*k^2*(-5 + 3*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^2 + 16*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^4))/(k^5*Sqrt[1 + k^2/(2*c - I*k0)^2]) + (6*(k^4*(-5 + Sqrt[1 + k^2/(3*c - I*k0)^2]) + 4*k^2*(-5 + 3*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^2 + 16*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^4))/(k^5*Sqrt[1 + k^2/(3*c - I*k0)^2]) - (4*(k^4*(-5 + Sqrt[1 + k^2/(4*c - I*k0)^2]) + 4*k^2*(-5 + 3*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^2 + 16*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^4))/(k^5*Sqrt[1 + k^2/(4*c - I*k0)^2]) + (k^4*(-5 + Sqrt[1 + k^2/(5*c - I*k0)^2]) + 4*k^2*(-5 + 3*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^2 + 16*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^4)/(k^5*Sqrt[1 + k^2/(5*c - I*k0)^2]))/k0 -SeriesData[k, Infinity, {(384*c^4)/(k*k0), ((945*I)*c^4)/k - (2835*c^5)/(k*k0), 0, (3465*(30*c^7 - (28*I)*c^6*k0 - 9*c^5*k0^2 + I*c^4*k0^3))/(2*k*k0), 0, (-9009*(2025*c^9 - (2979*I)*c^8*k0 - 1800*c^7*k0^2 + (560*I)*c^6*k0^3 + 90*c^5*k0^4 - (6*I)*c^4*k0^5))/(16*k*k0)}, 4, 11, 1] diff --git a/besseltransforms/4-1-6 b/besseltransforms/4-1-6 deleted file mode 100644 index 73f1ea6..0000000 --- a/besseltransforms/4-1-6 +++ /dev/null @@ -1,2 +0,0 @@ -((k^6 - 6*k^4*(-3 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^2 + 16*k^2*(3 - 2*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^4 - 32*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^6)/(k^6*Sqrt[1 + k^2/(c - I*k0)^2]*(c - I*k0)) - (4*(k^6 - 6*k^4*(-3 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^2 + 16*k^2*(3 - 2*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^4 - 32*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^6))/(k^6*Sqrt[1 + k^2/(2*c - I*k0)^2]*(2*c - I*k0)) + (6*(k^6 - 6*k^4*(-3 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^2 + 16*k^2*(3 - 2*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^4 - 32*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^6))/(k^6*Sqrt[1 + k^2/(3*c - I*k0)^2]*(3*c - I*k0)) - (4*(k^6 - 6*k^4*(-3 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^2 + 16*k^2*(3 - 2*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^4 - 32*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^6))/(k^6*Sqrt[1 + k^2/(4*c - I*k0)^2]*(4*c - I*k0)) + (k^6 - 6*k^4*(-3 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^2 + 16*k^2*(3 - 2*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^4 - 32*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^6)/(k^6*Sqrt[1 + k^2/(5*c - I*k0)^2]*(5*c - I*k0)))/k0 -SeriesData[k, Infinity, {(945*c^4)/(k*k0), ((3840*I)*c^4)/k - (11520*c^5)/(k*k0), (3465*(28*c^6 - (18*I)*c^5*k0 - 3*c^4*k0^2))/(2*k*k0), 0, (-9009*(993*c^8 - (1200*I)*c^7*k0 - 560*c^6*k0^2 + (120*I)*c^5*k0^3 + 10*c^4*k0^4))/(16*k*k0), 0, (6435*(49346*c^10 - (85050*I)*c^9*k0 - 62559*c^8*k0^2 + (25200*I)*c^7*k0^3 + 5880*c^6*k0^4 - (756*I)*c^5*k0^5 - 42*c^4*k0^6))/(32*k*k0)}, 4, 11, 1] diff --git a/besseltransforms/4-1-7 b/besseltransforms/4-1-7 deleted file mode 100644 index fd7b764..0000000 --- a/besseltransforms/4-1-7 +++ /dev/null @@ -1,2 +0,0 @@ -((k^6*(-7 + Sqrt[1 + k^2/(c - I*k0)^2]) + 8*k^4*(-7 + 3*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^2 + 16*k^2*(-7 + 5*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^4 + 64*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^6)/(k^7*Sqrt[1 + k^2/(c - I*k0)^2]) - (4*(k^6*(-7 + Sqrt[1 + k^2/(2*c - I*k0)^2]) + 8*k^4*(-7 + 3*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^2 + 16*k^2*(-7 + 5*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^4 + 64*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^6))/(k^7*Sqrt[1 + k^2/(2*c - I*k0)^2]) + (6*(k^6*(-7 + Sqrt[1 + k^2/(3*c - I*k0)^2]) + 8*k^4*(-7 + 3*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^2 + 16*k^2*(-7 + 5*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^4 + 64*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^6))/(k^7*Sqrt[1 + k^2/(3*c - I*k0)^2]) - (4*(k^6*(-7 + Sqrt[1 + k^2/(4*c - I*k0)^2]) + 8*k^4*(-7 + 3*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^2 + 16*k^2*(-7 + 5*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^4 + 64*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^6))/(k^7*Sqrt[1 + k^2/(4*c - I*k0)^2]) + (k^6*(-7 + Sqrt[1 + k^2/(5*c - I*k0)^2]) + 8*k^4*(-7 + 3*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^2 + 16*k^2*(-7 + 5*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^4 + 64*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^6)/(k^7*Sqrt[1 + k^2/(5*c - I*k0)^2]))/k0 -SeriesData[k, Infinity, {(1920*c^4)/(k*k0), ((10395*I)*c^4)/k - (31185*c^5)/(k*k0), (7680*(28*c^6 - (18*I)*c^5*k0 - 3*c^4*k0^2))/(k*k0), (-45045*(30*c^7 - (28*I)*c^6*k0 - 9*c^5*k0^2 + I*c^4*k0^3))/(2*k*k0), 0, (45045*(2025*c^9 - (2979*I)*c^8*k0 - 1800*c^7*k0^2 + (560*I)*c^6*k0^3 + 90*c^5*k0^4 - (6*I)*c^4*k0^5))/(16*k*k0)}, 4, 11, 1] diff --git a/besseltransforms/4-2-0 b/besseltransforms/4-2-0 deleted file mode 100644 index 788e5e7..0000000 --- a/besseltransforms/4-2-0 +++ /dev/null @@ -1 +0,0 @@ -Integrate[(E^(I*k0*x)*(-1 + E^(-(c*x)))^4*BesselJ[0, k*x])/(k0^2*x), {x, 0, Infinity}, Assumptions -> n == 0 && q == 2 && κ == 4] diff --git a/besseltransforms/4-2-1 b/besseltransforms/4-2-1 deleted file mode 100644 index c73799a..0000000 --- a/besseltransforms/4-2-1 +++ /dev/null @@ -1,2 +0,0 @@ -((-4*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0))/k + (6*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0))/k - (4*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0))/k + ((-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0))/k + (Sqrt[Pi]*(Piecewise[{{0, k^2/k0^2 <= 1}}, (2*Sqrt[k^2 - k0^2])/(k*Sqrt[Pi])] + I*Piecewise[{{(2*k0)/(k*Sqrt[Pi]), k0^2/k^2 < 1}, {(2*(k0 - Sqrt[-k^2 + k0^2]))/(k*Sqrt[Pi]), k0^2/k^2 > 1}}, 0]))/2)/k0^2 -Piecewise[{{SeriesData[k, Infinity, {(-3*c^4)/k0^2, 0, (-45*c^4)/2 + (195*c^6)/(2*k0^2) - ((90*I)*c^5)/k0, 0, (6825*c^6)/4 - (25515*c^8)/(16*k0^2) + ((2625*I)*c^7)/k0 - (525*I)*c^5*k0 - (525*c^4*k0^2)/8, 0, (105*(6821*c^10 - (15540*I)*c^9*k0 - 15309*c^8*k0^2 + (8400*I)*c^7*k0^3 + 2730*c^6*k0^4 - (504*I)*c^5*k0^5 - 42*c^4*k0^6))/(32*k0^2)}, 4, 11, 1], (k0 <= 0 && k^2/k0^2 > 1) || k0 > 0}}, SeriesData[k, Infinity, {-k0^(-2), 0, 1/2, 0, ((c*(c - I*k0)^3)/2 - (3*c*(2*c - I*k0)^3)/2 + (3*c*(3*c - I*k0)^3)/2 - (c*(4*c - I*k0)^3)/2 - I/2*(c - I*k0)^3*k0 + (3*I)/4*(2*c - I*k0)^3*k0 - I/2*(3*c - I*k0)^3*k0 + I/8*(4*c - I*k0)^3*k0)/k0^2, 0, (-(c*(c - I*k0)^5)/4 + (3*c*(2*c - I*k0)^5)/4 - (3*c*(3*c - I*k0)^5)/4 + (c*(4*c - I*k0)^5)/4 + I/4*(c - I*k0)^5*k0 - (3*I)/8*(2*c - I*k0)^5*k0 + I/4*(3*c - I*k0)^5*k0 - I/16*(4*c - I*k0)^5*k0)/k0^2, 0, ((5*c*(c - I*k0)^7)/32 - (15*c*(2*c - I*k0)^7)/32 + (15*c*(3*c - I*k0)^7)/32 - (5*c*(4*c - I*k0)^7)/32 - (5*I)/32*(c - I*k0)^7*k0 + (15*I)/64*(2*c - I*k0)^7*k0 - (5*I)/32*(3*c - I*k0)^7*k0 + (5*I)/128*(4*c - I*k0)^7*k0)/k0^2, 0, ((-7*c*(c - I*k0)^9)/64 + (21*c*(2*c - I*k0)^9)/64 - (21*c*(3*c - I*k0)^9)/64 + (7*c*(4*c - I*k0)^9)/64 + (7*I)/64*(c - I*k0)^9*k0 - (21*I)/128*(2*c - I*k0)^9*k0 + (7*I)/64*(3*c - I*k0)^9*k0 - (7*I)/256*(4*c - I*k0)^9*k0)/k0^2}, 0, 11, 1]] diff --git a/besseltransforms/4-2-2 b/besseltransforms/4-2-2 deleted file mode 100644 index e78fb3f..0000000 --- a/besseltransforms/4-2-2 +++ /dev/null @@ -1,2 +0,0 @@ -(-k^2 + 8*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^2 - 12*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^2 + 8*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^2 - 2*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^2 + k^2*Sqrt[Pi]*(I*Piecewise[{{0, k^2/k0^2 <= 1}}, (2*k0*Sqrt[k^2 - k0^2])/(k^2*Sqrt[Pi])] + Piecewise[{{(k^2 + 2*k0*(-k0 + Sqrt[-k^2 + k0^2]))/(k^2*Sqrt[Pi]), k^2/k0^2 < 1}, {(1 - (2*k0^2)/k^2)/Sqrt[Pi], k^2/k0^2 > 1}}, 0]))/(2*k^2*k0^2) -SeriesData[k, Infinity, {(30*c^5)/k0^2 - ((15*I)*c^4)/k0, 0, 315*c^5 - (525*c^7)/k0^2 + ((1365*I)/2*c^6)/k0 - (105*I)/2*c^4*k0, 0, (315*(370*c^9 - (729*I)*c^8*k0 - 600*c^7*k0^2 + (260*I)*c^6*k0^3 + 60*c^5*k0^4 - (6*I)*c^4*k0^5))/(16*k0^2)}, 5, 11, 1] diff --git a/besseltransforms/4-2-3 b/besseltransforms/4-2-3 deleted file mode 100644 index 00c163d..0000000 --- a/besseltransforms/4-2-3 +++ /dev/null @@ -1,2 +0,0 @@ -(k^2*(-3 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0) + 4*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^3 - 4*k^2*(-3 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0) - 16*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^3 + 6*k^2*(-3 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0) + 24*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^3 - 4*k^2*(-3 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0) - 16*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^3 + k^2*(-3 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0) + 4*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^3)/(3*k^3*k0^2) -SeriesData[k, Infinity, {(15*c^4)/k0^2, 0, (105*c^4)/2 - (490*c^6)/k0^2 + ((315*I)*c^5)/k0, 0, -6615*c^6 + (187677*c^8)/(16*k0^2) - ((14175*I)*c^7)/k0 + (2835*I)/2*c^5*k0 + (945*c^4*k0^2)/8, 0, (-165*(49346*c^10 - (85050*I)*c^9*k0 - 62559*c^8*k0^2 + (25200*I)*c^7*k0^3 + 5880*c^6*k0^4 - (756*I)*c^5*k0^5 - 42*c^4*k0^6))/(32*k0^2)}, 4, 11, 1] diff --git a/besseltransforms/4-2-4 b/besseltransforms/4-2-4 deleted file mode 100644 index e20a9a3..0000000 --- a/besseltransforms/4-2-4 +++ /dev/null @@ -1,2 +0,0 @@ --((k^2*(-2 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^2 + 2*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^4 - 4*k^2*(-2 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^2 - 8*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^4 + 6*k^2*(-2 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^2 + 12*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^4 - 4*k^2*(-2 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^2 - 8*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^4 + k^2*(-2 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^2 + 2*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^4)/(k^4*k0^2)) -SeriesData[k, Infinity, {(48*c^4)/k0^2, (-315*c^5)/k0^2 + ((105*I)*c^4)/k0, 0, (-2835*c^5)/2 + (4725*c^7)/k0^2 - ((4410*I)*c^6)/k0 + (315*I)/2*c^4*k0, 0, (-693*(2025*c^9 - (2979*I)*c^8*k0 - 1800*c^7*k0^2 + (560*I)*c^6*k0^3 + 90*c^5*k0^4 - (6*I)*c^4*k0^5))/(16*k0^2)}, 4, 11, 1] diff --git a/besseltransforms/4-2-5 b/besseltransforms/4-2-5 deleted file mode 100644 index 42dda30..0000000 --- a/besseltransforms/4-2-5 +++ /dev/null @@ -1,2 +0,0 @@ -(-4*(k^4*(-5 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0) + 4*k^2*(-5 + 3*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^3 + 16*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^5) + 6*(k^4*(-5 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0) + 4*k^2*(-5 + 3*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^3 + 16*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^5) - 4*(k^4*(-5 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0) + 4*k^2*(-5 + 3*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^3 + 16*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^5) + k^4*(-5 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0) + 4*k^2*(-5 + 3*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^3 + 16*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^5 + k^4*(-5 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0) + 4*k^2*(-5 + 3*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^3 + 16*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^5)/(5*k^5*k0^2) -SeriesData[k, Infinity, {(105*c^4)/k0^2, (-1152*c^5)/k0^2 + ((384*I)*c^4)/k0, (-945*c^4)/2 + (4410*c^6)/k0^2 - ((2835*I)*c^5)/k0, 0, 24255*c^6 - (688149*c^8)/(16*k0^2) + ((51975*I)*c^7)/k0 - (10395*I)/2*c^5*k0 - (3465*c^4*k0^2)/8, 0, (429*(49346*c^10 - (85050*I)*c^9*k0 - 62559*c^8*k0^2 + (25200*I)*c^7*k0^3 + 5880*c^6*k0^4 - (756*I)*c^5*k0^5 - 42*c^4*k0^6))/(32*k0^2)}, 4, 11, 1] diff --git a/besseltransforms/4-2-6 b/besseltransforms/4-2-6 deleted file mode 100644 index 09ab4c6..0000000 --- a/besseltransforms/4-2-6 +++ /dev/null @@ -1,2 +0,0 @@ -(-3*k^4*(-3 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^2 + 8*k^2*(3 - 2*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^4 - 16*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^6 + 12*k^4*(-3 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^2 + 32*k^2*(-3 + 2*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^4 + 64*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^6 - 18*k^4*(-3 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^2 + 48*k^2*(3 - 2*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^4 - 96*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^6 + 12*k^4*(-3 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^2 + 32*k^2*(-3 + 2*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^4 + 64*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^6 - 3*k^4*(-3 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^2 + 8*k^2*(3 - 2*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^4 - 16*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^6)/(3*k^6*k0^2) -SeriesData[k, Infinity, {(192*c^4)/k0^2, (-2835*c^5)/k0^2 + ((945*I)*c^4)/k0, -1920*c^4 + (17920*c^6)/k0^2 - ((11520*I)*c^5)/k0, (31185*c^5)/2 - (51975*c^7)/k0^2 + ((48510*I)*c^6)/k0 - (3465*I)/2*c^4*k0, 0, (3003*(2025*c^9 - (2979*I)*c^8*k0 - 1800*c^7*k0^2 + (560*I)*c^6*k0^3 + 90*c^5*k0^4 - (6*I)*c^4*k0^5))/(16*k0^2)}, 4, 11, 1] diff --git a/besseltransforms/4-2-7 b/besseltransforms/4-2-7 deleted file mode 100644 index 68ec2cc..0000000 --- a/besseltransforms/4-2-7 +++ /dev/null @@ -1,2 +0,0 @@ -(-4*(k^6*(-7 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0) + 8*k^4*(-7 + 3*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^3 + 16*k^2*(-7 + 5*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^5 + 64*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^7) + 6*(k^6*(-7 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0) + 8*k^4*(-7 + 3*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^3 + 16*k^2*(-7 + 5*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^5 + 64*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^7) - 4*(k^6*(-7 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0) + 8*k^4*(-7 + 3*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^3 + 16*k^2*(-7 + 5*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^5 + 64*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^7) + k^6*(-7 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0) + 8*k^4*(-7 + 3*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^3 + 16*k^2*(-7 + 5*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^5 + 64*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^7 + k^6*(-7 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0) + 8*k^4*(-7 + 3*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^3 + 16*k^2*(-7 + 5*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^5 + 64*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^7)/(7*k^7*k0^2) -SeriesData[k, Infinity, {(315*c^4)/k0^2, (-1920*(3*c^5 - I*c^4*k0))/k0^2, (3465*(28*c^6 - (18*I)*c^5*k0 - 3*c^4*k0^2))/(2*k0^2), (-7680*(30*c^7 - (28*I)*c^6*k0 - 9*c^5*k0^2 + I*c^4*k0^3))/k0^2, (9009*(993*c^8 - (1200*I)*c^7*k0 - 560*c^6*k0^2 + (120*I)*c^5*k0^3 + 10*c^4*k0^4))/(16*k0^2), 0, (-2145*(49346*c^10 - (85050*I)*c^9*k0 - 62559*c^8*k0^2 + (25200*I)*c^7*k0^3 + 5880*c^6*k0^4 - (756*I)*c^5*k0^5 - 42*c^4*k0^6))/(32*k0^2)}, 4, 11, 1] diff --git a/besseltransforms/4-3-0 b/besseltransforms/4-3-0 deleted file mode 100644 index c39b980..0000000 --- a/besseltransforms/4-3-0 +++ /dev/null @@ -1,2 +0,0 @@ - -Simplify::time: Time spent on a transformation exceeded 300. seconds, and the transformation was aborted. Increasing the value of TimeConstraint option may improve the result of simplification. diff --git a/besseltransforms/4-3-1 b/besseltransforms/4-3-1 deleted file mode 100644 index c39b980..0000000 --- a/besseltransforms/4-3-1 +++ /dev/null @@ -1,2 +0,0 @@ - -Simplify::time: Time spent on a transformation exceeded 300. seconds, and the transformation was aborted. Increasing the value of TimeConstraint option may improve the result of simplification. diff --git a/besseltransforms/4-3-2 b/besseltransforms/4-3-2 deleted file mode 100644 index 592b772..0000000 --- a/besseltransforms/4-3-2 +++ /dev/null @@ -1,2 +0,0 @@ -(8*k^2*(3 - 2*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0) - 16*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^3 + 12*k^2*(-3 + 2*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0) + 24*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^3 + 8*k^2*(3 - 2*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0) - 16*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^3 + 2*k^2*(-3 + 2*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0) + 4*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^3 + 3*k^2*k0*Sqrt[Pi]*(Piecewise[{{0, k^2/k0^2 <= 1}}, (4*(k^2 - k0^2)^(3/2))/(3*k^2*k0*Sqrt[Pi])] + I*Piecewise[{{(-2*(2*k0*(k0 - Sqrt[-k^2 + k0^2]) + k^2*(-3 + (2*Sqrt[-k^2 + k0^2])/k0)))/(3*k^2*Sqrt[Pi]), k^2/k0^2 < 1}, {(2*(1 - (2*k0^2)/(3*k^2)))/Sqrt[Pi], k^2/k0^2 > 1}}, 0]))/(12*k^2*k0^3) -SeriesData[k, Infinity, {(3*c^4)/k0^3, 0, (-5*(13*c^6 - (12*I)*c^5*k0 - 3*c^4*k0^2))/(2*k0^3), 0, (105*I)*c^5 + (5103*c^8)/(16*k0^3) - ((525*I)*c^7)/k0^2 - (1365*c^6)/(4*k0) + (105*c^4*k0)/8, 0, (-15*(6821*c^10 - (15540*I)*c^9*k0 - 15309*c^8*k0^2 + (8400*I)*c^7*k0^3 + 2730*c^6*k0^4 - (504*I)*c^5*k0^5 - 42*c^4*k0^6))/(32*k0^3)}, 3, 11, 1] diff --git a/besseltransforms/4-3-3 b/besseltransforms/4-3-3 deleted file mode 100644 index 6b9f3e5..0000000 --- a/besseltransforms/4-3-3 +++ /dev/null @@ -1,2 +0,0 @@ -(k^2*(3 - 2*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^2 - 2*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^4 + 4*k^2*(-3 + 2*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^2 + 8*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^4 + 6*k^2*(3 - 2*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^2 - 12*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^4 + 4*k^2*(-3 + 2*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^2 + 8*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^4 + k^2*(3 - 2*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^2 - 2*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^4)/(6*k^3*k0^3) -SeriesData[k, Infinity, {(8*c^4)/k0^3, (-45*c^5)/k0^3 + ((15*I)*c^4)/k0^2, 0, (35*I)/2*c^4 + (525*c^7)/k0^3 - ((490*I)*c^6)/k0^2 - (315*c^5)/(2*k0), 0, (-63*(2025*c^9 - (2979*I)*c^8*k0 - 1800*c^7*k0^2 + (560*I)*c^6*k0^3 + 90*c^5*k0^4 - (6*I)*c^4*k0^5))/(16*k0^3), 0, (165*(25080*c^11 - (49346*I)*c^10*k0 - 42525*c^9*k0^2 + (20853*I)*c^8*k0^3 + 6300*c^7*k0^4 - (1176*I)*c^6*k0^5 - 126*c^5*k0^6 + (6*I)*c^4*k0^7))/(32*k0^3)}, 3, 11, 1] diff --git a/besseltransforms/4-3-4 b/besseltransforms/4-3-4 deleted file mode 100644 index e2fc380..0000000 --- a/besseltransforms/4-3-4 +++ /dev/null @@ -1,2 +0,0 @@ -(-4*(k^4*(-15 + 4*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0) + 4*k^2*(-10 + 7*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^3 + 24*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^5) + 6*(k^4*(-15 + 4*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0) + 4*k^2*(-10 + 7*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^3 + 24*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^5) - 4*(k^4*(-15 + 4*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0) + 4*k^2*(-10 + 7*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^3 + 24*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^5) + k^4*(-15 + 4*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0) + 4*k^2*(-10 + 7*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^3 + 24*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^5 + k^4*(-15 + 4*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0) + 4*k^2*(-10 + 7*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^3 + 24*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^5)/(60*k^4*k0^3) -SeriesData[k, Infinity, {(15*c^4)/k0^3, (-48*(3*c^5 - I*c^4*k0))/k0^3, (35*(28*c^6 - (18*I)*c^5*k0 - 3*c^4*k0^2))/(2*k0^3), 0, (-63*(993*c^8 - (1200*I)*c^7*k0 - 560*c^6*k0^2 + (120*I)*c^5*k0^3 + 10*c^4*k0^4))/(16*k0^3), 0, (33*(49346*c^10 - (85050*I)*c^9*k0 - 62559*c^8*k0^2 + (25200*I)*c^7*k0^3 + 5880*c^6*k0^4 - (756*I)*c^5*k0^5 - 42*c^4*k0^6))/(32*k0^3)}, 3, 11, 1] diff --git a/besseltransforms/4-3-5 b/besseltransforms/4-3-5 deleted file mode 100644 index bafde08..0000000 --- a/besseltransforms/4-3-5 +++ /dev/null @@ -1,2 +0,0 @@ -((5*k^6 + 12*k^4*(5 - 2*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^2 + 8*k^2*(15 - 11*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^4 - 64*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^6)/(120*k^5) - (5*k^6 + 12*k^4*(5 - 2*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^2 + 8*k^2*(15 - 11*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^4 - 64*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^6)/(30*k^5) + (5*k^6 + 12*k^4*(5 - 2*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^2 + 8*k^2*(15 - 11*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^4 - 64*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^6)/(20*k^5) - (5*k^6 + 12*k^4*(5 - 2*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^2 + 8*k^2*(15 - 11*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^4 - 64*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^6)/(30*k^5) + (5*k^6 + 12*k^4*(5 - 2*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^2 + 8*k^2*(15 - 11*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^4 - 64*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^6)/(120*k^5))/k0^3 -SeriesData[k, Infinity, {(24*c^4)/k0^3, (-315*c^5)/k0^3 + ((105*I)*c^4)/k0^2, (1792*c^6)/k0^3 - ((1152*I)*c^5)/k0^2 - (192*c^4)/k0, (-315*I)/2*c^4 - (4725*c^7)/k0^3 + ((4410*I)*c^6)/k0^2 + (2835*c^5)/(2*k0), 0, (231*(2025*c^9 - (2979*I)*c^8*k0 - 1800*c^7*k0^2 + (560*I)*c^6*k0^3 + 90*c^5*k0^4 - (6*I)*c^4*k0^5))/(16*k0^3), 0, (-429*(25080*c^11 - (49346*I)*c^10*k0 - 42525*c^9*k0^2 + (20853*I)*c^8*k0^3 + 6300*c^7*k0^4 - (1176*I)*c^6*k0^5 - 126*c^5*k0^6 + (6*I)*c^4*k0^7))/(32*k0^3)}, 3, 11, 1] diff --git a/besseltransforms/4-3-6 b/besseltransforms/4-3-6 deleted file mode 100644 index 4ff87d3..0000000 --- a/besseltransforms/4-3-6 +++ /dev/null @@ -1,2 +0,0 @@ -((k^6*(-35 + 6*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0) + 6*k^4*(-35 + 17*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^3 + 16*k^2*(-21 + 16*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^5 + 160*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^7)/(210*k^6) - (2*(k^6*(-35 + 6*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0) + 6*k^4*(-35 + 17*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^3 + 16*k^2*(-21 + 16*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^5 + 160*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^7))/(105*k^6) + (k^6*(-35 + 6*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0) + 6*k^4*(-35 + 17*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^3 + 16*k^2*(-21 + 16*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^5 + 160*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^7)/(35*k^6) - (2*(k^6*(-35 + 6*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0) + 6*k^4*(-35 + 17*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^3 + 16*k^2*(-21 + 16*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^5 + 160*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^7))/(105*k^6) + (k^6*(-35 + 6*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0) + 6*k^4*(-35 + 17*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^3 + 16*k^2*(-21 + 16*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^5 + 160*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^7)/(210*k^6))/k0^3 -SeriesData[k, Infinity, {(35*c^4)/k0^3, (-576*c^5)/k0^3 + ((192*I)*c^4)/k0^2, (4410*c^6)/k0^3 - ((2835*I)*c^5)/k0^2 - (945*c^4)/(2*k0), (-640*I)*c^4 - (19200*c^7)/k0^3 + ((17920*I)*c^6)/k0^2 + (5760*c^5)/k0, (10395*I)/2*c^5 + (688149*c^8)/(16*k0^3) - ((51975*I)*c^7)/k0^2 - (24255*c^6)/k0 + (3465*c^4*k0)/8, 0, (-143*(49346*c^10 - (85050*I)*c^9*k0 - 62559*c^8*k0^2 + (25200*I)*c^7*k0^3 + 5880*c^6*k0^4 - (756*I)*c^5*k0^5 - 42*c^4*k0^6))/(32*k0^3)}, 3, 11, 1] diff --git a/besseltransforms/4-3-7 b/besseltransforms/4-3-7 deleted file mode 100644 index 532099c..0000000 --- a/besseltransforms/4-3-7 +++ /dev/null @@ -1,2 +0,0 @@ -((7*k^8 + 24*k^6*(7 - 2*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^2 + 16*k^4*(42 - 23*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^4 + 64*k^2*(14 - 11*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^6 - 384*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^8)/(336*k^7) - (7*k^8 + 24*k^6*(7 - 2*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^2 + 16*k^4*(42 - 23*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^4 + 64*k^2*(14 - 11*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^6 - 384*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^8)/(84*k^7) + (7*k^8 + 24*k^6*(7 - 2*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^2 + 16*k^4*(42 - 23*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^4 + 64*k^2*(14 - 11*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^6 - 384*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^8)/(56*k^7) - (7*k^8 + 24*k^6*(7 - 2*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^2 + 16*k^4*(42 - 23*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^4 + 64*k^2*(14 - 11*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^6 - 384*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^8)/(84*k^7) + (7*k^8 + 24*k^6*(7 - 2*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^2 + 16*k^4*(42 - 23*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^4 + 64*k^2*(14 - 11*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^6 - 384*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^8)/(336*k^7))/k0^3 -SeriesData[k, Infinity, {(48*c^4)/k0^3, (-945*c^5)/k0^3 + ((315*I)*c^4)/k0^2, (8960*c^6)/k0^3 - ((5760*I)*c^5)/k0^2 - (960*c^4)/k0, (-3465*I)/2*c^4 - (51975*c^7)/k0^3 + ((48510*I)*c^6)/k0^2 + (31185*c^5)/(2*k0), (23040*I)*c^5 + (190656*c^8)/k0^3 - ((230400*I)*c^7)/k0^2 - (107520*c^6)/k0 + 1920*c^4*k0, (-3003*(2025*c^9 - (2979*I)*c^8*k0 - 1800*c^7*k0^2 + (560*I)*c^6*k0^3 + 90*c^5*k0^4 - (6*I)*c^4*k0^5))/(16*k0^3), 0, (2145*(25080*c^11 - (49346*I)*c^10*k0 - 42525*c^9*k0^2 + (20853*I)*c^8*k0^3 + 6300*c^7*k0^4 - (1176*I)*c^6*k0^5 - 126*c^5*k0^6 + (6*I)*c^4*k0^7))/(32*k0^3)}, 3, 11, 1] diff --git a/besseltransforms/4-4-0 b/besseltransforms/4-4-0 deleted file mode 100644 index def0ce6..0000000 --- a/besseltransforms/4-4-0 +++ /dev/null @@ -1,9 +0,0 @@ -Integrate[(E^(-(c*x) + I*k0*x)*(1 - E^(-(c*x)))^4*BesselJ[0, k*x])/(k0^4*x^3), {x, 0, Infinity}, Assumptions -> n == 0 && q == 4 && κ == 4 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0] - - -5 c x + I k0 x c x 4 2 2 4 4 6 6 8 8 Pi 2 2 4 4 6 6 8 8 - E (-1 + E ) ((-418854310875 + 29682132480 k x - 3901685760 k x + 1258291200 k x - 2147483648 k x ) Cos[-- + k x] + 4 Sqrt[2] k x (13043905875 - 1229437440 k x + 240844800 k x - 150994944 k x + 2147483648 k x ) (Cos[k x] + Sin[k x])) - 4 -Integrate::idiv: Integral of ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ does not converge on {0, Infinity}. - 19/2 4 25/2 - 8589934592 k k0 Sqrt[2 Pi] x -Series[Integrate[(E^(-(c*x) + I*k0*x)*(1 - E^(-(c*x)))^4*BesselJ[0, k*x])/(k0^4*x^3), {x, 0, Infinity}, Assumptions -> n == 0 && q == 4 && κ == 4 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0], {k, Infinity, 10}] diff --git a/besseltransforms/4-4-1 b/besseltransforms/4-4-1 deleted file mode 100644 index 54ab46a..0000000 --- a/besseltransforms/4-4-1 +++ /dev/null @@ -1,9 +0,0 @@ -Integrate[(E^(-(c*x) + I*k0*x)*(1 - E^(-(c*x)))^4*BesselJ[1, k*x])/(k0^4*x^3), {x, 0, Infinity}, Assumptions -> n == 1 && q == 4 && κ == 4 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0] - - -5 c x + I k0 x c x 4 2 2 4 4 6 6 8 8 Pi 2 2 4 4 6 6 8 8 Pi - -(E (-1 + E ) (8 k x (-14783093325 + 1452971520 k x - 309657600 k x + 251658240 k x + 2147483648 k x ) Cos[-- + k x] - 3 (156043762875 - 11416204800 k x + 1589575680 k x - 587202560 k x + 2147483648 k x ) Sin[-- + k x])) - 4 4 -Integrate::idiv: Integral of ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ does not converge on {0, Infinity}. - 19/2 4 25/2 - 8589934592 k k0 Sqrt[2 Pi] x -Series[Integrate[(E^(-(c*x) + I*k0*x)*(1 - E^(-(c*x)))^4*BesselJ[1, k*x])/(k0^4*x^3), {x, 0, Infinity}, Assumptions -> n == 1 && q == 4 && κ == 4 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0], {k, Infinity, 10}] diff --git a/besseltransforms/4-4-2 b/besseltransforms/4-4-2 deleted file mode 100644 index b12fe80..0000000 --- a/besseltransforms/4-4-2 +++ /dev/null @@ -1,9 +0,0 @@ -Integrate[(E^(-(c*x) + I*k0*x)*(1 - E^(-(c*x)))^4*BesselJ[2, k*x])/(k0^4*x^3), {x, 0, Infinity}, Assumptions -> n == 2 && q == 4 && κ == 4 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0] - - -5 c x + I k0 x c x 4 2 2 4 4 6 6 8 8 Pi 2 2 4 4 6 6 8 8 - -(E (-1 + E ) (15 (-43692253605 + 3528645120 k x - 590413824 k x + 352321536 k x + 2147483648 k x ) Cos[-- + k x] + 4 Sqrt[2] k x (21606059475 - 2421619200 k x + 681246720 k x - 1761607680 k x + 2147483648 k x ) (Cos[k x] + Sin[k x]))) - 4 -Integrate::idiv: Integral of --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- does not converge on {0, Infinity}. - 19/2 4 25/2 - 8589934592 k k0 Sqrt[2 Pi] x -Series[Integrate[(E^(-(c*x) + I*k0*x)*(1 - E^(-(c*x)))^4*BesselJ[2, k*x])/(k0^4*x^3), {x, 0, Infinity}, Assumptions -> n == 2 && q == 4 && κ == 4 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0], {k, Infinity, 10}] diff --git a/besseltransforms/4-4-3 b/besseltransforms/4-4-3 deleted file mode 100644 index 203d301..0000000 --- a/besseltransforms/4-4-3 +++ /dev/null @@ -1,2 +0,0 @@ -(-4*(k^4*(-15 + 8*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0) + 4*k^2*(-5 + 4*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^3 + 8*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^5) + 6*(k^4*(-15 + 8*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0) + 4*k^2*(-5 + 4*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^3 + 8*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^5) - 4*(k^4*(-15 + 8*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0) + 4*k^2*(-5 + 4*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^3 + 8*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^5) + k^4*(-15 + 8*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0) + 4*k^2*(-5 + 4*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^3 + 8*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^5 + k^4*(-15 + 8*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0) + 4*k^2*(-5 + 4*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^3 + 8*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^5)/(120*k^3*k0^4) -SeriesData[k, Infinity, {(3*c^4)/k0^4, (-8*(3*c^5 - I*c^4*k0))/k0^4, (5*(28*c^6 - (18*I)*c^5*k0 - 3*c^4*k0^2))/(2*k0^4), 0, (-7*(993*c^8 - (1200*I)*c^7*k0 - 560*c^6*k0^2 + (120*I)*c^5*k0^3 + 10*c^4*k0^4))/(16*k0^4), 0, (3*(49346*c^10 - (85050*I)*c^9*k0 - 62559*c^8*k0^2 + (25200*I)*c^7*k0^3 + 5880*c^6*k0^4 - (756*I)*c^5*k0^5 - 42*c^4*k0^6))/(32*k0^4), 0, ((-5*(c - I*k0)^12)/128 + (5*(2*c - I*k0)^12)/32 - (15*(3*c - I*k0)^12)/64 + (5*(4*c - I*k0)^12)/32 - (5*(5*c - I*k0)^12)/128)/(120*k0^4)}, 2, 11, 1] diff --git a/besseltransforms/4-4-4 b/besseltransforms/4-4-4 deleted file mode 100644 index b9f00a9..0000000 --- a/besseltransforms/4-4-4 +++ /dev/null @@ -1,2 +0,0 @@ -((5*k^6 + 2*k^4*(15 - 8*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^2 + 8*k^2*(5 - 4*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^4 - 16*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^6)/(240*k^4) - (5*k^6 + 2*k^4*(15 - 8*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^2 + 8*k^2*(5 - 4*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^4 - 16*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^6)/(60*k^4) + (5*k^6 + 2*k^4*(15 - 8*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^2 + 8*k^2*(5 - 4*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^4 - 16*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^6)/(40*k^4) - (5*k^6 + 2*k^4*(15 - 8*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^2 + 8*k^2*(5 - 4*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^4 - 16*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^6)/(60*k^4) + (5*k^6 + 2*k^4*(15 - 8*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^2 + 8*k^2*(5 - 4*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^4 - 16*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^6)/(240*k^4))/k0^4 -SeriesData[k, Infinity, {(4*c^4)/k0^4, (-45*c^5)/k0^4 + ((15*I)*c^4)/k0^3, (224*c^6)/k0^4 - ((144*I)*c^5)/k0^3 - (24*c^4)/k0^2, (-35*(30*c^7 - (28*I)*c^6*k0 - 9*c^5*k0^2 + I*c^4*k0^3))/(2*k0^4), 0, (21*(2025*c^9 - (2979*I)*c^8*k0 - 1800*c^7*k0^2 + (560*I)*c^6*k0^3 + 90*c^5*k0^4 - (6*I)*c^4*k0^5))/(16*k0^4), 0, (-33*(25080*c^11 - (49346*I)*c^10*k0 - 42525*c^9*k0^2 + (20853*I)*c^8*k0^3 + 6300*c^7*k0^4 - (1176*I)*c^6*k0^5 - 126*c^5*k0^6 + (6*I)*c^4*k0^7))/(32*k0^4)}, 2, 11, 1] diff --git a/besseltransforms/4-4-5 b/besseltransforms/4-4-5 deleted file mode 100644 index b225d16..0000000 --- a/besseltransforms/4-4-5 +++ /dev/null @@ -1,2 +0,0 @@ -((k^6*(-35 + 8*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0) + 20*k^4*(-7 + 4*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^3 + 8*k^2*(-21 + 17*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^5 + 64*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^7)/(840*k^5) - (k^6*(-35 + 8*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0) + 20*k^4*(-7 + 4*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^3 + 8*k^2*(-21 + 17*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^5 + 64*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^7)/(210*k^5) + (k^6*(-35 + 8*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0) + 20*k^4*(-7 + 4*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^3 + 8*k^2*(-21 + 17*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^5 + 64*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^7)/(140*k^5) - (k^6*(-35 + 8*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0) + 20*k^4*(-7 + 4*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^3 + 8*k^2*(-21 + 17*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^5 + 64*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^7)/(210*k^5) + (k^6*(-35 + 8*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0) + 20*k^4*(-7 + 4*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^3 + 8*k^2*(-21 + 17*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^5 + 64*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^7)/(840*k^5))/k0^4 -SeriesData[k, Infinity, {(5*c^4)/k0^4, (-72*c^5)/k0^4 + ((24*I)*c^4)/k0^3, (490*c^6)/k0^4 - ((315*I)*c^5)/k0^3 - (105*c^4)/(2*k0^2), (-1920*c^7)/k0^4 + ((1792*I)*c^6)/k0^3 + (576*c^5)/k0^2 - ((64*I)*c^4)/k0, (63*(993*c^8 - (1200*I)*c^7*k0 - 560*c^6*k0^2 + (120*I)*c^5*k0^3 + 10*c^4*k0^4))/(16*k0^4), 0, (-11*(49346*c^10 - (85050*I)*c^9*k0 - 62559*c^8*k0^2 + (25200*I)*c^7*k0^3 + 5880*c^6*k0^4 - (756*I)*c^5*k0^5 - 42*c^4*k0^6))/(32*k0^4), 0, (143*(682591*c^12 - (1504800*I)*c^11*k0 - 1480380*c^10*k0^2 + (850500*I)*c^9*k0^3 + 312795*c^8*k0^4 - (75600*I)*c^7*k0^5 - 11760*c^6*k0^6 + (1080*I)*c^5*k0^7 + 45*c^4*k0^8))/(640*k0^4)}, 2, 11, 1] diff --git a/besseltransforms/4-4-6 b/besseltransforms/4-4-6 deleted file mode 100644 index 9c77b74..0000000 --- a/besseltransforms/4-4-6 +++ /dev/null @@ -1,2 +0,0 @@ -((35*k^8 + 16*k^6*(35 - 12*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^2 + 16*k^4*(105 - 64*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^4 + 64*k^2*(28 - 23*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^6 - 640*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^8)/(6720*k^6) - (35*k^8 + 16*k^6*(35 - 12*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^2 + 16*k^4*(105 - 64*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^4 + 64*k^2*(28 - 23*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^6 - 640*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^8)/(1680*k^6) + (35*k^8 + 16*k^6*(35 - 12*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^2 + 16*k^4*(105 - 64*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^4 + 64*k^2*(28 - 23*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^6 - 640*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^8)/(1120*k^6) - (35*k^8 + 16*k^6*(35 - 12*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^2 + 16*k^4*(105 - 64*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^4 + 64*k^2*(28 - 23*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^6 - 640*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^8)/(1680*k^6) + (35*k^8 + 16*k^6*(35 - 12*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^2 + 16*k^4*(105 - 64*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^4 + 64*k^2*(28 - 23*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^6 - 640*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^8)/(6720*k^6))/k0^4 -SeriesData[k, Infinity, {(6*c^4)/k0^4, (-105*c^5)/k0^4 + ((35*I)*c^4)/k0^3, (896*c^6)/k0^4 - ((576*I)*c^5)/k0^3 - (96*c^4)/k0^2, (-315*(30*c^7 - (28*I)*c^6*k0 - 9*c^5*k0^2 + I*c^4*k0^3))/(2*k0^4), 160*c^4 + (15888*c^8)/k0^4 - ((19200*I)*c^7)/k0^3 - (8960*c^6)/k0^2 + ((1920*I)*c^5)/k0, (-231*(2025*c^9 - (2979*I)*c^8*k0 - 1800*c^7*k0^2 + (560*I)*c^6*k0^3 + 90*c^5*k0^4 - (6*I)*c^4*k0^5))/(16*k0^4), 0, (143*(25080*c^11 - (49346*I)*c^10*k0 - 42525*c^9*k0^2 + (20853*I)*c^8*k0^3 + 6300*c^7*k0^4 - (1176*I)*c^6*k0^5 - 126*c^5*k0^6 + (6*I)*c^4*k0^7))/(32*k0^4)}, 2, 11, 1] diff --git a/besseltransforms/4-4-7 b/besseltransforms/4-4-7 deleted file mode 100644 index 0ba1e1c..0000000 --- a/besseltransforms/4-4-7 +++ /dev/null @@ -1,2 +0,0 @@ -((k^8*(-105 + 16*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0) + 8*k^6*(-105 + 44*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^3 + 144*k^4*(-14 + 9*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^5 + 320*k^2*(-6 + 5*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^7 + 640*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^9)/(5040*k^7) - (k^8*(-105 + 16*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0) + 8*k^6*(-105 + 44*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^3 + 144*k^4*(-14 + 9*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^5 + 320*k^2*(-6 + 5*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^7 + 640*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^9)/(1260*k^7) + (k^8*(-105 + 16*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0) + 8*k^6*(-105 + 44*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^3 + 144*k^4*(-14 + 9*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^5 + 320*k^2*(-6 + 5*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^7 + 640*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^9)/(840*k^7) - (k^8*(-105 + 16*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0) + 8*k^6*(-105 + 44*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^3 + 144*k^4*(-14 + 9*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^5 + 320*k^2*(-6 + 5*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^7 + 640*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^9)/(1260*k^7) + (k^8*(-105 + 16*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0) + 8*k^6*(-105 + 44*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^3 + 144*k^4*(-14 + 9*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^5 + 320*k^2*(-6 + 5*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^7 + 640*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^9)/(5040*k^7))/k0^4 -SeriesData[k, Infinity, {(7*c^4)/k0^4, (-48*(3*c^5 - I*c^4*k0))/k0^4, (105*(28*c^6 - (18*I)*c^5*k0 - 3*c^4*k0^2))/(2*k0^4), (-320*(30*c^7 - (28*I)*c^6*k0 - 9*c^5*k0^2 + I*c^4*k0^3))/k0^4, (693*(993*c^8 - (1200*I)*c^7*k0 - 560*c^6*k0^2 + (120*I)*c^5*k0^3 + 10*c^4*k0^4))/(16*k0^4), (-64*(2025*c^9 - (2979*I)*c^8*k0 - 1800*c^7*k0^2 + (560*I)*c^6*k0^3 + 90*c^5*k0^4 - (6*I)*c^4*k0^5))/k0^4, (143*(49346*c^10 - (85050*I)*c^9*k0 - 62559*c^8*k0^2 + (25200*I)*c^7*k0^3 + 5880*c^6*k0^4 - (756*I)*c^5*k0^5 - 42*c^4*k0^6))/(32*k0^4), 0, ((-13*(c - I*k0)^12)/3072 + (13*(2*c - I*k0)^12)/768 - (13*(3*c - I*k0)^12)/512 + (13*(4*c - I*k0)^12)/768 - (13*(5*c - I*k0)^12)/3072)/k0^4}, 2, 11, 1] diff --git a/besseltransforms/5-1-0.REMOVED.git-id b/besseltransforms/5-1-0.REMOVED.git-id deleted file mode 100644 index f2b0b13..0000000 --- a/besseltransforms/5-1-0.REMOVED.git-id +++ /dev/null @@ -1 +0,0 @@ -6b5039445ac40a8e4dde06ee71a446ec8c971871 \ No newline at end of file diff --git a/besseltransforms/5-1-1.REMOVED.git-id b/besseltransforms/5-1-1.REMOVED.git-id deleted file mode 100644 index 4a3c8ee..0000000 --- a/besseltransforms/5-1-1.REMOVED.git-id +++ /dev/null @@ -1 +0,0 @@ -f5594061661eec519d31142141692d67f7b41978 \ No newline at end of file diff --git a/besseltransforms/5-1-2.REMOVED.git-id b/besseltransforms/5-1-2.REMOVED.git-id deleted file mode 100644 index 67c9a9d..0000000 --- a/besseltransforms/5-1-2.REMOVED.git-id +++ /dev/null @@ -1 +0,0 @@ -a1c5acb5509b38870c8f208e65cec91b86716900 \ No newline at end of file diff --git a/besseltransforms/5-1-3 b/besseltransforms/5-1-3 deleted file mode 100644 index b07afd3..0000000 --- a/besseltransforms/5-1-3 +++ /dev/null @@ -1,2 +0,0 @@ -((k^2*(-3 + Sqrt[1 + k^2/(c - I*k0)^2]) + 4*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^2)/(k^3*Sqrt[1 + k^2/(c - I*k0)^2]) - (5*(k^2*(-3 + Sqrt[1 + k^2/(2*c - I*k0)^2]) + 4*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^2))/(k^3*Sqrt[1 + k^2/(2*c - I*k0)^2]) + (10*(k^2*(-3 + Sqrt[1 + k^2/(3*c - I*k0)^2]) + 4*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^2))/(k^3*Sqrt[1 + k^2/(3*c - I*k0)^2]) - (10*(k^2*(-3 + Sqrt[1 + k^2/(4*c - I*k0)^2]) + 4*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^2))/(k^3*Sqrt[1 + k^2/(4*c - I*k0)^2]) + (5*(k^2*(-3 + Sqrt[1 + k^2/(5*c - I*k0)^2]) + 4*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^2))/(k^3*Sqrt[1 + k^2/(5*c - I*k0)^2]) - (k^2*(-3 + Sqrt[1 + k^2/(6*c - I*k0)^2]) + 4*(-1 + Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^2)/(k^3*Sqrt[1 + k^2/(6*c - I*k0)^2]))/k0 -SeriesData[k, Infinity, {(-105*c^5)/(k*k0), 0, (945*(38*c^7 - (21*I)*c^6*k0 - 3*c^5*k0^2))/(2*k*k0), 0, (-17325*(1087*c^9 - (1134*I)*c^8*k0 - 456*c^7*k0^2 + (84*I)*c^6*k0^3 + 6*c^5*k0^4))/(16*k*k0)}, 5, 11, 1] diff --git a/besseltransforms/5-1-4 b/besseltransforms/5-1-4 deleted file mode 100644 index 6567ab6..0000000 --- a/besseltransforms/5-1-4 +++ /dev/null @@ -1,2 +0,0 @@ -((k^4 - 4*k^2*(-2 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^2 - 8*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^4)/(k^4*Sqrt[1 + k^2/(c - I*k0)^2]*(c - I*k0)) - (5*(k^4 - 4*k^2*(-2 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^2 - 8*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^4))/(k^4*Sqrt[1 + k^2/(2*c - I*k0)^2]*(2*c - I*k0)) + (10*(k^4 - 4*k^2*(-2 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^2 - 8*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^4))/(k^4*Sqrt[1 + k^2/(3*c - I*k0)^2]*(3*c - I*k0)) - (10*(k^4 - 4*k^2*(-2 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^2 - 8*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^4))/(k^4*Sqrt[1 + k^2/(4*c - I*k0)^2]*(4*c - I*k0)) + (5*(k^4 - 4*k^2*(-2 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^2 - 8*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^4))/(k^4*Sqrt[1 + k^2/(5*c - I*k0)^2]*(5*c - I*k0)) - (k^4 - 4*k^2*(-2 + Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^2 - 8*(-1 + Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^4)/(k^4*Sqrt[1 + k^2/(6*c - I*k0)^2]*(6*c - I*k0)))/k0 -SeriesData[k, Infinity, {((-945*I)*c^5)/k + (6615*c^6)/(2*k*k0), 0, (-10395*(189*c^8 - (152*I)*c^7*k0 - 42*c^6*k0^2 + (4*I)*c^5*k0^3))/(8*k*k0), 0, (45045*(8547*c^10 - (10870*I)*c^9*k0 - 5670*c^8*k0^2 + (1520*I)*c^7*k0^3 + 210*c^6*k0^4 - (12*I)*c^5*k0^5))/(32*k*k0)}, 6, 11, 1] diff --git a/besseltransforms/5-1-5 b/besseltransforms/5-1-5 deleted file mode 100644 index 52d673d..0000000 --- a/besseltransforms/5-1-5 +++ /dev/null @@ -1,2 +0,0 @@ -((k^4*(-5 + Sqrt[1 + k^2/(c - I*k0)^2]) + 4*k^2*(-5 + 3*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^2 + 16*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^4)/(k^5*Sqrt[1 + k^2/(c - I*k0)^2]) - (5*(k^4*(-5 + Sqrt[1 + k^2/(2*c - I*k0)^2]) + 4*k^2*(-5 + 3*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^2 + 16*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^4))/(k^5*Sqrt[1 + k^2/(2*c - I*k0)^2]) + (10*(k^4*(-5 + Sqrt[1 + k^2/(3*c - I*k0)^2]) + 4*k^2*(-5 + 3*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^2 + 16*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^4))/(k^5*Sqrt[1 + k^2/(3*c - I*k0)^2]) - (10*(k^4*(-5 + Sqrt[1 + k^2/(4*c - I*k0)^2]) + 4*k^2*(-5 + 3*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^2 + 16*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^4))/(k^5*Sqrt[1 + k^2/(4*c - I*k0)^2]) + (5*(k^4*(-5 + Sqrt[1 + k^2/(5*c - I*k0)^2]) + 4*k^2*(-5 + 3*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^2 + 16*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^4))/(k^5*Sqrt[1 + k^2/(5*c - I*k0)^2]) - (k^4*(-5 + Sqrt[1 + k^2/(6*c - I*k0)^2]) + 4*k^2*(-5 + 3*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^2 + 16*(-1 + Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^4)/(k^5*Sqrt[1 + k^2/(6*c - I*k0)^2]))/k0 -SeriesData[k, Infinity, {(945*c^5)/(k*k0), 0, (-3465*(38*c^7 - (21*I)*c^6*k0 - 3*c^5*k0^2))/(2*k*k0), 0, (45045*(1087*c^9 - (1134*I)*c^8*k0 - 456*c^7*k0^2 + (84*I)*c^6*k0^3 + 6*c^5*k0^4))/(16*k*k0)}, 5, 11, 1] diff --git a/besseltransforms/5-1-6 b/besseltransforms/5-1-6 deleted file mode 100644 index 6b35f98..0000000 --- a/besseltransforms/5-1-6 +++ /dev/null @@ -1,2 +0,0 @@ -((k^6 - 6*k^4*(-3 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^2 + 16*k^2*(3 - 2*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^4 - 32*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^6)/(k^6*Sqrt[1 + k^2/(c - I*k0)^2]*(c - I*k0)) - (5*(k^6 - 6*k^4*(-3 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^2 + 16*k^2*(3 - 2*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^4 - 32*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^6))/(k^6*Sqrt[1 + k^2/(2*c - I*k0)^2]*(2*c - I*k0)) + (10*(k^6 - 6*k^4*(-3 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^2 + 16*k^2*(3 - 2*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^4 - 32*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^6))/(k^6*Sqrt[1 + k^2/(3*c - I*k0)^2]*(3*c - I*k0)) - (10*(k^6 - 6*k^4*(-3 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^2 + 16*k^2*(3 - 2*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^4 - 32*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^6))/(k^6*Sqrt[1 + k^2/(4*c - I*k0)^2]*(4*c - I*k0)) + (5*(k^6 - 6*k^4*(-3 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^2 + 16*k^2*(3 - 2*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^4 - 32*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^6))/(k^6*Sqrt[1 + k^2/(5*c - I*k0)^2]*(5*c - I*k0)) - (k^6 - 6*k^4*(-3 + Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^2 + 16*k^2*(3 - 2*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^4 - 32*(-1 + Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^6)/(k^6*Sqrt[1 + k^2/(6*c - I*k0)^2]*(6*c - I*k0)))/k0 -SeriesData[k, Infinity, {(3840*c^5)/(k*k0), ((10395*I)*c^5)/k - (72765*c^6)/(2*k*k0), 0, (45045*(189*c^8 - (152*I)*c^7*k0 - 42*c^6*k0^2 + (4*I)*c^5*k0^3))/(8*k*k0), 0, (-135135*(8547*c^10 - (10870*I)*c^9*k0 - 5670*c^8*k0^2 + (1520*I)*c^7*k0^3 + 210*c^6*k0^4 - (12*I)*c^5*k0^5))/(32*k*k0)}, 5, 11, 1] diff --git a/besseltransforms/5-1-7 b/besseltransforms/5-1-7 deleted file mode 100644 index 2c7756e..0000000 --- a/besseltransforms/5-1-7 +++ /dev/null @@ -1,2 +0,0 @@ -((k^6*(-7 + Sqrt[1 + k^2/(c - I*k0)^2]) + 8*k^4*(-7 + 3*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^2 + 16*k^2*(-7 + 5*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^4 + 64*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^6)/(k^7*Sqrt[1 + k^2/(c - I*k0)^2]) - (5*(k^6*(-7 + Sqrt[1 + k^2/(2*c - I*k0)^2]) + 8*k^4*(-7 + 3*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^2 + 16*k^2*(-7 + 5*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^4 + 64*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^6))/(k^7*Sqrt[1 + k^2/(2*c - I*k0)^2]) + (10*(k^6*(-7 + Sqrt[1 + k^2/(3*c - I*k0)^2]) + 8*k^4*(-7 + 3*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^2 + 16*k^2*(-7 + 5*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^4 + 64*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^6))/(k^7*Sqrt[1 + k^2/(3*c - I*k0)^2]) - (10*(k^6*(-7 + Sqrt[1 + k^2/(4*c - I*k0)^2]) + 8*k^4*(-7 + 3*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^2 + 16*k^2*(-7 + 5*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^4 + 64*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^6))/(k^7*Sqrt[1 + k^2/(4*c - I*k0)^2]) + (5*(k^6*(-7 + Sqrt[1 + k^2/(5*c - I*k0)^2]) + 8*k^4*(-7 + 3*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^2 + 16*k^2*(-7 + 5*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^4 + 64*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^6))/(k^7*Sqrt[1 + k^2/(5*c - I*k0)^2]) - (k^6*(-7 + Sqrt[1 + k^2/(6*c - I*k0)^2]) + 8*k^4*(-7 + 3*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^2 + 16*k^2*(-7 + 5*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^4 + 64*(-1 + Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^6)/(k^7*Sqrt[1 + k^2/(6*c - I*k0)^2]))/k0 -SeriesData[k, Infinity, {(10395*c^5)/(k*k0), ((46080*I)*c^5)/k - (161280*c^6)/(k*k0), (45045*(38*c^7 - (21*I)*c^6*k0 - 3*c^5*k0^2))/(2*k*k0), 0, (-225225*(1087*c^9 - (1134*I)*c^8*k0 - 456*c^7*k0^2 + (84*I)*c^6*k0^3 + 6*c^5*k0^4))/(16*k*k0)}, 5, 11, 1] diff --git a/besseltransforms/5-2-0 b/besseltransforms/5-2-0 deleted file mode 100644 index f3c61c3..0000000 --- a/besseltransforms/5-2-0 +++ /dev/null @@ -1,9 +0,0 @@ -Integrate[(E^(I*k0*x)*(1 - E^(-(c*x)))^5*BesselJ[0, k*x])/(k0^2*x), {x, 0, Infinity}, Assumptions -> n == 0 && q == 2 && κ == 5] - - I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi I k0 x 2 Pi -5 c x + I k0 x 2 Pi -4 c x + I k0 x 2 Pi -3 c x + I k0 x 2 Pi -2 c x + I k0 x 2 Pi -(c x) + I k0 x 2 Pi I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi - 13043905875 E Cos[-- - k x] 13043905875 E Cos[-- - k x] 65219529375 E Cos[-- - k x] 65219529375 E Cos[-- - k x] 65219529375 E Cos[-- - k x] 65219529375 E Cos[-- - k x] 2401245 E Cos[-- - k x] 2401245 E Cos[-- - k x] 12006225 E Cos[-- - k x] 12006225 E Cos[-- - k x] 12006225 E Cos[-- - k x] 12006225 E Cos[-- - k x] 3675 E Cos[-- - k x] 3675 E Cos[-- - k x] 18375 E Cos[-- - k x] 18375 E Cos[-- - k x] 18375 E Cos[-- - k x] 18375 E Cos[-- - k x] 9 E Cos[-- - k x] 9 E Cos[-- - k x] 45 E Cos[-- - k x] 45 E Cos[-- - k x] 45 E Cos[-- - k x] 45 E Cos[-- - k x] E Sqrt[--] Cos[-- - k x] E Sqrt[--] Cos[-- - k x] 5 E Sqrt[--] Cos[-- - k x] 10 E Sqrt[--] Cos[-- - k x] 10 E Sqrt[--] Cos[-- - k x] 5 E Sqrt[--] Cos[-- - k x] 418854310875 E Sin[-- - k x] 418854310875 E Sin[-- - k x] 2094271554375 E Sin[-- - k x] 2094271554375 E Sin[-- - k x] 2094271554375 E Sin[-- - k x] 2094271554375 E Sin[-- - k x] 57972915 E Sin[-- - k x] 57972915 E Sin[-- - k x] 289864575 E Sin[-- - k x] 289864575 E Sin[-- - k x] 289864575 E Sin[-- - k x] 289864575 E Sin[-- - k x] 59535 E Sin[-- - k x] 59535 E Sin[-- - k x] 297675 E Sin[-- - k x] 297675 E Sin[-- - k x] 297675 E Sin[-- - k x] 297675 E Sin[-- - k x] 75 E Sin[-- - k x] 75 E Sin[-- - k x] 375 E Sin[-- - k x] 375 E Sin[-- - k x] 375 E Sin[-- - k x] 375 E Sin[-- - k x] E Sin[-- - k x] E Sin[-- - k x] 5 E Sin[-- - k x] 5 E Sin[-- - k x] 5 E Sin[-- - k x] 5 E Sin[-- - k x] - 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 Pi 4 Pi 4 Pi 4 Pi 4 Pi 4 Pi 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 -Integrate::idiv: Integral of ------------------------------------- - ------------------------------------------ + ------------------------------------------ - ------------------------------------------ + ------------------------------------------ - ------------------------------------------ - ---------------------------------- + -------------------------------------- - --------------------------------------- + --------------------------------------- - --------------------------------------- + --------------------------------------- + ------------------------------- - ----------------------------------- + ------------------------------------ - ------------------------------------ + ------------------------------------ - ------------------------------------ - --------------------------- + -------------------------------- - --------------------------------- + --------------------------------- - --------------------------------- + --------------------------------- + ------------------------------ - --------------------------------------- + ----------------------------------------- - ------------------------------------------ + ------------------------------------------ - ----------------------------------------- - ------------------------------------- + ------------------------------------------- - -------------------------------------------- + -------------------------------------------- - -------------------------------------------- + -------------------------------------------- + ----------------------------------- - --------------------------------------- + ---------------------------------------- - ---------------------------------------- + ---------------------------------------- - ---------------------------------------- - --------------------------------- + ------------------------------------ - ------------------------------------- + ------------------------------------- - ------------------------------------- + ------------------------------------- + ---------------------------- - --------------------------------- + ---------------------------------- - ---------------------------------- + ---------------------------------- - ---------------------------------- - -------------------------- + ------------------------------ - -------------------------------- + -------------------------------- - -------------------------------- + -------------------------------- does not converge on {0, Infinity}. - 17/2 2 19/2 17/2 2 19/2 17/2 2 19/2 17/2 2 19/2 17/2 2 19/2 17/2 2 19/2 13/2 2 15/2 13/2 2 15/2 13/2 2 15/2 13/2 2 15/2 13/2 2 15/2 13/2 2 15/2 9/2 2 11/2 9/2 2 11/2 9/2 2 11/2 9/2 2 11/2 9/2 2 11/2 9/2 2 11/2 5/2 2 7/2 5/2 2 7/2 5/2 2 7/2 5/2 2 7/2 5/2 2 7/2 5/2 2 7/2 2 3/2 2 3/2 2 3/2 2 3/2 2 3/2 2 3/2 19/2 2 21/2 19/2 2 21/2 19/2 2 21/2 19/2 2 21/2 19/2 2 21/2 19/2 2 21/2 15/2 2 17/2 15/2 2 17/2 15/2 2 17/2 15/2 2 17/2 15/2 2 17/2 15/2 2 17/2 11/2 2 13/2 11/2 2 13/2 11/2 2 13/2 11/2 2 13/2 11/2 2 13/2 11/2 2 13/2 7/2 2 9/2 7/2 2 9/2 7/2 2 9/2 7/2 2 9/2 7/2 2 9/2 7/2 2 9/2 3/2 2 5/2 3/2 2 5/2 3/2 2 5/2 3/2 2 5/2 3/2 2 5/2 3/2 2 5/2 - 1073741824 k k0 Sqrt[2 Pi] x 1073741824 k k0 Sqrt[2 Pi] x 1073741824 k k0 Sqrt[2 Pi] x 536870912 k k0 Sqrt[2 Pi] x 536870912 k k0 Sqrt[2 Pi] x 1073741824 k k0 Sqrt[2 Pi] x 2097152 k k0 Sqrt[2 Pi] x 2097152 k k0 Sqrt[2 Pi] x 2097152 k k0 Sqrt[2 Pi] x 1048576 k k0 Sqrt[2 Pi] x 1048576 k k0 Sqrt[2 Pi] x 2097152 k k0 Sqrt[2 Pi] x 16384 k k0 Sqrt[2 Pi] x 16384 k k0 Sqrt[2 Pi] x 16384 k k0 Sqrt[2 Pi] x 8192 k k0 Sqrt[2 Pi] x 8192 k k0 Sqrt[2 Pi] x 16384 k k0 Sqrt[2 Pi] x 64 k k0 Sqrt[2 Pi] x 64 k k0 Sqrt[2 Pi] x 64 k k0 Sqrt[2 Pi] x 32 k k0 Sqrt[2 Pi] x 32 k k0 Sqrt[2 Pi] x 64 k k0 Sqrt[2 Pi] x Sqrt[k] k0 x Sqrt[k] k0 x Sqrt[k] k0 x Sqrt[k] k0 x Sqrt[k] k0 x Sqrt[k] k0 x 8589934592 k k0 Sqrt[2 Pi] x 8589934592 k k0 Sqrt[2 Pi] x 8589934592 k k0 Sqrt[2 Pi] x 4294967296 k k0 Sqrt[2 Pi] x 4294967296 k k0 Sqrt[2 Pi] x 8589934592 k k0 Sqrt[2 Pi] x 16777216 k k0 Sqrt[2 Pi] x 16777216 k k0 Sqrt[2 Pi] x 16777216 k k0 Sqrt[2 Pi] x 8388608 k k0 Sqrt[2 Pi] x 8388608 k k0 Sqrt[2 Pi] x 16777216 k k0 Sqrt[2 Pi] x 131072 k k0 Sqrt[2 Pi] x 131072 k k0 Sqrt[2 Pi] x 131072 k k0 Sqrt[2 Pi] x 65536 k k0 Sqrt[2 Pi] x 65536 k k0 Sqrt[2 Pi] x 131072 k k0 Sqrt[2 Pi] x 512 k k0 Sqrt[2 Pi] x 512 k k0 Sqrt[2 Pi] x 512 k k0 Sqrt[2 Pi] x 256 k k0 Sqrt[2 Pi] x 256 k k0 Sqrt[2 Pi] x 512 k k0 Sqrt[2 Pi] x 4 k k0 Sqrt[2 Pi] x 4 k k0 Sqrt[2 Pi] x 4 k k0 Sqrt[2 Pi] x 2 k k0 Sqrt[2 Pi] x 2 k k0 Sqrt[2 Pi] x 4 k k0 Sqrt[2 Pi] x -Series[Integrate[(E^(I*k0*x)*(1 - E^(-(c*x)))^5*BesselJ[0, k*x])/(k0^2*x), {x, 0, Infinity}, Assumptions -> n == 0 && q == 2 && κ == 5], {k, Infinity, 10}] diff --git a/besseltransforms/5-2-1 b/besseltransforms/5-2-1 deleted file mode 100644 index 53b8241..0000000 --- a/besseltransforms/5-2-1 +++ /dev/null @@ -1,2 +0,0 @@ -(-10*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0) + 20*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0) - 20*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0) + 10*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0) - 2*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0) + k*Sqrt[Pi]*(Piecewise[{{0, k^2/k0^2 <= 1}}, (2*Sqrt[k^2 - k0^2])/(k*Sqrt[Pi])] + I*Piecewise[{{(2*k0)/(k*Sqrt[Pi]), k0^2/k^2 < 1}, {(2*(k0 - Sqrt[-k^2 + k0^2]))/(k*Sqrt[Pi]), k0^2/k^2 > 1}}, 0]))/(2*k*k0^2) -Piecewise[{{SeriesData[k, Infinity, {(-225*c^6)/(2*k0^2) + ((45*I)*c^5)/k0, 0, (-7875*c^6)/4 + (39375*c^8)/(8*k0^2) - ((5250*I)*c^7)/k0 + (525*I)/2*c^5*k0, 0, (-2205*(2025*c^10 - (3310*I)*c^9*k0 - 2250*c^8*k0^2 + (800*I)*c^7*k0^3 + 150*c^6*k0^4 - (12*I)*c^5*k0^5))/(32*k0^2)}, 6, 11, 1], (k0 <= 0 && k^2/k0^2 > 1) || k0 > 0}}, SeriesData[k, Infinity, {-k0^(-2), 0, 1/2, 0, ((5*c*(c - I*k0)^3)/8 - (5*c*(2*c - I*k0)^3)/2 + (15*c*(3*c - I*k0)^3)/4 - (5*c*(4*c - I*k0)^3)/2 + (5*c*(5*c - I*k0)^3)/8 - (5*I)/8*(c - I*k0)^3*k0 + (5*I)/4*(2*c - I*k0)^3*k0 - (5*I)/4*(3*c - I*k0)^3*k0 + (5*I)/8*(4*c - I*k0)^3*k0 - I/8*(5*c - I*k0)^3*k0)/k0^2, 0, ((-5*c*(c - I*k0)^5)/16 + (5*c*(2*c - I*k0)^5)/4 - (15*c*(3*c - I*k0)^5)/8 + (5*c*(4*c - I*k0)^5)/4 - (5*c*(5*c - I*k0)^5)/16 + (5*I)/16*(c - I*k0)^5*k0 - (5*I)/8*(2*c - I*k0)^5*k0 + (5*I)/8*(3*c - I*k0)^5*k0 - (5*I)/16*(4*c - I*k0)^5*k0 + I/16*(5*c - I*k0)^5*k0)/k0^2, 0, ((25*c*(c - I*k0)^7)/128 - (25*c*(2*c - I*k0)^7)/32 + (75*c*(3*c - I*k0)^7)/64 - (25*c*(4*c - I*k0)^7)/32 + (25*c*(5*c - I*k0)^7)/128 - (25*I)/128*(c - I*k0)^7*k0 + (25*I)/64*(2*c - I*k0)^7*k0 - (25*I)/64*(3*c - I*k0)^7*k0 + (25*I)/128*(4*c - I*k0)^7*k0 - (5*I)/128*(5*c - I*k0)^7*k0)/k0^2, 0, ((-35*c*(c - I*k0)^9)/256 + (35*c*(2*c - I*k0)^9)/64 - (105*c*(3*c - I*k0)^9)/128 + (35*c*(4*c - I*k0)^9)/64 - (35*c*(5*c - I*k0)^9)/256 + (35*I)/256*(c - I*k0)^9*k0 - (35*I)/128*(2*c - I*k0)^9*k0 + (35*I)/128*(3*c - I*k0)^9*k0 - (35*I)/256*(4*c - I*k0)^9*k0 + (7*I)/256*(5*c - I*k0)^9*k0)/k0^2}, 0, 11, 1]] diff --git a/besseltransforms/5-2-2 b/besseltransforms/5-2-2 deleted file mode 100644 index bad9bad..0000000 --- a/besseltransforms/5-2-2 +++ /dev/null @@ -1,2 +0,0 @@ -(-k^2 + 10*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^2 - 20*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^2 + 20*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^2 - 10*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^2 + 2*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^2 + k^2*Sqrt[Pi]*(I*Piecewise[{{0, k^2/k0^2 <= 1}}, (2*k0*Sqrt[k^2 - k0^2])/(k^2*Sqrt[Pi])] + Piecewise[{{(k^2 + 2*k0*(-k0 + Sqrt[-k^2 + k0^2]))/(k^2*Sqrt[Pi]), k^2/k0^2 < 1}, {(1 - (2*k0^2)/k^2)/Sqrt[Pi], k^2/k0^2 > 1}}, 0]))/(2*k^2*k0^2) -SeriesData[k, Infinity, {(-15*c^5)/k0^2, 0, (-315*c^5)/2 + (1050*c^7)/k0^2 - ((1575*I)/2*c^6)/k0, 0, (-1575*(331*c^9 - (450*I)*c^8*k0 - 240*c^7*k0^2 + (60*I)*c^6*k0^3 + 6*c^5*k0^4))/(16*k0^2)}, 5, 11, 1] diff --git a/besseltransforms/5-2-3 b/besseltransforms/5-2-3 deleted file mode 100644 index ad65f50..0000000 --- a/besseltransforms/5-2-3 +++ /dev/null @@ -1,2 +0,0 @@ -(k^2*(-3 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0) + 4*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^3 - 5*k^2*(-3 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0) - 20*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^3 + 10*k^2*(-3 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0) + 40*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^3 - 10*k^2*(-3 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0) - 40*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^3 + 5*k^2*(-3 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0) + 20*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^3 - k^2*(-3 + Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0) - 4*(-1 + Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^3)/(3*k^3*k0^2) -SeriesData[k, Infinity, {(735*c^6)/(2*k0^2) - ((105*I)*c^5)/k0, 0, (19845*c^6)/4 - (178605*c^8)/(8*k0^2) + ((17955*I)*c^7)/k0 - (945*I)/2*c^5*k0, 0, (3465*(8547*c^10 - (10870*I)*c^9*k0 - 5670*c^8*k0^2 + (1520*I)*c^7*k0^3 + 210*c^6*k0^4 - (12*I)*c^5*k0^5))/(32*k0^2)}, 6, 11, 1] diff --git a/besseltransforms/5-2-4 b/besseltransforms/5-2-4 deleted file mode 100644 index 85a0280..0000000 --- a/besseltransforms/5-2-4 +++ /dev/null @@ -1,2 +0,0 @@ -(-(k^2*(-2 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^2) - 2*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^4 + 5*k^2*(-2 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^2 + 10*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^4 - 10*k^2*(-2 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^2 - 20*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^4 + 10*k^2*(-2 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^2 + 20*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^4 - 5*k^2*(-2 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^2 - 10*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^4 + k^2*(-2 + Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^2 + 2*(-1 + Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^4)/(k^4*k0^2) -SeriesData[k, Infinity, {(105*c^5)/k0^2, 0, (945*c^5)/2 - (5985*c^7)/k0^2 + ((6615*I)/2*c^6)/k0, 0, (3465*(1087*c^9 - (1134*I)*c^8*k0 - 456*c^7*k0^2 + (84*I)*c^6*k0^3 + 6*c^5*k0^4))/(16*k0^2)}, 5, 11, 1] diff --git a/besseltransforms/5-2-5 b/besseltransforms/5-2-5 deleted file mode 100644 index 78e9161..0000000 --- a/besseltransforms/5-2-5 +++ /dev/null @@ -1,2 +0,0 @@ -((k^4*(-5 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0) + 4*k^2*(-5 + 3*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^3 + 16*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^5)/(5*k^5) - (k^4*(-5 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0) + 4*k^2*(-5 + 3*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^3 + 16*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^5)/k^5 + (2*(k^4*(-5 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0) + 4*k^2*(-5 + 3*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^3 + 16*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^5))/k^5 - (2*(k^4*(-5 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0) + 4*k^2*(-5 + 3*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^3 + 16*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^5))/k^5 + (k^4*(-5 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0) + 4*k^2*(-5 + 3*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^3 + 16*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^5)/k^5 - (k^4*(-5 + Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0) + 4*k^2*(-5 + 3*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^3 + 16*(-1 + Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^5)/(5*k^5))/k0^2 -SeriesData[k, Infinity, {(384*c^5)/k0^2, (-6615*c^6)/(2*k0^2) + ((945*I)*c^5)/k0, 0, (-72765*c^6)/4 + (654885*c^8)/(8*k0^2) - ((65835*I)*c^7)/k0 + (3465*I)/2*c^5*k0, 0, (-9009*(8547*c^10 - (10870*I)*c^9*k0 - 5670*c^8*k0^2 + (1520*I)*c^7*k0^3 + 210*c^6*k0^4 - (12*I)*c^5*k0^5))/(32*k0^2)}, 5, 11, 1] diff --git a/besseltransforms/5-2-6 b/besseltransforms/5-2-6 deleted file mode 100644 index aa76553..0000000 --- a/besseltransforms/5-2-6 +++ /dev/null @@ -1,2 +0,0 @@ -((k^6 - 6*k^4*(-3 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^2 + 16*k^2*(3 - 2*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^4 - 32*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^6)/(6*k^6) - (5*(k^6 - 6*k^4*(-3 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^2 + 16*k^2*(3 - 2*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^4 - 32*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^6))/(6*k^6) + (5*(k^6 - 6*k^4*(-3 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^2 + 16*k^2*(3 - 2*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^4 - 32*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^6))/(3*k^6) - (5*(k^6 - 6*k^4*(-3 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^2 + 16*k^2*(3 - 2*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^4 - 32*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^6))/(3*k^6) + (5*(k^6 - 6*k^4*(-3 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^2 + 16*k^2*(3 - 2*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^4 - 32*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^6))/(6*k^6) - (k^6 - 6*k^4*(-3 + Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^2 + 16*k^2*(3 - 2*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^4 - 32*(-1 + Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^6)/(6*k^6))/k0^2 -SeriesData[k, Infinity, {(945*c^5)/k0^2, (-13440*c^6)/k0^2 + ((3840*I)*c^5)/k0, (-10395*c^5)/2 + (65835*c^7)/k0^2 - ((72765*I)/2*c^6)/k0, 0, (-15015*(1087*c^9 - (1134*I)*c^8*k0 - 456*c^7*k0^2 + (84*I)*c^6*k0^3 + 6*c^5*k0^4))/(16*k0^2)}, 5, 11, 1] diff --git a/besseltransforms/5-2-7 b/besseltransforms/5-2-7 deleted file mode 100644 index 8797403..0000000 --- a/besseltransforms/5-2-7 +++ /dev/null @@ -1,2 +0,0 @@ -((k^6*(-7 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0) + 8*k^4*(-7 + 3*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^3 + 16*k^2*(-7 + 5*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^5 + 64*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^7)/(7*k^7) - (5*(k^6*(-7 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0) + 8*k^4*(-7 + 3*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^3 + 16*k^2*(-7 + 5*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^5 + 64*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^7))/(7*k^7) + (10*(k^6*(-7 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0) + 8*k^4*(-7 + 3*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^3 + 16*k^2*(-7 + 5*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^5 + 64*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^7))/(7*k^7) - (10*(k^6*(-7 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0) + 8*k^4*(-7 + 3*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^3 + 16*k^2*(-7 + 5*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^5 + 64*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^7))/(7*k^7) + (5*(k^6*(-7 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0) + 8*k^4*(-7 + 3*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^3 + 16*k^2*(-7 + 5*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^5 + 64*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^7))/(7*k^7) - (k^6*(-7 + Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0) + 8*k^4*(-7 + 3*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^3 + 16*k^2*(-7 + 5*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^5 + 64*(-1 + Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^7)/(7*k^7))/k0^2 -SeriesData[k, Infinity, {(1920*c^5)/k0^2, (-72765*c^6)/(2*k0^2) + ((10395*I)*c^5)/k0, -23040*c^5 + (291840*c^7)/k0^2 - ((161280*I)*c^6)/k0, (945945*c^6)/4 - (8513505*c^8)/(8*k0^2) + ((855855*I)*c^7)/k0 - (45045*I)/2*c^5*k0, 0, (45045*(8547*c^10 - (10870*I)*c^9*k0 - 5670*c^8*k0^2 + (1520*I)*c^7*k0^3 + 210*c^6*k0^4 - (12*I)*c^5*k0^5))/(32*k0^2)}, 5, 11, 1] diff --git a/besseltransforms/5-3-0 b/besseltransforms/5-3-0 deleted file mode 100644 index c39b980..0000000 --- a/besseltransforms/5-3-0 +++ /dev/null @@ -1,2 +0,0 @@ - -Simplify::time: Time spent on a transformation exceeded 300. seconds, and the transformation was aborted. Increasing the value of TimeConstraint option may improve the result of simplification. diff --git a/besseltransforms/5-3-1 b/besseltransforms/5-3-1 deleted file mode 100644 index c39b980..0000000 --- a/besseltransforms/5-3-1 +++ /dev/null @@ -1,2 +0,0 @@ - -Simplify::time: Time spent on a transformation exceeded 300. seconds, and the transformation was aborted. Increasing the value of TimeConstraint option may improve the result of simplification. diff --git a/besseltransforms/5-3-2 b/besseltransforms/5-3-2 deleted file mode 100644 index bd05e82..0000000 --- a/besseltransforms/5-3-2 +++ /dev/null @@ -1,2 +0,0 @@ -(10*k^2*(3 - 2*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0) - 20*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^3 + 20*k^2*(-3 + 2*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0) + 40*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^3 + 20*k^2*(3 - 2*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0) - 40*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^3 + 10*k^2*(-3 + 2*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0) + 20*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^3 + 2*k^2*(3 - 2*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0) - 4*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^3 + 3*k^2*k0*Sqrt[Pi]*(Piecewise[{{0, k^2/k0^2 <= 1}}, (4*(k^2 - k0^2)^(3/2))/(3*k^2*k0*Sqrt[Pi])] + I*Piecewise[{{(-2*(2*k0*(k0 - Sqrt[-k^2 + k0^2]) + k^2*(-3 + (2*Sqrt[-k^2 + k0^2])/k0)))/(3*k^2*Sqrt[Pi]), k^2/k0^2 < 1}, {(2*(1 - (2*k0^2)/(3*k^2)))/Sqrt[Pi], k^2/k0^2 > 1}}, 0]))/(12*k^2*k0^3) -SeriesData[k, Infinity, {(75*c^6)/(2*k0^3) - ((15*I)*c^5)/k0^2, 0, (-105*(75*c^8 - (80*I)*c^7*k0 - 30*c^6*k0^2 + (4*I)*c^5*k0^3))/(8*k0^3), 0, (315*(2025*c^10 - (3310*I)*c^9*k0 - 2250*c^8*k0^2 + (800*I)*c^7*k0^3 + 150*c^6*k0^4 - (12*I)*c^5*k0^5))/(32*k0^3)}, 5, 11, 1] diff --git a/besseltransforms/5-3-3 b/besseltransforms/5-3-3 deleted file mode 100644 index cf02c58..0000000 --- a/besseltransforms/5-3-3 +++ /dev/null @@ -1,2 +0,0 @@ -((3*k^4 + 4*k^2*(3 - 2*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^2 - 8*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^4)/(24*k^3) - (5*(3*k^4 + 4*k^2*(3 - 2*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^2 - 8*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^4))/(24*k^3) + (5*(3*k^4 + 4*k^2*(3 - 2*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^2 - 8*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^4))/(12*k^3) - (5*(3*k^4 + 4*k^2*(3 - 2*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^2 - 8*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^4))/(12*k^3) + (5*(3*k^4 + 4*k^2*(3 - 2*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^2 - 8*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^4))/(24*k^3) - (3*k^4 + 4*k^2*(3 - 2*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^2 - 8*(-1 + Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^4)/(24*k^3))/k0^3 -SeriesData[k, Infinity, {(15*c^5)/k0^3, 0, (-35*(38*c^7 - (21*I)*c^6*k0 - 3*c^5*k0^2))/(2*k0^3), 0, (315*(1087*c^9 - (1134*I)*c^8*k0 - 456*c^7*k0^2 + (84*I)*c^6*k0^3 + 6*c^5*k0^4))/(16*k0^3), 0, (-165*(120332*c^11 - (179487*I)*c^10*k0 - 114135*c^9*k0^2 + (39690*I)*c^8*k0^3 + 7980*c^7*k0^4 - (882*I)*c^6*k0^5 - 42*c^5*k0^6))/(32*k0^3)}, 4, 11, 1] diff --git a/besseltransforms/5-3-4 b/besseltransforms/5-3-4 deleted file mode 100644 index a0ae761..0000000 --- a/besseltransforms/5-3-4 +++ /dev/null @@ -1,2 +0,0 @@ -((k^4*(-15 + 4*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0) + 4*k^2*(-10 + 7*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^3 + 24*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^5)/(60*k^4) - (k^4*(-15 + 4*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0) + 4*k^2*(-10 + 7*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^3 + 24*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^5)/(12*k^4) + (k^4*(-15 + 4*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0) + 4*k^2*(-10 + 7*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^3 + 24*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^5)/(6*k^4) - (k^4*(-15 + 4*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0) + 4*k^2*(-10 + 7*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^3 + 24*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^5)/(6*k^4) + (k^4*(-15 + 4*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0) + 4*k^2*(-10 + 7*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^3 + 24*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^5)/(12*k^4) - (k^4*(-15 + 4*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0) + 4*k^2*(-10 + 7*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^3 + 24*(-1 + Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^5)/(60*k^4))/k0^3 -SeriesData[k, Infinity, {(48*c^5)/k0^3, (-735*c^6)/(2*k0^3) + ((105*I)*c^5)/k0^2, 0, (315*(189*c^8 - (152*I)*c^7*k0 - 42*c^6*k0^2 + (4*I)*c^5*k0^3))/(8*k0^3), 0, (-693*(8547*c^10 - (10870*I)*c^9*k0 - 5670*c^8*k0^2 + (1520*I)*c^7*k0^3 + 210*c^6*k0^4 - (12*I)*c^5*k0^5))/(32*k0^3)}, 4, 11, 1] diff --git a/besseltransforms/5-3-5 b/besseltransforms/5-3-5 deleted file mode 100644 index 03014f2..0000000 --- a/besseltransforms/5-3-5 +++ /dev/null @@ -1,2 +0,0 @@ -((5*k^6 + 12*k^4*(5 - 2*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^2 + 8*k^2*(15 - 11*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^4 - 64*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^6)/(120*k^5) - (5*k^6 + 12*k^4*(5 - 2*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^2 + 8*k^2*(15 - 11*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^4 - 64*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^6)/(24*k^5) + (5*k^6 + 12*k^4*(5 - 2*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^2 + 8*k^2*(15 - 11*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^4 - 64*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^6)/(12*k^5) - (5*k^6 + 12*k^4*(5 - 2*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^2 + 8*k^2*(15 - 11*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^4 - 64*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^6)/(12*k^5) + (5*k^6 + 12*k^4*(5 - 2*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^2 + 8*k^2*(15 - 11*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^4 - 64*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^6)/(24*k^5) - (5*k^6 + 12*k^4*(5 - 2*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^2 + 8*k^2*(15 - 11*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^4 - 64*(-1 + Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^6)/(120*k^5))/k0^3 -SeriesData[k, Infinity, {(105*c^5)/k0^3, (-1344*c^6)/k0^3 + ((384*I)*c^5)/k0^2, (315*(38*c^7 - (21*I)*c^6*k0 - 3*c^5*k0^2))/(2*k0^3), 0, (-1155*(1087*c^9 - (1134*I)*c^8*k0 - 456*c^7*k0^2 + (84*I)*c^6*k0^3 + 6*c^5*k0^4))/(16*k0^3), 0, (429*(120332*c^11 - (179487*I)*c^10*k0 - 114135*c^9*k0^2 + (39690*I)*c^8*k0^3 + 7980*c^7*k0^4 - (882*I)*c^6*k0^5 - 42*c^5*k0^6))/(32*k0^3)}, 4, 11, 1] diff --git a/besseltransforms/5-3-6 b/besseltransforms/5-3-6 deleted file mode 100644 index abac3c1..0000000 --- a/besseltransforms/5-3-6 +++ /dev/null @@ -1,2 +0,0 @@ -((k^6*(-35 + 6*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0) + 6*k^4*(-35 + 17*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^3 + 16*k^2*(-21 + 16*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^5 + 160*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^7)/(210*k^6) - (k^6*(-35 + 6*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0) + 6*k^4*(-35 + 17*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^3 + 16*k^2*(-21 + 16*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^5 + 160*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^7)/(42*k^6) + (k^6*(-35 + 6*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0) + 6*k^4*(-35 + 17*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^3 + 16*k^2*(-21 + 16*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^5 + 160*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^7)/(21*k^6) - (k^6*(-35 + 6*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0) + 6*k^4*(-35 + 17*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^3 + 16*k^2*(-21 + 16*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^5 + 160*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^7)/(21*k^6) + (k^6*(-35 + 6*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0) + 6*k^4*(-35 + 17*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^3 + 16*k^2*(-21 + 16*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^5 + 160*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^7)/(42*k^6) - (k^6*(-35 + 6*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0) + 6*k^4*(-35 + 17*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^3 + 16*k^2*(-21 + 16*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^5 + 160*(-1 + Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^7)/(210*k^6))/k0^3 -SeriesData[k, Infinity, {(192*c^5)/k0^3, (-6615*c^6)/(2*k0^3) + ((945*I)*c^5)/k0^2, (24320*c^7)/k0^3 - ((13440*I)*c^6)/k0^2 - (1920*c^5)/k0, (-3465*(189*c^8 - (152*I)*c^7*k0 - 42*c^6*k0^2 + (4*I)*c^5*k0^3))/(8*k0^3), 0, (3003*(8547*c^10 - (10870*I)*c^9*k0 - 5670*c^8*k0^2 + (1520*I)*c^7*k0^3 + 210*c^6*k0^4 - (12*I)*c^5*k0^5))/(32*k0^3)}, 4, 11, 1] diff --git a/besseltransforms/5-3-7 b/besseltransforms/5-3-7 deleted file mode 100644 index 6b8e845..0000000 --- a/besseltransforms/5-3-7 +++ /dev/null @@ -1,2 +0,0 @@ -((7*k^8 + 24*k^6*(7 - 2*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^2 + 16*k^4*(42 - 23*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^4 + 64*k^2*(14 - 11*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^6 - 384*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^8)/(336*k^7) - (5*(7*k^8 + 24*k^6*(7 - 2*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^2 + 16*k^4*(42 - 23*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^4 + 64*k^2*(14 - 11*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^6 - 384*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^8))/(336*k^7) + (5*(7*k^8 + 24*k^6*(7 - 2*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^2 + 16*k^4*(42 - 23*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^4 + 64*k^2*(14 - 11*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^6 - 384*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^8))/(168*k^7) - (5*(7*k^8 + 24*k^6*(7 - 2*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^2 + 16*k^4*(42 - 23*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^4 + 64*k^2*(14 - 11*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^6 - 384*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^8))/(168*k^7) + (5*(7*k^8 + 24*k^6*(7 - 2*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^2 + 16*k^4*(42 - 23*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^4 + 64*k^2*(14 - 11*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^6 - 384*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^8))/(336*k^7) - (7*k^8 + 24*k^6*(7 - 2*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^2 + 16*k^4*(42 - 23*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^4 + 64*k^2*(14 - 11*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^6 - 384*(-1 + Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^8)/(336*k^7))/k0^3 -SeriesData[k, Infinity, {(315*c^5)/k0^3, (-6720*c^6)/k0^3 + ((1920*I)*c^5)/k0^2, (3465*(38*c^7 - (21*I)*c^6*k0 - 3*c^5*k0^2))/(2*k0^3), (-7680*I)*c^5 - (362880*c^8)/k0^3 + ((291840*I)*c^7)/k0^2 + (80640*c^6)/k0, (15015*(1087*c^9 - (1134*I)*c^8*k0 - 456*c^7*k0^2 + (84*I)*c^6*k0^3 + 6*c^5*k0^4))/(16*k0^3), 0, (-2145*(120332*c^11 - (179487*I)*c^10*k0 - 114135*c^9*k0^2 + (39690*I)*c^8*k0^3 + 7980*c^7*k0^4 - (882*I)*c^6*k0^5 - 42*c^5*k0^6))/(32*k0^3)}, 4, 11, 1] diff --git a/besseltransforms/5-4-0 b/besseltransforms/5-4-0 deleted file mode 100644 index 0bee104..0000000 --- a/besseltransforms/5-4-0 +++ /dev/null @@ -1,9 +0,0 @@ -Integrate[(E^(-(c*x) + I*k0*x)*(1 - E^(-(c*x)))^5*BesselJ[0, k*x])/(k0^4*x^3), {x, 0, Infinity}, Assumptions -> n == 0 && q == 4 && κ == 5 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0] - - -6 c x + I k0 x c x 5 2 2 4 4 6 6 8 8 Pi 2 2 4 4 6 6 8 8 - E (-1 + E ) ((-418854310875 + 29682132480 k x - 3901685760 k x + 1258291200 k x - 2147483648 k x ) Cos[-- + k x] + 4 Sqrt[2] k x (13043905875 - 1229437440 k x + 240844800 k x - 150994944 k x + 2147483648 k x ) (Cos[k x] + Sin[k x])) - 4 -Integrate::idiv: Integral of ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ does not converge on {0, Infinity}. - 19/2 4 25/2 - 8589934592 k k0 Sqrt[2 Pi] x -Series[Integrate[(E^(-(c*x) + I*k0*x)*(1 - E^(-(c*x)))^5*BesselJ[0, k*x])/(k0^4*x^3), {x, 0, Infinity}, Assumptions -> n == 0 && q == 4 && κ == 5 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0], {k, Infinity, 10}] diff --git a/besseltransforms/5-4-1 b/besseltransforms/5-4-1 deleted file mode 100644 index 5307eb9..0000000 --- a/besseltransforms/5-4-1 +++ /dev/null @@ -1,9 +0,0 @@ -Integrate[(E^(-(c*x) + I*k0*x)*(1 - E^(-(c*x)))^5*BesselJ[1, k*x])/(k0^4*x^3), {x, 0, Infinity}, Assumptions -> n == 1 && q == 4 && κ == 5 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0] - - -6 c x + I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi -6 c x + I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi -6 c x + I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi -6 c x + I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi -6 c x + I k0 x 2 Pi -5 c x + I k0 x 2 Pi -4 c x + I k0 x 2 Pi -3 c x + I k0 x 2 Pi -2 c x + I k0 x 2 Pi -(c x) + I k0 x 2 Pi -6 c x + I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi -6 c x + I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi -6 c x + I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi -6 c x + I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi -6 c x + I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi - -14783093325 E Cos[-- + k x] 73915466625 E Cos[-- + k x] 73915466625 E Cos[-- + k x] 73915466625 E Cos[-- + k x] 73915466625 E Cos[-- + k x] 14783093325 E Cos[-- + k x] 2837835 E Cos[-- + k x] 14189175 E Cos[-- + k x] 14189175 E Cos[-- + k x] 14189175 E Cos[-- + k x] 14189175 E Cos[-- + k x] 2837835 E Cos[-- + k x] 4725 E Cos[-- + k x] 23625 E Cos[-- + k x] 23625 E Cos[-- + k x] 23625 E Cos[-- + k x] 23625 E Cos[-- + k x] 4725 E Cos[-- + k x] 15 E Cos[-- + k x] 75 E Cos[-- + k x] 75 E Cos[-- + k x] 75 E Cos[-- + k x] 75 E Cos[-- + k x] 15 E Cos[-- + k x] E Sqrt[--] Cos[-- + k x] 5 E Sqrt[--] Cos[-- + k x] 10 E Sqrt[--] Cos[-- + k x] 10 E Sqrt[--] Cos[-- + k x] 5 E Sqrt[--] Cos[-- + k x] E Sqrt[--] Cos[-- + k x] 468131288625 E Sin[-- + k x] 2340656443125 E Sin[-- + k x] 2340656443125 E Sin[-- + k x] 2340656443125 E Sin[-- + k x] 2340656443125 E Sin[-- + k x] 468131288625 E Sin[-- + k x] 66891825 E Sin[-- + k x] 334459125 E Sin[-- + k x] 334459125 E Sin[-- + k x] 334459125 E Sin[-- + k x] 334459125 E Sin[-- + k x] 66891825 E Sin[-- + k x] 72765 E Sin[-- + k x] 363825 E Sin[-- + k x] 363825 E Sin[-- + k x] 363825 E Sin[-- + k x] 363825 E Sin[-- + k x] 72765 E Sin[-- + k x] 105 E Sin[-- + k x] 525 E Sin[-- + k x] 525 E Sin[-- + k x] 525 E Sin[-- + k x] 525 E Sin[-- + k x] 105 E Sin[-- + k x] 3 E Sin[-- + k x] 15 E Sin[-- + k x] 15 E Sin[-- + k x] 15 E Sin[-- + k x] 15 E Sin[-- + k x] 3 E Sin[-- + k x] - 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 Pi 4 Pi 4 Pi 4 Pi 4 Pi 4 Pi 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 -Integrate::idiv: Integral of ------------------------------------------- + ------------------------------------------ - ------------------------------------------ + ------------------------------------------ - ------------------------------------------ + ------------------------------------------ + -------------------------------------- - --------------------------------------- + --------------------------------------- - --------------------------------------- + --------------------------------------- - -------------------------------------- - ----------------------------------- + ------------------------------------ - ------------------------------------ + ------------------------------------ - ------------------------------------ + ----------------------------------- + --------------------------------- - --------------------------------- + --------------------------------- - --------------------------------- + --------------------------------- - --------------------------------- + --------------------------------------- - ----------------------------------------- + ------------------------------------------ - ------------------------------------------ + ----------------------------------------- - --------------------------------------- - ------------------------------------------- + -------------------------------------------- - -------------------------------------------- + -------------------------------------------- - -------------------------------------------- + ------------------------------------------- + --------------------------------------- - ---------------------------------------- + ---------------------------------------- - ---------------------------------------- + ---------------------------------------- - --------------------------------------- - ------------------------------------ + ------------------------------------- - ------------------------------------- + ------------------------------------- - ------------------------------------- + ------------------------------------ + ---------------------------------- - ---------------------------------- + ---------------------------------- - ---------------------------------- + ---------------------------------- - ---------------------------------- - -------------------------------- + --------------------------------- - --------------------------------- + --------------------------------- - --------------------------------- + -------------------------------- does not converge on {0, Infinity}. - 17/2 4 23/2 17/2 4 23/2 17/2 4 23/2 17/2 4 23/2 17/2 4 23/2 17/2 4 23/2 13/2 4 19/2 13/2 4 19/2 13/2 4 19/2 13/2 4 19/2 13/2 4 19/2 13/2 4 19/2 9/2 4 15/2 9/2 4 15/2 9/2 4 15/2 9/2 4 15/2 9/2 4 15/2 9/2 4 15/2 5/2 4 11/2 5/2 4 11/2 5/2 4 11/2 5/2 4 11/2 5/2 4 11/2 5/2 4 11/2 4 7/2 4 7/2 4 7/2 4 7/2 4 7/2 4 7/2 19/2 4 25/2 19/2 4 25/2 19/2 4 25/2 19/2 4 25/2 19/2 4 25/2 19/2 4 25/2 15/2 4 21/2 15/2 4 21/2 15/2 4 21/2 15/2 4 21/2 15/2 4 21/2 15/2 4 21/2 11/2 4 17/2 11/2 4 17/2 11/2 4 17/2 11/2 4 17/2 11/2 4 17/2 11/2 4 17/2 7/2 4 13/2 7/2 4 13/2 7/2 4 13/2 7/2 4 13/2 7/2 4 13/2 7/2 4 13/2 3/2 4 9/2 3/2 4 9/2 3/2 4 9/2 3/2 4 9/2 3/2 4 9/2 3/2 4 9/2 - 1073741824 k k0 Sqrt[2 Pi] x 1073741824 k k0 Sqrt[2 Pi] x 536870912 k k0 Sqrt[2 Pi] x 536870912 k k0 Sqrt[2 Pi] x 1073741824 k k0 Sqrt[2 Pi] x 1073741824 k k0 Sqrt[2 Pi] x 2097152 k k0 Sqrt[2 Pi] x 2097152 k k0 Sqrt[2 Pi] x 1048576 k k0 Sqrt[2 Pi] x 1048576 k k0 Sqrt[2 Pi] x 2097152 k k0 Sqrt[2 Pi] x 2097152 k k0 Sqrt[2 Pi] x 16384 k k0 Sqrt[2 Pi] x 16384 k k0 Sqrt[2 Pi] x 8192 k k0 Sqrt[2 Pi] x 8192 k k0 Sqrt[2 Pi] x 16384 k k0 Sqrt[2 Pi] x 16384 k k0 Sqrt[2 Pi] x 64 k k0 Sqrt[2 Pi] x 64 k k0 Sqrt[2 Pi] x 32 k k0 Sqrt[2 Pi] x 32 k k0 Sqrt[2 Pi] x 64 k k0 Sqrt[2 Pi] x 64 k k0 Sqrt[2 Pi] x Sqrt[k] k0 x Sqrt[k] k0 x Sqrt[k] k0 x Sqrt[k] k0 x Sqrt[k] k0 x Sqrt[k] k0 x 8589934592 k k0 Sqrt[2 Pi] x 8589934592 k k0 Sqrt[2 Pi] x 4294967296 k k0 Sqrt[2 Pi] x 4294967296 k k0 Sqrt[2 Pi] x 8589934592 k k0 Sqrt[2 Pi] x 8589934592 k k0 Sqrt[2 Pi] x 16777216 k k0 Sqrt[2 Pi] x 16777216 k k0 Sqrt[2 Pi] x 8388608 k k0 Sqrt[2 Pi] x 8388608 k k0 Sqrt[2 Pi] x 16777216 k k0 Sqrt[2 Pi] x 16777216 k k0 Sqrt[2 Pi] x 131072 k k0 Sqrt[2 Pi] x 131072 k k0 Sqrt[2 Pi] x 65536 k k0 Sqrt[2 Pi] x 65536 k k0 Sqrt[2 Pi] x 131072 k k0 Sqrt[2 Pi] x 131072 k k0 Sqrt[2 Pi] x 512 k k0 Sqrt[2 Pi] x 512 k k0 Sqrt[2 Pi] x 256 k k0 Sqrt[2 Pi] x 256 k k0 Sqrt[2 Pi] x 512 k k0 Sqrt[2 Pi] x 512 k k0 Sqrt[2 Pi] x 4 k k0 Sqrt[2 Pi] x 4 k k0 Sqrt[2 Pi] x 2 k k0 Sqrt[2 Pi] x 2 k k0 Sqrt[2 Pi] x 4 k k0 Sqrt[2 Pi] x 4 k k0 Sqrt[2 Pi] x -Series[Integrate[(E^(-(c*x) + I*k0*x)*(1 - E^(-(c*x)))^5*BesselJ[1, k*x])/(k0^4*x^3), {x, 0, Infinity}, Assumptions -> n == 1 && q == 4 && κ == 5 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0], {k, Infinity, 10}] diff --git a/besseltransforms/5-4-2 b/besseltransforms/5-4-2 deleted file mode 100644 index 9e864cd..0000000 --- a/besseltransforms/5-4-2 +++ /dev/null @@ -1,9 +0,0 @@ -Integrate[(E^(-(c*x) + I*k0*x)*(1 - E^(-(c*x)))^5*BesselJ[2, k*x])/(k0^4*x^3), {x, 0, Infinity}, Assumptions -> n == 2 && q == 4 && κ == 5 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0] - - -6 c x + I k0 x c x 5 2 2 4 4 6 6 8 8 Pi 2 2 4 4 6 6 8 8 - -(E (-1 + E ) (15 (-43692253605 + 3528645120 k x - 590413824 k x + 352321536 k x + 2147483648 k x ) Cos[-- + k x] + 4 Sqrt[2] k x (21606059475 - 2421619200 k x + 681246720 k x - 1761607680 k x + 2147483648 k x ) (Cos[k x] + Sin[k x]))) - 4 -Integrate::idiv: Integral of --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- does not converge on {0, Infinity}. - 19/2 4 25/2 - 8589934592 k k0 Sqrt[2 Pi] x -Series[Integrate[(E^(-(c*x) + I*k0*x)*(1 - E^(-(c*x)))^5*BesselJ[2, k*x])/(k0^4*x^3), {x, 0, Infinity}, Assumptions -> n == 2 && q == 4 && κ == 5 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0], {k, Infinity, 10}] diff --git a/besseltransforms/5-4-3 b/besseltransforms/5-4-3 deleted file mode 100644 index a9c50ff..0000000 --- a/besseltransforms/5-4-3 +++ /dev/null @@ -1,2 +0,0 @@ -((k^4*(-15 + 8*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0) + 4*k^2*(-5 + 4*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^3 + 8*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^5)/(120*k^3) - (k^4*(-15 + 8*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0) + 4*k^2*(-5 + 4*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^3 + 8*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^5)/(24*k^3) + (k^4*(-15 + 8*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0) + 4*k^2*(-5 + 4*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^3 + 8*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^5)/(12*k^3) - (k^4*(-15 + 8*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0) + 4*k^2*(-5 + 4*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^3 + 8*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^5)/(12*k^3) + (k^4*(-15 + 8*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0) + 4*k^2*(-5 + 4*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^3 + 8*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^5)/(24*k^3) - (k^4*(-15 + 8*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0) + 4*k^2*(-5 + 4*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^3 + 8*(-1 + Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^5)/(120*k^3))/k0^4 -SeriesData[k, Infinity, {(8*c^5)/k0^4, (-105*c^6)/(2*k0^4) + ((15*I)*c^5)/k0^3, 0, (35*(189*c^8 - (152*I)*c^7*k0 - 42*c^6*k0^2 + (4*I)*c^5*k0^3))/(8*k0^4), 0, (-63*(8547*c^10 - (10870*I)*c^9*k0 - 5670*c^8*k0^2 + (1520*I)*c^7*k0^3 + 210*c^6*k0^4 - (12*I)*c^5*k0^5))/(32*k0^4), 0, (165*(141232*c^12 - (240664*I)*c^11*k0 - 179487*c^10*k0^2 + (76090*I)*c^9*k0^3 + 19845*c^8*k0^4 - (3192*I)*c^7*k0^5 - 294*c^6*k0^6 + (12*I)*c^5*k0^7))/(64*k0^4)}, 3, 11, 1] diff --git a/besseltransforms/5-4-4 b/besseltransforms/5-4-4 deleted file mode 100644 index 5e9e365..0000000 --- a/besseltransforms/5-4-4 +++ /dev/null @@ -1,2 +0,0 @@ -((5*k^6 + 2*k^4*(15 - 8*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^2 + 8*k^2*(5 - 4*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^4 - 16*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^6)/(240*k^4) - (5*k^6 + 2*k^4*(15 - 8*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^2 + 8*k^2*(5 - 4*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^4 - 16*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^6)/(48*k^4) + (5*k^6 + 2*k^4*(15 - 8*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^2 + 8*k^2*(5 - 4*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^4 - 16*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^6)/(24*k^4) - (5*k^6 + 2*k^4*(15 - 8*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^2 + 8*k^2*(5 - 4*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^4 - 16*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^6)/(24*k^4) + (5*k^6 + 2*k^4*(15 - 8*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^2 + 8*k^2*(5 - 4*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^4 - 16*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^6)/(48*k^4) - (5*k^6 + 2*k^4*(15 - 8*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^2 + 8*k^2*(5 - 4*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^4 - 16*(-1 + Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^6)/(240*k^4))/k0^4 -SeriesData[k, Infinity, {(15*c^5)/k0^4, (-168*c^6)/k0^4 + ((48*I)*c^5)/k0^3, (35*(38*c^7 - (21*I)*c^6*k0 - 3*c^5*k0^2))/(2*k0^4), 0, (-105*(1087*c^9 - (1134*I)*c^8*k0 - 456*c^7*k0^2 + (84*I)*c^6*k0^3 + 6*c^5*k0^4))/(16*k0^4), 0, (33*(120332*c^11 - (179487*I)*c^10*k0 - 114135*c^9*k0^2 + (39690*I)*c^8*k0^3 + 7980*c^7*k0^4 - (882*I)*c^6*k0^5 - 42*c^5*k0^6))/(32*k0^4)}, 3, 11, 1] diff --git a/besseltransforms/5-4-5 b/besseltransforms/5-4-5 deleted file mode 100644 index 120e442..0000000 --- a/besseltransforms/5-4-5 +++ /dev/null @@ -1,2 +0,0 @@ -((k^6*(-35 + 8*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0) + 20*k^4*(-7 + 4*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^3 + 8*k^2*(-21 + 17*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^5 + 64*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^7)/(840*k^5) - (k^6*(-35 + 8*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0) + 20*k^4*(-7 + 4*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^3 + 8*k^2*(-21 + 17*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^5 + 64*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^7)/(168*k^5) + (k^6*(-35 + 8*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0) + 20*k^4*(-7 + 4*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^3 + 8*k^2*(-21 + 17*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^5 + 64*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^7)/(84*k^5) - (k^6*(-35 + 8*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0) + 20*k^4*(-7 + 4*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^3 + 8*k^2*(-21 + 17*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^5 + 64*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^7)/(84*k^5) + (k^6*(-35 + 8*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0) + 20*k^4*(-7 + 4*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^3 + 8*k^2*(-21 + 17*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^5 + 64*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^7)/(168*k^5) - (k^6*(-35 + 8*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0) + 20*k^4*(-7 + 4*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^3 + 8*k^2*(-21 + 17*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^5 + 64*(-1 + Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^7)/(840*k^5))/k0^4 -SeriesData[k, Infinity, {(24*c^5)/k0^4, (-735*c^6)/(2*k0^4) + ((105*I)*c^5)/k0^3, (2432*c^7)/k0^4 - ((1344*I)*c^6)/k0^3 - (192*c^5)/k0^2, (-315*(189*c^8 - (152*I)*c^7*k0 - 42*c^6*k0^2 + (4*I)*c^5*k0^3))/(8*k0^4), 0, (231*(8547*c^10 - (10870*I)*c^9*k0 - 5670*c^8*k0^2 + (1520*I)*c^7*k0^3 + 210*c^6*k0^4 - (12*I)*c^5*k0^5))/(32*k0^4), 0, (-429*(141232*c^12 - (240664*I)*c^11*k0 - 179487*c^10*k0^2 + (76090*I)*c^9*k0^3 + 19845*c^8*k0^4 - (3192*I)*c^7*k0^5 - 294*c^6*k0^6 + (12*I)*c^5*k0^7))/(64*k0^4)}, 3, 11, 1] diff --git a/besseltransforms/5-4-6 b/besseltransforms/5-4-6 deleted file mode 100644 index a9776fd..0000000 --- a/besseltransforms/5-4-6 +++ /dev/null @@ -1,2 +0,0 @@ -((35*k^8 + 16*k^6*(35 - 12*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^2 + 16*k^4*(105 - 64*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^4 + 64*k^2*(28 - 23*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^6 - 640*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^8)/(6720*k^6) - (35*k^8 + 16*k^6*(35 - 12*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^2 + 16*k^4*(105 - 64*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^4 + 64*k^2*(28 - 23*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^6 - 640*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^8)/(1344*k^6) + (35*k^8 + 16*k^6*(35 - 12*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^2 + 16*k^4*(105 - 64*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^4 + 64*k^2*(28 - 23*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^6 - 640*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^8)/(672*k^6) - (35*k^8 + 16*k^6*(35 - 12*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^2 + 16*k^4*(105 - 64*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^4 + 64*k^2*(28 - 23*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^6 - 640*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^8)/(672*k^6) + (35*k^8 + 16*k^6*(35 - 12*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^2 + 16*k^4*(105 - 64*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^4 + 64*k^2*(28 - 23*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^6 - 640*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^8)/(1344*k^6) - (35*k^8 + 16*k^6*(35 - 12*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^2 + 16*k^4*(105 - 64*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^4 + 64*k^2*(28 - 23*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^6 - 640*(-1 + Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^8)/(6720*k^6))/k0^4 -SeriesData[k, Infinity, {(35*c^5)/k0^4, (-672*c^6)/k0^4 + ((192*I)*c^5)/k0^3, (315*(38*c^7 - (21*I)*c^6*k0 - 3*c^5*k0^2))/(2*k0^4), (-30240*c^8)/k0^4 + ((24320*I)*c^7)/k0^3 + (6720*c^6)/k0^2 - ((640*I)*c^5)/k0, (1155*(1087*c^9 - (1134*I)*c^8*k0 - 456*c^7*k0^2 + (84*I)*c^6*k0^3 + 6*c^5*k0^4))/(16*k0^4), 0, (-143*(120332*c^11 - (179487*I)*c^10*k0 - 114135*c^9*k0^2 + (39690*I)*c^8*k0^3 + 7980*c^7*k0^4 - (882*I)*c^6*k0^5 - 42*c^5*k0^6))/(32*k0^4)}, 3, 11, 1] diff --git a/besseltransforms/5-4-7 b/besseltransforms/5-4-7 deleted file mode 100644 index f0941eb..0000000 --- a/besseltransforms/5-4-7 +++ /dev/null @@ -1,2 +0,0 @@ -((k^8*(-105 + 16*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0) + 8*k^6*(-105 + 44*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^3 + 144*k^4*(-14 + 9*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^5 + 320*k^2*(-6 + 5*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^7 + 640*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^9)/(5040*k^7) - (k^8*(-105 + 16*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0) + 8*k^6*(-105 + 44*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^3 + 144*k^4*(-14 + 9*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^5 + 320*k^2*(-6 + 5*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^7 + 640*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^9)/(1008*k^7) + (k^8*(-105 + 16*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0) + 8*k^6*(-105 + 44*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^3 + 144*k^4*(-14 + 9*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^5 + 320*k^2*(-6 + 5*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^7 + 640*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^9)/(504*k^7) - (k^8*(-105 + 16*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0) + 8*k^6*(-105 + 44*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^3 + 144*k^4*(-14 + 9*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^5 + 320*k^2*(-6 + 5*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^7 + 640*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^9)/(504*k^7) + (k^8*(-105 + 16*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0) + 8*k^6*(-105 + 44*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^3 + 144*k^4*(-14 + 9*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^5 + 320*k^2*(-6 + 5*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^7 + 640*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^9)/(1008*k^7) - (k^8*(-105 + 16*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0) + 8*k^6*(-105 + 44*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^3 + 144*k^4*(-14 + 9*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^5 + 320*k^2*(-6 + 5*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^7 + 640*(-1 + Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^9)/(5040*k^7))/k0^4 -SeriesData[k, Infinity, {(48*c^5)/k0^4, (-2205*c^6)/(2*k0^4) + ((315*I)*c^5)/k0^3, (12160*c^7)/k0^4 - ((6720*I)*c^6)/k0^3 - (960*c^5)/k0^2, (-3465*(189*c^8 - (152*I)*c^7*k0 - 42*c^6*k0^2 + (4*I)*c^5*k0^3))/(8*k0^4), 1920*c^5 + (347840*c^9)/k0^4 - ((362880*I)*c^8)/k0^3 - (145920*c^7)/k0^2 + ((26880*I)*c^6)/k0, (-3003*(8547*c^10 - (10870*I)*c^9*k0 - 5670*c^8*k0^2 + (1520*I)*c^7*k0^3 + 210*c^6*k0^4 - (12*I)*c^5*k0^5))/(32*k0^4), 0, (2145*(141232*c^12 - (240664*I)*c^11*k0 - 179487*c^10*k0^2 + (76090*I)*c^9*k0^3 + 19845*c^8*k0^4 - (3192*I)*c^7*k0^5 - 294*c^6*k0^6 + (12*I)*c^5*k0^7))/(64*k0^4)}, 3, 11, 1] diff --git a/besseltransforms/5-5-0 b/besseltransforms/5-5-0 deleted file mode 100644 index 9d67bbd..0000000 --- a/besseltransforms/5-5-0 +++ /dev/null @@ -1,9 +0,0 @@ -Integrate[(E^(-(c*x) + I*k0*x)*(1 - E^(-(c*x)))^5*BesselJ[0, k*x])/(k0^5*x^4), {x, 0, Infinity}, Assumptions -> n == 0 && q == 5 && κ == 5 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0] - - -6 c x + I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi -6 c x + I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi -6 c x + I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi -6 c x + I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi -6 c x + I k0 x 2 Pi -5 c x + I k0 x 2 Pi -4 c x + I k0 x 2 Pi -3 c x + I k0 x 2 Pi -2 c x + I k0 x 2 Pi -(c x) + I k0 x 2 Pi -6 c x + I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi -6 c x + I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi -6 c x + I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi -6 c x + I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi -6 c x + I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi - -13043905875 E Cos[-- - k x] 65219529375 E Cos[-- - k x] 65219529375 E Cos[-- - k x] 65219529375 E Cos[-- - k x] 65219529375 E Cos[-- - k x] 13043905875 E Cos[-- - k x] 2401245 E Cos[-- - k x] 12006225 E Cos[-- - k x] 12006225 E Cos[-- - k x] 12006225 E Cos[-- - k x] 12006225 E Cos[-- - k x] 2401245 E Cos[-- - k x] 3675 E Cos[-- - k x] 18375 E Cos[-- - k x] 18375 E Cos[-- - k x] 18375 E Cos[-- - k x] 18375 E Cos[-- - k x] 3675 E Cos[-- - k x] 9 E Cos[-- - k x] 45 E Cos[-- - k x] 45 E Cos[-- - k x] 45 E Cos[-- - k x] 45 E Cos[-- - k x] 9 E Cos[-- - k x] E Sqrt[--] Cos[-- - k x] 5 E Sqrt[--] Cos[-- - k x] 10 E Sqrt[--] Cos[-- - k x] 10 E Sqrt[--] Cos[-- - k x] 5 E Sqrt[--] Cos[-- - k x] E Sqrt[--] Cos[-- - k x] 418854310875 E Sin[-- - k x] 2094271554375 E Sin[-- - k x] 2094271554375 E Sin[-- - k x] 2094271554375 E Sin[-- - k x] 2094271554375 E Sin[-- - k x] 418854310875 E Sin[-- - k x] 57972915 E Sin[-- - k x] 289864575 E Sin[-- - k x] 289864575 E Sin[-- - k x] 289864575 E Sin[-- - k x] 289864575 E Sin[-- - k x] 57972915 E Sin[-- - k x] 59535 E Sin[-- - k x] 297675 E Sin[-- - k x] 297675 E Sin[-- - k x] 297675 E Sin[-- - k x] 297675 E Sin[-- - k x] 59535 E Sin[-- - k x] 75 E Sin[-- - k x] 375 E Sin[-- - k x] 375 E Sin[-- - k x] 375 E Sin[-- - k x] 375 E Sin[-- - k x] 75 E Sin[-- - k x] E Sin[-- - k x] 5 E Sin[-- - k x] 5 E Sin[-- - k x] 5 E Sin[-- - k x] 5 E Sin[-- - k x] E Sin[-- - k x] - 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 Pi 4 Pi 4 Pi 4 Pi 4 Pi 4 Pi 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 -Integrate::idiv: Integral of ------------------------------------------- + ------------------------------------------ - ------------------------------------------ + ------------------------------------------ - ------------------------------------------ + ------------------------------------------ + -------------------------------------- - --------------------------------------- + --------------------------------------- - --------------------------------------- + --------------------------------------- - -------------------------------------- - ----------------------------------- + ------------------------------------ - ------------------------------------ + ------------------------------------ - ------------------------------------ + ----------------------------------- + -------------------------------- - --------------------------------- + --------------------------------- - --------------------------------- + --------------------------------- - -------------------------------- - --------------------------------------- + ----------------------------------------- - ------------------------------------------ + ------------------------------------------ - ----------------------------------------- + --------------------------------------- + ------------------------------------------- - -------------------------------------------- + -------------------------------------------- - -------------------------------------------- + -------------------------------------------- - ------------------------------------------- - --------------------------------------- + ---------------------------------------- - ---------------------------------------- + ---------------------------------------- - ---------------------------------------- + --------------------------------------- + ------------------------------------ - ------------------------------------- + ------------------------------------- - ------------------------------------- + ------------------------------------- - ------------------------------------ - --------------------------------- + ---------------------------------- - ---------------------------------- + ---------------------------------- - ---------------------------------- + --------------------------------- + ------------------------------ - -------------------------------- + -------------------------------- - -------------------------------- + -------------------------------- - ------------------------------ does not converge on {0, Infinity}. - 17/2 5 25/2 17/2 5 25/2 17/2 5 25/2 17/2 5 25/2 17/2 5 25/2 17/2 5 25/2 13/2 5 21/2 13/2 5 21/2 13/2 5 21/2 13/2 5 21/2 13/2 5 21/2 13/2 5 21/2 9/2 5 17/2 9/2 5 17/2 9/2 5 17/2 9/2 5 17/2 9/2 5 17/2 9/2 5 17/2 5/2 5 13/2 5/2 5 13/2 5/2 5 13/2 5/2 5 13/2 5/2 5 13/2 5/2 5 13/2 5 9/2 5 9/2 5 9/2 5 9/2 5 9/2 5 9/2 19/2 5 27/2 19/2 5 27/2 19/2 5 27/2 19/2 5 27/2 19/2 5 27/2 19/2 5 27/2 15/2 5 23/2 15/2 5 23/2 15/2 5 23/2 15/2 5 23/2 15/2 5 23/2 15/2 5 23/2 11/2 5 19/2 11/2 5 19/2 11/2 5 19/2 11/2 5 19/2 11/2 5 19/2 11/2 5 19/2 7/2 5 15/2 7/2 5 15/2 7/2 5 15/2 7/2 5 15/2 7/2 5 15/2 7/2 5 15/2 3/2 5 11/2 3/2 5 11/2 3/2 5 11/2 3/2 5 11/2 3/2 5 11/2 3/2 5 11/2 - 1073741824 k k0 Sqrt[2 Pi] x 1073741824 k k0 Sqrt[2 Pi] x 536870912 k k0 Sqrt[2 Pi] x 536870912 k k0 Sqrt[2 Pi] x 1073741824 k k0 Sqrt[2 Pi] x 1073741824 k k0 Sqrt[2 Pi] x 2097152 k k0 Sqrt[2 Pi] x 2097152 k k0 Sqrt[2 Pi] x 1048576 k k0 Sqrt[2 Pi] x 1048576 k k0 Sqrt[2 Pi] x 2097152 k k0 Sqrt[2 Pi] x 2097152 k k0 Sqrt[2 Pi] x 16384 k k0 Sqrt[2 Pi] x 16384 k k0 Sqrt[2 Pi] x 8192 k k0 Sqrt[2 Pi] x 8192 k k0 Sqrt[2 Pi] x 16384 k k0 Sqrt[2 Pi] x 16384 k k0 Sqrt[2 Pi] x 64 k k0 Sqrt[2 Pi] x 64 k k0 Sqrt[2 Pi] x 32 k k0 Sqrt[2 Pi] x 32 k k0 Sqrt[2 Pi] x 64 k k0 Sqrt[2 Pi] x 64 k k0 Sqrt[2 Pi] x Sqrt[k] k0 x Sqrt[k] k0 x Sqrt[k] k0 x Sqrt[k] k0 x Sqrt[k] k0 x Sqrt[k] k0 x 8589934592 k k0 Sqrt[2 Pi] x 8589934592 k k0 Sqrt[2 Pi] x 4294967296 k k0 Sqrt[2 Pi] x 4294967296 k k0 Sqrt[2 Pi] x 8589934592 k k0 Sqrt[2 Pi] x 8589934592 k k0 Sqrt[2 Pi] x 16777216 k k0 Sqrt[2 Pi] x 16777216 k k0 Sqrt[2 Pi] x 8388608 k k0 Sqrt[2 Pi] x 8388608 k k0 Sqrt[2 Pi] x 16777216 k k0 Sqrt[2 Pi] x 16777216 k k0 Sqrt[2 Pi] x 131072 k k0 Sqrt[2 Pi] x 131072 k k0 Sqrt[2 Pi] x 65536 k k0 Sqrt[2 Pi] x 65536 k k0 Sqrt[2 Pi] x 131072 k k0 Sqrt[2 Pi] x 131072 k k0 Sqrt[2 Pi] x 512 k k0 Sqrt[2 Pi] x 512 k k0 Sqrt[2 Pi] x 256 k k0 Sqrt[2 Pi] x 256 k k0 Sqrt[2 Pi] x 512 k k0 Sqrt[2 Pi] x 512 k k0 Sqrt[2 Pi] x 4 k k0 Sqrt[2 Pi] x 4 k k0 Sqrt[2 Pi] x 2 k k0 Sqrt[2 Pi] x 2 k k0 Sqrt[2 Pi] x 4 k k0 Sqrt[2 Pi] x 4 k k0 Sqrt[2 Pi] x -Series[Integrate[(E^(-(c*x) + I*k0*x)*(1 - E^(-(c*x)))^5*BesselJ[0, k*x])/(k0^5*x^4), {x, 0, Infinity}, Assumptions -> n == 0 && q == 5 && κ == 5 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0], {k, Infinity, 10}] diff --git a/besseltransforms/5-5-1 b/besseltransforms/5-5-1 deleted file mode 100644 index 003ca0a..0000000 --- a/besseltransforms/5-5-1 +++ /dev/null @@ -1,9 +0,0 @@ -Integrate[(E^(-(c*x) + I*k0*x)*(1 - E^(-(c*x)))^5*BesselJ[1, k*x])/(k0^5*x^4), {x, 0, Infinity}, Assumptions -> n == 1 && q == 5 && κ == 5 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0] - - -6 c x + I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi -6 c x + I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi -6 c x + I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi -6 c x + I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi -6 c x + I k0 x 2 Pi -5 c x + I k0 x 2 Pi -4 c x + I k0 x 2 Pi -3 c x + I k0 x 2 Pi -2 c x + I k0 x 2 Pi -(c x) + I k0 x 2 Pi -6 c x + I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi -6 c x + I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi -6 c x + I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi -6 c x + I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi -6 c x + I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi - -14783093325 E Cos[-- + k x] 73915466625 E Cos[-- + k x] 73915466625 E Cos[-- + k x] 73915466625 E Cos[-- + k x] 73915466625 E Cos[-- + k x] 14783093325 E Cos[-- + k x] 2837835 E Cos[-- + k x] 14189175 E Cos[-- + k x] 14189175 E Cos[-- + k x] 14189175 E Cos[-- + k x] 14189175 E Cos[-- + k x] 2837835 E Cos[-- + k x] 4725 E Cos[-- + k x] 23625 E Cos[-- + k x] 23625 E Cos[-- + k x] 23625 E Cos[-- + k x] 23625 E Cos[-- + k x] 4725 E Cos[-- + k x] 15 E Cos[-- + k x] 75 E Cos[-- + k x] 75 E Cos[-- + k x] 75 E Cos[-- + k x] 75 E Cos[-- + k x] 15 E Cos[-- + k x] E Sqrt[--] Cos[-- + k x] 5 E Sqrt[--] Cos[-- + k x] 10 E Sqrt[--] Cos[-- + k x] 10 E Sqrt[--] Cos[-- + k x] 5 E Sqrt[--] Cos[-- + k x] E Sqrt[--] Cos[-- + k x] 468131288625 E Sin[-- + k x] 2340656443125 E Sin[-- + k x] 2340656443125 E Sin[-- + k x] 2340656443125 E Sin[-- + k x] 2340656443125 E Sin[-- + k x] 468131288625 E Sin[-- + k x] 66891825 E Sin[-- + k x] 334459125 E Sin[-- + k x] 334459125 E Sin[-- + k x] 334459125 E Sin[-- + k x] 334459125 E Sin[-- + k x] 66891825 E Sin[-- + k x] 72765 E Sin[-- + k x] 363825 E Sin[-- + k x] 363825 E Sin[-- + k x] 363825 E Sin[-- + k x] 363825 E Sin[-- + k x] 72765 E Sin[-- + k x] 105 E Sin[-- + k x] 525 E Sin[-- + k x] 525 E Sin[-- + k x] 525 E Sin[-- + k x] 525 E Sin[-- + k x] 105 E Sin[-- + k x] 3 E Sin[-- + k x] 15 E Sin[-- + k x] 15 E Sin[-- + k x] 15 E Sin[-- + k x] 15 E Sin[-- + k x] 3 E Sin[-- + k x] - 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 Pi 4 Pi 4 Pi 4 Pi 4 Pi 4 Pi 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 -Integrate::idiv: Integral of ------------------------------------------- + ------------------------------------------ - ------------------------------------------ + ------------------------------------------ - ------------------------------------------ + ------------------------------------------ + -------------------------------------- - --------------------------------------- + --------------------------------------- - --------------------------------------- + --------------------------------------- - -------------------------------------- - ----------------------------------- + ------------------------------------ - ------------------------------------ + ------------------------------------ - ------------------------------------ + ----------------------------------- + --------------------------------- - --------------------------------- + --------------------------------- - --------------------------------- + --------------------------------- - --------------------------------- + --------------------------------------- - ----------------------------------------- + ------------------------------------------ - ------------------------------------------ + ----------------------------------------- - --------------------------------------- - ------------------------------------------- + -------------------------------------------- - -------------------------------------------- + -------------------------------------------- - -------------------------------------------- + ------------------------------------------- + --------------------------------------- - ---------------------------------------- + ---------------------------------------- - ---------------------------------------- + ---------------------------------------- - --------------------------------------- - ------------------------------------ + ------------------------------------- - ------------------------------------- + ------------------------------------- - ------------------------------------- + ------------------------------------ + ---------------------------------- - ---------------------------------- + ---------------------------------- - ---------------------------------- + ---------------------------------- - ---------------------------------- - -------------------------------- + --------------------------------- - --------------------------------- + --------------------------------- - --------------------------------- + -------------------------------- does not converge on {0, Infinity}. - 17/2 5 25/2 17/2 5 25/2 17/2 5 25/2 17/2 5 25/2 17/2 5 25/2 17/2 5 25/2 13/2 5 21/2 13/2 5 21/2 13/2 5 21/2 13/2 5 21/2 13/2 5 21/2 13/2 5 21/2 9/2 5 17/2 9/2 5 17/2 9/2 5 17/2 9/2 5 17/2 9/2 5 17/2 9/2 5 17/2 5/2 5 13/2 5/2 5 13/2 5/2 5 13/2 5/2 5 13/2 5/2 5 13/2 5/2 5 13/2 5 9/2 5 9/2 5 9/2 5 9/2 5 9/2 5 9/2 19/2 5 27/2 19/2 5 27/2 19/2 5 27/2 19/2 5 27/2 19/2 5 27/2 19/2 5 27/2 15/2 5 23/2 15/2 5 23/2 15/2 5 23/2 15/2 5 23/2 15/2 5 23/2 15/2 5 23/2 11/2 5 19/2 11/2 5 19/2 11/2 5 19/2 11/2 5 19/2 11/2 5 19/2 11/2 5 19/2 7/2 5 15/2 7/2 5 15/2 7/2 5 15/2 7/2 5 15/2 7/2 5 15/2 7/2 5 15/2 3/2 5 11/2 3/2 5 11/2 3/2 5 11/2 3/2 5 11/2 3/2 5 11/2 3/2 5 11/2 - 1073741824 k k0 Sqrt[2 Pi] x 1073741824 k k0 Sqrt[2 Pi] x 536870912 k k0 Sqrt[2 Pi] x 536870912 k k0 Sqrt[2 Pi] x 1073741824 k k0 Sqrt[2 Pi] x 1073741824 k k0 Sqrt[2 Pi] x 2097152 k k0 Sqrt[2 Pi] x 2097152 k k0 Sqrt[2 Pi] x 1048576 k k0 Sqrt[2 Pi] x 1048576 k k0 Sqrt[2 Pi] x 2097152 k k0 Sqrt[2 Pi] x 2097152 k k0 Sqrt[2 Pi] x 16384 k k0 Sqrt[2 Pi] x 16384 k k0 Sqrt[2 Pi] x 8192 k k0 Sqrt[2 Pi] x 8192 k k0 Sqrt[2 Pi] x 16384 k k0 Sqrt[2 Pi] x 16384 k k0 Sqrt[2 Pi] x 64 k k0 Sqrt[2 Pi] x 64 k k0 Sqrt[2 Pi] x 32 k k0 Sqrt[2 Pi] x 32 k k0 Sqrt[2 Pi] x 64 k k0 Sqrt[2 Pi] x 64 k k0 Sqrt[2 Pi] x Sqrt[k] k0 x Sqrt[k] k0 x Sqrt[k] k0 x Sqrt[k] k0 x Sqrt[k] k0 x Sqrt[k] k0 x 8589934592 k k0 Sqrt[2 Pi] x 8589934592 k k0 Sqrt[2 Pi] x 4294967296 k k0 Sqrt[2 Pi] x 4294967296 k k0 Sqrt[2 Pi] x 8589934592 k k0 Sqrt[2 Pi] x 8589934592 k k0 Sqrt[2 Pi] x 16777216 k k0 Sqrt[2 Pi] x 16777216 k k0 Sqrt[2 Pi] x 8388608 k k0 Sqrt[2 Pi] x 8388608 k k0 Sqrt[2 Pi] x 16777216 k k0 Sqrt[2 Pi] x 16777216 k k0 Sqrt[2 Pi] x 131072 k k0 Sqrt[2 Pi] x 131072 k k0 Sqrt[2 Pi] x 65536 k k0 Sqrt[2 Pi] x 65536 k k0 Sqrt[2 Pi] x 131072 k k0 Sqrt[2 Pi] x 131072 k k0 Sqrt[2 Pi] x 512 k k0 Sqrt[2 Pi] x 512 k k0 Sqrt[2 Pi] x 256 k k0 Sqrt[2 Pi] x 256 k k0 Sqrt[2 Pi] x 512 k k0 Sqrt[2 Pi] x 512 k k0 Sqrt[2 Pi] x 4 k k0 Sqrt[2 Pi] x 4 k k0 Sqrt[2 Pi] x 2 k k0 Sqrt[2 Pi] x 2 k k0 Sqrt[2 Pi] x 4 k k0 Sqrt[2 Pi] x 4 k k0 Sqrt[2 Pi] x -Series[Integrate[(E^(-(c*x) + I*k0*x)*(1 - E^(-(c*x)))^5*BesselJ[1, k*x])/(k0^5*x^4), {x, 0, Infinity}, Assumptions -> n == 1 && q == 5 && κ == 5 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0], {k, Infinity, 10}] diff --git a/besseltransforms/5-5-2 b/besseltransforms/5-5-2 deleted file mode 100644 index 67d7ff3..0000000 --- a/besseltransforms/5-5-2 +++ /dev/null @@ -1,9 +0,0 @@ -Integrate[(E^(-(c*x) + I*k0*x)*(1 - E^(-(c*x)))^5*BesselJ[2, k*x])/(k0^5*x^4), {x, 0, Infinity}, Assumptions -> n == 2 && q == 5 && κ == 5 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0] - - -6 c x + I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi -6 c x + I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi -6 c x + I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi -6 c x + I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi -6 c x + I k0 x 2 Pi -5 c x + I k0 x 2 Pi -4 c x + I k0 x 2 Pi -3 c x + I k0 x 2 Pi -2 c x + I k0 x 2 Pi -(c x) + I k0 x 2 Pi -6 c x + I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi -6 c x + I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi -6 c x + I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi -6 c x + I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi -6 c x + I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi - 21606059475 E Cos[-- - k x] 108030297375 E Cos[-- - k x] 108030297375 E Cos[-- - k x] 108030297375 E Cos[-- - k x] 108030297375 E Cos[-- - k x] 21606059475 E Cos[-- - k x] 4729725 E Cos[-- - k x] 23648625 E Cos[-- - k x] 23648625 E Cos[-- - k x] 23648625 E Cos[-- - k x] 23648625 E Cos[-- - k x] 4729725 E Cos[-- - k x] 10395 E Cos[-- - k x] 51975 E Cos[-- - k x] 51975 E Cos[-- - k x] 51975 E Cos[-- - k x] 51975 E Cos[-- - k x] 10395 E Cos[-- - k x] 105 E Cos[-- - k x] 525 E Cos[-- - k x] 525 E Cos[-- - k x] 525 E Cos[-- - k x] 525 E Cos[-- - k x] 105 E Cos[-- - k x] E Sqrt[--] Cos[-- - k x] 5 E Sqrt[--] Cos[-- - k x] 10 E Sqrt[--] Cos[-- - k x] 10 E Sqrt[--] Cos[-- - k x] 5 E Sqrt[--] Cos[-- - k x] E Sqrt[--] Cos[-- - k x] 655383804075 E Sin[-- - k x] 3276919020375 E Sin[-- - k x] 3276919020375 E Sin[-- - k x] 3276919020375 E Sin[-- - k x] 3276919020375 E Sin[-- - k x] 655383804075 E Sin[-- - k x] 103378275 E Sin[-- - k x] 516891375 E Sin[-- - k x] 516891375 E Sin[-- - k x] 516891375 E Sin[-- - k x] 516891375 E Sin[-- - k x] 103378275 E Sin[-- - k x] 135135 E Sin[-- - k x] 675675 E Sin[-- - k x] 675675 E Sin[-- - k x] 675675 E Sin[-- - k x] 675675 E Sin[-- - k x] 135135 E Sin[-- - k x] 315 E Sin[-- - k x] 1575 E Sin[-- - k x] 1575 E Sin[-- - k x] 1575 E Sin[-- - k x] 1575 E Sin[-- - k x] 315 E Sin[-- - k x] 15 E Sin[-- - k x] 75 E Sin[-- - k x] 75 E Sin[-- - k x] 75 E Sin[-- - k x] 75 E Sin[-- - k x] 15 E Sin[-- - k x] - 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 Pi 4 Pi 4 Pi 4 Pi 4 Pi 4 Pi 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 -Integrate::idiv: Integral of ------------------------------------------ - ------------------------------------------- + ------------------------------------------- - ------------------------------------------- + ------------------------------------------- - ------------------------------------------ - -------------------------------------- + --------------------------------------- - --------------------------------------- + --------------------------------------- - --------------------------------------- + -------------------------------------- + ------------------------------------ - ------------------------------------ + ------------------------------------ - ------------------------------------ + ------------------------------------ - ------------------------------------ - ---------------------------------- + ---------------------------------- - ---------------------------------- + ---------------------------------- - ---------------------------------- + ---------------------------------- + --------------------------------------- - ----------------------------------------- + ------------------------------------------ - ------------------------------------------ + ----------------------------------------- - --------------------------------------- - ------------------------------------------- + -------------------------------------------- - -------------------------------------------- + -------------------------------------------- - -------------------------------------------- + ------------------------------------------- + ---------------------------------------- - ---------------------------------------- + ---------------------------------------- - ---------------------------------------- + ---------------------------------------- - ---------------------------------------- - ------------------------------------- + ------------------------------------- - ------------------------------------- + ------------------------------------- - ------------------------------------- + ------------------------------------- + ---------------------------------- - ----------------------------------- + ----------------------------------- - ----------------------------------- + ----------------------------------- - ---------------------------------- + --------------------------------- - --------------------------------- + --------------------------------- - --------------------------------- + --------------------------------- - --------------------------------- does not converge on {0, Infinity}. - 17/2 5 25/2 17/2 5 25/2 17/2 5 25/2 17/2 5 25/2 17/2 5 25/2 17/2 5 25/2 13/2 5 21/2 13/2 5 21/2 13/2 5 21/2 13/2 5 21/2 13/2 5 21/2 13/2 5 21/2 9/2 5 17/2 9/2 5 17/2 9/2 5 17/2 9/2 5 17/2 9/2 5 17/2 9/2 5 17/2 5/2 5 13/2 5/2 5 13/2 5/2 5 13/2 5/2 5 13/2 5/2 5 13/2 5/2 5 13/2 5 9/2 5 9/2 5 9/2 5 9/2 5 9/2 5 9/2 19/2 5 27/2 19/2 5 27/2 19/2 5 27/2 19/2 5 27/2 19/2 5 27/2 19/2 5 27/2 15/2 5 23/2 15/2 5 23/2 15/2 5 23/2 15/2 5 23/2 15/2 5 23/2 15/2 5 23/2 11/2 5 19/2 11/2 5 19/2 11/2 5 19/2 11/2 5 19/2 11/2 5 19/2 11/2 5 19/2 7/2 5 15/2 7/2 5 15/2 7/2 5 15/2 7/2 5 15/2 7/2 5 15/2 7/2 5 15/2 3/2 5 11/2 3/2 5 11/2 3/2 5 11/2 3/2 5 11/2 3/2 5 11/2 3/2 5 11/2 - 1073741824 k k0 Sqrt[2 Pi] x 1073741824 k k0 Sqrt[2 Pi] x 536870912 k k0 Sqrt[2 Pi] x 536870912 k k0 Sqrt[2 Pi] x 1073741824 k k0 Sqrt[2 Pi] x 1073741824 k k0 Sqrt[2 Pi] x 2097152 k k0 Sqrt[2 Pi] x 2097152 k k0 Sqrt[2 Pi] x 1048576 k k0 Sqrt[2 Pi] x 1048576 k k0 Sqrt[2 Pi] x 2097152 k k0 Sqrt[2 Pi] x 2097152 k k0 Sqrt[2 Pi] x 16384 k k0 Sqrt[2 Pi] x 16384 k k0 Sqrt[2 Pi] x 8192 k k0 Sqrt[2 Pi] x 8192 k k0 Sqrt[2 Pi] x 16384 k k0 Sqrt[2 Pi] x 16384 k k0 Sqrt[2 Pi] x 64 k k0 Sqrt[2 Pi] x 64 k k0 Sqrt[2 Pi] x 32 k k0 Sqrt[2 Pi] x 32 k k0 Sqrt[2 Pi] x 64 k k0 Sqrt[2 Pi] x 64 k k0 Sqrt[2 Pi] x Sqrt[k] k0 x Sqrt[k] k0 x Sqrt[k] k0 x Sqrt[k] k0 x Sqrt[k] k0 x Sqrt[k] k0 x 8589934592 k k0 Sqrt[2 Pi] x 8589934592 k k0 Sqrt[2 Pi] x 4294967296 k k0 Sqrt[2 Pi] x 4294967296 k k0 Sqrt[2 Pi] x 8589934592 k k0 Sqrt[2 Pi] x 8589934592 k k0 Sqrt[2 Pi] x 16777216 k k0 Sqrt[2 Pi] x 16777216 k k0 Sqrt[2 Pi] x 8388608 k k0 Sqrt[2 Pi] x 8388608 k k0 Sqrt[2 Pi] x 16777216 k k0 Sqrt[2 Pi] x 16777216 k k0 Sqrt[2 Pi] x 131072 k k0 Sqrt[2 Pi] x 131072 k k0 Sqrt[2 Pi] x 65536 k k0 Sqrt[2 Pi] x 65536 k k0 Sqrt[2 Pi] x 131072 k k0 Sqrt[2 Pi] x 131072 k k0 Sqrt[2 Pi] x 512 k k0 Sqrt[2 Pi] x 512 k k0 Sqrt[2 Pi] x 256 k k0 Sqrt[2 Pi] x 256 k k0 Sqrt[2 Pi] x 512 k k0 Sqrt[2 Pi] x 512 k k0 Sqrt[2 Pi] x 4 k k0 Sqrt[2 Pi] x 4 k k0 Sqrt[2 Pi] x 2 k k0 Sqrt[2 Pi] x 2 k k0 Sqrt[2 Pi] x 4 k k0 Sqrt[2 Pi] x 4 k k0 Sqrt[2 Pi] x -Series[Integrate[(E^(-(c*x) + I*k0*x)*(1 - E^(-(c*x)))^5*BesselJ[2, k*x])/(k0^5*x^4), {x, 0, Infinity}, Assumptions -> n == 2 && q == 5 && κ == 5 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0], {k, Infinity, 10}] diff --git a/besseltransforms/5-5-3 b/besseltransforms/5-5-3 deleted file mode 100644 index f8bcb24..0000000 --- a/besseltransforms/5-5-3 +++ /dev/null @@ -1,9 +0,0 @@ -Integrate[(E^(-(c*x) + I*k0*x)*(1 - E^(-(c*x)))^5*BesselJ[3, k*x])/(k0^5*x^4), {x, 0, Infinity}, Assumptions -> n == 3 && q == 5 && κ == 5 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0] - - -6 c x + I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi -6 c x + I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi -6 c x + I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi -6 c x + I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi -6 c x + I k0 x 2 Pi -5 c x + I k0 x 2 Pi -4 c x + I k0 x 2 Pi -3 c x + I k0 x 2 Pi -2 c x + I k0 x 2 Pi -(c x) + I k0 x 2 Pi -6 c x + I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi -6 c x + I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi -6 c x + I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi -6 c x + I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi -6 c x + I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi - 41247931725 E Cos[-- + k x] 206239658625 E Cos[-- + k x] 206239658625 E Cos[-- + k x] 206239658625 E Cos[-- + k x] 206239658625 E Cos[-- + k x] 41247931725 E Cos[-- + k x] 11486475 E Cos[-- + k x] 57432375 E Cos[-- + k x] 57432375 E Cos[-- + k x] 57432375 E Cos[-- + k x] 57432375 E Cos[-- + k x] 11486475 E Cos[-- + k x] 45045 E Cos[-- + k x] 225225 E Cos[-- + k x] 225225 E Cos[-- + k x] 225225 E Cos[-- + k x] 225225 E Cos[-- + k x] 45045 E Cos[-- + k x] 945 E Cos[-- + k x] 4725 E Cos[-- + k x] 4725 E Cos[-- + k x] 4725 E Cos[-- + k x] 4725 E Cos[-- + k x] 945 E Cos[-- + k x] E Sqrt[--] Cos[-- + k x] 5 E Sqrt[--] Cos[-- + k x] 10 E Sqrt[--] Cos[-- + k x] 10 E Sqrt[--] Cos[-- + k x] 5 E Sqrt[--] Cos[-- + k x] E Sqrt[--] Cos[-- + k x] 1159525191825 E Sin[-- + k x] 5797625959125 E Sin[-- + k x] 5797625959125 E Sin[-- + k x] 5797625959125 E Sin[-- + k x] 5797625959125 E Sin[-- + k x] 1159525191825 E Sin[-- + k x] 218243025 E Sin[-- + k x] 1091215125 E Sin[-- + k x] 1091215125 E Sin[-- + k x] 1091215125 E Sin[-- + k x] 1091215125 E Sin[-- + k x] 218243025 E Sin[-- + k x] 405405 E Sin[-- + k x] 2027025 E Sin[-- + k x] 2027025 E Sin[-- + k x] 2027025 E Sin[-- + k x] 2027025 E Sin[-- + k x] 405405 E Sin[-- + k x] 3465 E Sin[-- + k x] 17325 E Sin[-- + k x] 17325 E Sin[-- + k x] 17325 E Sin[-- + k x] 17325 E Sin[-- + k x] 3465 E Sin[-- + k x] 35 E Sin[-- + k x] 175 E Sin[-- + k x] 175 E Sin[-- + k x] 175 E Sin[-- + k x] 175 E Sin[-- + k x] 35 E Sin[-- + k x] - 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 Pi 4 Pi 4 Pi 4 Pi 4 Pi 4 Pi 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 -Integrate::idiv: Integral of ------------------------------------------ - ------------------------------------------- + ------------------------------------------- - ------------------------------------------- + ------------------------------------------- - ------------------------------------------ - --------------------------------------- + --------------------------------------- - --------------------------------------- + --------------------------------------- - --------------------------------------- + --------------------------------------- + ------------------------------------ - ------------------------------------- + ------------------------------------- - ------------------------------------- + ------------------------------------- - ------------------------------------ + ---------------------------------- - ----------------------------------- + ----------------------------------- - ----------------------------------- + ----------------------------------- - ---------------------------------- - --------------------------------------- + ----------------------------------------- - ------------------------------------------ + ------------------------------------------ - ----------------------------------------- + --------------------------------------- + -------------------------------------------- - -------------------------------------------- + -------------------------------------------- - -------------------------------------------- + -------------------------------------------- - -------------------------------------------- - ---------------------------------------- + ----------------------------------------- - ----------------------------------------- + ----------------------------------------- - ----------------------------------------- + ---------------------------------------- + ------------------------------------- - -------------------------------------- + -------------------------------------- - -------------------------------------- + -------------------------------------- - ------------------------------------- - ----------------------------------- + ------------------------------------ - ------------------------------------ + ------------------------------------ - ------------------------------------ + ----------------------------------- + --------------------------------- - ---------------------------------- + ---------------------------------- - ---------------------------------- + ---------------------------------- - --------------------------------- does not converge on {0, Infinity}. - 17/2 5 25/2 17/2 5 25/2 17/2 5 25/2 17/2 5 25/2 17/2 5 25/2 17/2 5 25/2 13/2 5 21/2 13/2 5 21/2 13/2 5 21/2 13/2 5 21/2 13/2 5 21/2 13/2 5 21/2 9/2 5 17/2 9/2 5 17/2 9/2 5 17/2 9/2 5 17/2 9/2 5 17/2 9/2 5 17/2 5/2 5 13/2 5/2 5 13/2 5/2 5 13/2 5/2 5 13/2 5/2 5 13/2 5/2 5 13/2 5 9/2 5 9/2 5 9/2 5 9/2 5 9/2 5 9/2 19/2 5 27/2 19/2 5 27/2 19/2 5 27/2 19/2 5 27/2 19/2 5 27/2 19/2 5 27/2 15/2 5 23/2 15/2 5 23/2 15/2 5 23/2 15/2 5 23/2 15/2 5 23/2 15/2 5 23/2 11/2 5 19/2 11/2 5 19/2 11/2 5 19/2 11/2 5 19/2 11/2 5 19/2 11/2 5 19/2 7/2 5 15/2 7/2 5 15/2 7/2 5 15/2 7/2 5 15/2 7/2 5 15/2 7/2 5 15/2 3/2 5 11/2 3/2 5 11/2 3/2 5 11/2 3/2 5 11/2 3/2 5 11/2 3/2 5 11/2 - 1073741824 k k0 Sqrt[2 Pi] x 1073741824 k k0 Sqrt[2 Pi] x 536870912 k k0 Sqrt[2 Pi] x 536870912 k k0 Sqrt[2 Pi] x 1073741824 k k0 Sqrt[2 Pi] x 1073741824 k k0 Sqrt[2 Pi] x 2097152 k k0 Sqrt[2 Pi] x 2097152 k k0 Sqrt[2 Pi] x 1048576 k k0 Sqrt[2 Pi] x 1048576 k k0 Sqrt[2 Pi] x 2097152 k k0 Sqrt[2 Pi] x 2097152 k k0 Sqrt[2 Pi] x 16384 k k0 Sqrt[2 Pi] x 16384 k k0 Sqrt[2 Pi] x 8192 k k0 Sqrt[2 Pi] x 8192 k k0 Sqrt[2 Pi] x 16384 k k0 Sqrt[2 Pi] x 16384 k k0 Sqrt[2 Pi] x 64 k k0 Sqrt[2 Pi] x 64 k k0 Sqrt[2 Pi] x 32 k k0 Sqrt[2 Pi] x 32 k k0 Sqrt[2 Pi] x 64 k k0 Sqrt[2 Pi] x 64 k k0 Sqrt[2 Pi] x Sqrt[k] k0 x Sqrt[k] k0 x Sqrt[k] k0 x Sqrt[k] k0 x Sqrt[k] k0 x Sqrt[k] k0 x 8589934592 k k0 Sqrt[2 Pi] x 8589934592 k k0 Sqrt[2 Pi] x 4294967296 k k0 Sqrt[2 Pi] x 4294967296 k k0 Sqrt[2 Pi] x 8589934592 k k0 Sqrt[2 Pi] x 8589934592 k k0 Sqrt[2 Pi] x 16777216 k k0 Sqrt[2 Pi] x 16777216 k k0 Sqrt[2 Pi] x 8388608 k k0 Sqrt[2 Pi] x 8388608 k k0 Sqrt[2 Pi] x 16777216 k k0 Sqrt[2 Pi] x 16777216 k k0 Sqrt[2 Pi] x 131072 k k0 Sqrt[2 Pi] x 131072 k k0 Sqrt[2 Pi] x 65536 k k0 Sqrt[2 Pi] x 65536 k k0 Sqrt[2 Pi] x 131072 k k0 Sqrt[2 Pi] x 131072 k k0 Sqrt[2 Pi] x 512 k k0 Sqrt[2 Pi] x 512 k k0 Sqrt[2 Pi] x 256 k k0 Sqrt[2 Pi] x 256 k k0 Sqrt[2 Pi] x 512 k k0 Sqrt[2 Pi] x 512 k k0 Sqrt[2 Pi] x 4 k k0 Sqrt[2 Pi] x 4 k k0 Sqrt[2 Pi] x 2 k k0 Sqrt[2 Pi] x 2 k k0 Sqrt[2 Pi] x 4 k k0 Sqrt[2 Pi] x 4 k k0 Sqrt[2 Pi] x -Series[Integrate[(E^(-(c*x) + I*k0*x)*(1 - E^(-(c*x)))^5*BesselJ[3, k*x])/(k0^5*x^4), {x, 0, Infinity}, Assumptions -> n == 3 && q == 5 && κ == 5 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0], {k, Infinity, 10}] diff --git a/besseltransforms/5-5-4 b/besseltransforms/5-5-4 deleted file mode 100644 index 6c06a03..0000000 --- a/besseltransforms/5-5-4 +++ /dev/null @@ -1,2 +0,0 @@ -((k^6*(-35 + 16*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0) + 2*k^4*(-35 + 24*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^3 + 8*k^2*(-7 + 6*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^5 + 16*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^7)/(1680*k^4) - (k^6*(-35 + 16*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0) + 2*k^4*(-35 + 24*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^3 + 8*k^2*(-7 + 6*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^5 + 16*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^7)/(336*k^4) + (k^6*(-35 + 16*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0) + 2*k^4*(-35 + 24*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^3 + 8*k^2*(-7 + 6*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^5 + 16*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^7)/(168*k^4) - (k^6*(-35 + 16*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0) + 2*k^4*(-35 + 24*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^3 + 8*k^2*(-7 + 6*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^5 + 16*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^7)/(168*k^4) + (k^6*(-35 + 16*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0) + 2*k^4*(-35 + 24*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^3 + 8*k^2*(-7 + 6*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^5 + 16*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^7)/(336*k^4) - (k^6*(-35 + 16*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0) + 2*k^4*(-35 + 24*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^3 + 8*k^2*(-7 + 6*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^5 + 16*(-1 + Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^7)/(1680*k^4))/k0^5 -SeriesData[k, Infinity, {(4*c^5)/k0^5, (-105*c^6)/(2*k0^5) + ((15*I)*c^5)/k0^4, (304*c^7)/k0^5 - ((168*I)*c^6)/k0^4 - (24*c^5)/k0^3, (-35*(189*c^8 - (152*I)*c^7*k0 - 42*c^6*k0^2 + (4*I)*c^5*k0^3))/(8*k0^5), 0, (21*(8547*c^10 - (10870*I)*c^9*k0 - 5670*c^8*k0^2 + (1520*I)*c^7*k0^3 + 210*c^6*k0^4 - (12*I)*c^5*k0^5))/(32*k0^5), 0, (-33*(141232*c^12 - (240664*I)*c^11*k0 - 179487*c^10*k0^2 + (76090*I)*c^9*k0^3 + 19845*c^8*k0^4 - (3192*I)*c^7*k0^5 - 294*c^6*k0^6 + (12*I)*c^5*k0^7))/(64*k0^5)}, 2, 11, 1] diff --git a/besseltransforms/5-5-5 b/besseltransforms/5-5-5 deleted file mode 100644 index 385e34f..0000000 --- a/besseltransforms/5-5-5 +++ /dev/null @@ -1,2 +0,0 @@ -((35*k^8 + 8*k^6*(35 - 16*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^2 + 16*k^4*(35 - 24*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^4 + 64*k^2*(7 - 6*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^6 - 128*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^8)/(13440*k^5) - (35*k^8 + 8*k^6*(35 - 16*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^2 + 16*k^4*(35 - 24*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^4 + 64*k^2*(7 - 6*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^6 - 128*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^8)/(2688*k^5) + (35*k^8 + 8*k^6*(35 - 16*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^2 + 16*k^4*(35 - 24*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^4 + 64*k^2*(7 - 6*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^6 - 128*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^8)/(1344*k^5) - (35*k^8 + 8*k^6*(35 - 16*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^2 + 16*k^4*(35 - 24*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^4 + 64*k^2*(7 - 6*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^6 - 128*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^8)/(1344*k^5) + (35*k^8 + 8*k^6*(35 - 16*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^2 + 16*k^4*(35 - 24*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^4 + 64*k^2*(7 - 6*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^6 - 128*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^8)/(2688*k^5) - (35*k^8 + 8*k^6*(35 - 16*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^2 + 16*k^4*(35 - 24*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^4 + 64*k^2*(7 - 6*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^6 - 128*(-1 + Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^8)/(13440*k^5))/k0^5 -SeriesData[k, Infinity, {(5*c^5)/k0^5, (-84*c^6)/k0^5 + ((24*I)*c^5)/k0^4, (35*(38*c^7 - (21*I)*c^6*k0 - 3*c^5*k0^2))/(2*k0^5), (-3024*c^8)/k0^5 + ((2432*I)*c^7)/k0^4 + (672*c^6)/k0^3 - ((64*I)*c^5)/k0^2, (105*(1087*c^9 - (1134*I)*c^8*k0 - 456*c^7*k0^2 + (84*I)*c^6*k0^3 + 6*c^5*k0^4))/(16*k0^5), 0, (-11*(120332*c^11 - (179487*I)*c^10*k0 - 114135*c^9*k0^2 + (39690*I)*c^8*k0^3 + 7980*c^7*k0^4 - (882*I)*c^6*k0^5 - 42*c^5*k0^6))/(32*k0^5), 0, (143*(443611*c^13 - (847392*I)*c^12*k0 - 721992*c^11*k0^2 + (358974*I)*c^10*k0^3 + 114135*c^9*k0^4 - (23814*I)*c^8*k0^5 - 3192*c^7*k0^6 + (252*I)*c^6*k0^7 + 9*c^5*k0^8))/(128*k0^5)}, 2, 11, 1] diff --git a/besseltransforms/5-5-6 b/besseltransforms/5-5-6 deleted file mode 100644 index f599039..0000000 --- a/besseltransforms/5-5-6 +++ /dev/null @@ -1,2 +0,0 @@ -((k^8*(-315 + 64*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0) + 16*k^6*(-105 + 52*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^3 + 48*k^4*(-63 + 44*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^5 + 64*k^2*(-36 + 31*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^7 + 640*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^9)/(60480*k^6) - (k^8*(-315 + 64*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0) + 16*k^6*(-105 + 52*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^3 + 48*k^4*(-63 + 44*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^5 + 64*k^2*(-36 + 31*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^7 + 640*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^9)/(12096*k^6) + (k^8*(-315 + 64*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0) + 16*k^6*(-105 + 52*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^3 + 48*k^4*(-63 + 44*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^5 + 64*k^2*(-36 + 31*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^7 + 640*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^9)/(6048*k^6) - (k^8*(-315 + 64*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0) + 16*k^6*(-105 + 52*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^3 + 48*k^4*(-63 + 44*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^5 + 64*k^2*(-36 + 31*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^7 + 640*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^9)/(6048*k^6) + (k^8*(-315 + 64*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0) + 16*k^6*(-105 + 52*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^3 + 48*k^4*(-63 + 44*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^5 + 64*k^2*(-36 + 31*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^7 + 640*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^9)/(12096*k^6) - (k^8*(-315 + 64*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0) + 16*k^6*(-105 + 52*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^3 + 48*k^4*(-63 + 44*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^5 + 64*k^2*(-36 + 31*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^7 + 640*(-1 + Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^9)/(60480*k^6))/k0^5 -SeriesData[k, Infinity, {(6*c^5)/k0^5, (-245*c^6)/(2*k0^5) + ((35*I)*c^5)/k0^4, (1216*c^7)/k0^5 - ((672*I)*c^6)/k0^4 - (96*c^5)/k0^3, (-315*(189*c^8 - (152*I)*c^7*k0 - 42*c^6*k0^2 + (4*I)*c^5*k0^3))/(8*k0^5), (86960*c^9)/(3*k0^5) - ((30240*I)*c^8)/k0^4 - (12160*c^7)/k0^3 + ((2240*I)*c^6)/k0^2 + (160*c^5)/k0, (-231*(8547*c^10 - (10870*I)*c^9*k0 - 5670*c^8*k0^2 + (1520*I)*c^7*k0^3 + 210*c^6*k0^4 - (12*I)*c^5*k0^5))/(32*k0^5), 0, (143*(141232*c^12 - (240664*I)*c^11*k0 - 179487*c^10*k0^2 + (76090*I)*c^9*k0^3 + 19845*c^8*k0^4 - (3192*I)*c^7*k0^5 - 294*c^6*k0^6 + (12*I)*c^5*k0^7))/(64*k0^5)}, 2, 11, 1] diff --git a/besseltransforms/5-5-7 b/besseltransforms/5-5-7 deleted file mode 100644 index 35af23d..0000000 --- a/besseltransforms/5-5-7 +++ /dev/null @@ -1,2 +0,0 @@ -((21*k^10 + 4*k^8*(105 - 32*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^2 + 112*k^6*(15 - 8*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^4 + 384*k^4*(7 - 5*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^6 + 128*k^2*(15 - 13*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^8 - 512*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^10)/(40320*k^7) - (21*k^10 + 4*k^8*(105 - 32*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^2 + 112*k^6*(15 - 8*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^4 + 384*k^4*(7 - 5*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^6 + 128*k^2*(15 - 13*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^8 - 512*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^10)/(8064*k^7) + (21*k^10 + 4*k^8*(105 - 32*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^2 + 112*k^6*(15 - 8*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^4 + 384*k^4*(7 - 5*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^6 + 128*k^2*(15 - 13*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^8 - 512*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^10)/(4032*k^7) - (21*k^10 + 4*k^8*(105 - 32*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^2 + 112*k^6*(15 - 8*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^4 + 384*k^4*(7 - 5*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^6 + 128*k^2*(15 - 13*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^8 - 512*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^10)/(4032*k^7) + (21*k^10 + 4*k^8*(105 - 32*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^2 + 112*k^6*(15 - 8*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^4 + 384*k^4*(7 - 5*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^6 + 128*k^2*(15 - 13*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^8 - 512*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^10)/(8064*k^7) - (21*k^10 + 4*k^8*(105 - 32*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^2 + 112*k^6*(15 - 8*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^4 + 384*k^4*(7 - 5*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^6 + 128*k^2*(15 - 13*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^8 - 512*(-1 + Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^10)/(40320*k^7))/k0^5 -SeriesData[k, Infinity, {(7*c^5)/k0^5, (-24*(7*c^6 - (2*I)*c^5*k0))/k0^5, (105*(38*c^7 - (21*I)*c^6*k0 - 3*c^5*k0^2))/(2*k0^5), (-80*(189*c^8 - (152*I)*c^7*k0 - 42*c^6*k0^2 + (4*I)*c^5*k0^3))/k0^5, (1155*(1087*c^9 - (1134*I)*c^8*k0 - 456*c^7*k0^2 + (84*I)*c^6*k0^3 + 6*c^5*k0^4))/(16*k0^5), (-32*(8547*c^10 - (10870*I)*c^9*k0 - 5670*c^8*k0^2 + (1520*I)*c^7*k0^3 + 210*c^6*k0^4 - (12*I)*c^5*k0^5))/k0^5, (143*(120332*c^11 - (179487*I)*c^10*k0 - 114135*c^9*k0^2 + (39690*I)*c^8*k0^3 + 7980*c^7*k0^4 - (882*I)*c^6*k0^5 - 42*c^5*k0^6))/(32*k0^5), 0, (-715*(443611*c^13 - (847392*I)*c^12*k0 - 721992*c^11*k0^2 + (358974*I)*c^10*k0^3 + 114135*c^9*k0^4 - (23814*I)*c^8*k0^5 - 3192*c^7*k0^6 + (252*I)*c^6*k0^7 + 9*c^5*k0^8))/(128*k0^5)}, 2, 11, 1] diff --git a/besseltransforms/6-1-0.REMOVED.git-id b/besseltransforms/6-1-0.REMOVED.git-id deleted file mode 100644 index 730bd75..0000000 --- a/besseltransforms/6-1-0.REMOVED.git-id +++ /dev/null @@ -1 +0,0 @@ -0f102e90aa5931a6786417ff8dc4af328dd43035 \ No newline at end of file diff --git a/besseltransforms/6-1-1.REMOVED.git-id b/besseltransforms/6-1-1.REMOVED.git-id deleted file mode 100644 index 7533791..0000000 --- a/besseltransforms/6-1-1.REMOVED.git-id +++ /dev/null @@ -1 +0,0 @@ -481803dc1d1b689b8e54b8e3f2965fa3f2ec3ac3 \ No newline at end of file diff --git a/besseltransforms/6-1-2.REMOVED.git-id b/besseltransforms/6-1-2.REMOVED.git-id deleted file mode 100644 index 326f61c..0000000 --- a/besseltransforms/6-1-2.REMOVED.git-id +++ /dev/null @@ -1 +0,0 @@ -9280f56d85a627d34557e5b7ee0692b99af6adf2 \ No newline at end of file diff --git a/besseltransforms/6-1-3 b/besseltransforms/6-1-3 deleted file mode 100644 index 1390128..0000000 --- a/besseltransforms/6-1-3 +++ /dev/null @@ -1,2 +0,0 @@ -((k^2*(-3 + Sqrt[1 + k^2/(c - I*k0)^2]) + 4*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^2)/(k^3*Sqrt[1 + k^2/(c - I*k0)^2]) - (6*(k^2*(-3 + Sqrt[1 + k^2/(2*c - I*k0)^2]) + 4*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^2))/(k^3*Sqrt[1 + k^2/(2*c - I*k0)^2]) + (15*(k^2*(-3 + Sqrt[1 + k^2/(3*c - I*k0)^2]) + 4*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^2))/(k^3*Sqrt[1 + k^2/(3*c - I*k0)^2]) - (20*(k^2*(-3 + Sqrt[1 + k^2/(4*c - I*k0)^2]) + 4*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^2))/(k^3*Sqrt[1 + k^2/(4*c - I*k0)^2]) + (15*(k^2*(-3 + Sqrt[1 + k^2/(5*c - I*k0)^2]) + 4*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^2))/(k^3*Sqrt[1 + k^2/(5*c - I*k0)^2]) - (6*(k^2*(-3 + Sqrt[1 + k^2/(6*c - I*k0)^2]) + 4*(-1 + Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^2))/(k^3*Sqrt[1 + k^2/(6*c - I*k0)^2]) + (k^2*(-3 + Sqrt[1 + k^2/(7*c - I*k0)^2]) + 4*(-1 + Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^2)/(k^3*Sqrt[1 + k^2/(7*c - I*k0)^2]))/k0 -SeriesData[k, Infinity, {((2835*I)*c^6)/k - (11340*c^7)/(k*k0), 0, (51975*(140*c^9 - (99*I)*c^8*k0 - 24*c^7*k0^2 + (2*I)*c^6*k0^3))/(4*k*k0)}, 7, 11, 1] diff --git a/besseltransforms/6-1-4 b/besseltransforms/6-1-4 deleted file mode 100644 index 6a73d23..0000000 --- a/besseltransforms/6-1-4 +++ /dev/null @@ -1,2 +0,0 @@ -((k^4 - 4*k^2*(-2 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^2 - 8*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^4)/(k^4*Sqrt[1 + k^2/(c - I*k0)^2]*(c - I*k0)) - (6*(k^4 - 4*k^2*(-2 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^2 - 8*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^4))/(k^4*Sqrt[1 + k^2/(2*c - I*k0)^2]*(2*c - I*k0)) + (15*(k^4 - 4*k^2*(-2 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^2 - 8*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^4))/(k^4*Sqrt[1 + k^2/(3*c - I*k0)^2]*(3*c - I*k0)) - (20*(k^4 - 4*k^2*(-2 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^2 - 8*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^4))/(k^4*Sqrt[1 + k^2/(4*c - I*k0)^2]*(4*c - I*k0)) + (15*(k^4 - 4*k^2*(-2 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^2 - 8*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^4))/(k^4*Sqrt[1 + k^2/(5*c - I*k0)^2]*(5*c - I*k0)) - (6*(k^4 - 4*k^2*(-2 + Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^2 - 8*(-1 + Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^4))/(k^4*Sqrt[1 + k^2/(6*c - I*k0)^2]*(6*c - I*k0)) + (k^4 - 4*k^2*(-2 + Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^2 - 8*(-1 + Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^4)/(k^4*Sqrt[1 + k^2/(7*c - I*k0)^2]*(7*c - I*k0)))/k0 -SeriesData[k, Infinity, {(-945*c^6)/(k*k0), 0, (31185*(33*c^8 - (16*I)*c^7*k0 - 2*c^6*k0^2))/(4*k*k0), 0, (-135135*(3047*c^10 - (2800*I)*c^9*k0 - 990*c^8*k0^2 + (160*I)*c^7*k0^3 + 10*c^6*k0^4))/(16*k*k0)}, 6, 11, 1] diff --git a/besseltransforms/6-1-5 b/besseltransforms/6-1-5 deleted file mode 100644 index afd5f59..0000000 --- a/besseltransforms/6-1-5 +++ /dev/null @@ -1,2 +0,0 @@ -((k^4*(-5 + Sqrt[1 + k^2/(c - I*k0)^2]) + 4*k^2*(-5 + 3*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^2 + 16*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^4)/(k^5*Sqrt[1 + k^2/(c - I*k0)^2]) - (6*(k^4*(-5 + Sqrt[1 + k^2/(2*c - I*k0)^2]) + 4*k^2*(-5 + 3*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^2 + 16*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^4))/(k^5*Sqrt[1 + k^2/(2*c - I*k0)^2]) + (15*(k^4*(-5 + Sqrt[1 + k^2/(3*c - I*k0)^2]) + 4*k^2*(-5 + 3*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^2 + 16*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^4))/(k^5*Sqrt[1 + k^2/(3*c - I*k0)^2]) - (20*(k^4*(-5 + Sqrt[1 + k^2/(4*c - I*k0)^2]) + 4*k^2*(-5 + 3*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^2 + 16*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^4))/(k^5*Sqrt[1 + k^2/(4*c - I*k0)^2]) + (15*(k^4*(-5 + Sqrt[1 + k^2/(5*c - I*k0)^2]) + 4*k^2*(-5 + 3*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^2 + 16*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^4))/(k^5*Sqrt[1 + k^2/(5*c - I*k0)^2]) - (6*(k^4*(-5 + Sqrt[1 + k^2/(6*c - I*k0)^2]) + 4*k^2*(-5 + 3*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^2 + 16*(-1 + Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^4))/(k^5*Sqrt[1 + k^2/(6*c - I*k0)^2]) + (k^4*(-5 + Sqrt[1 + k^2/(7*c - I*k0)^2]) + 4*k^2*(-5 + 3*Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^2 + 16*(-1 + Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^4)/(k^5*Sqrt[1 + k^2/(7*c - I*k0)^2]))/k0 -SeriesData[k, Infinity, {((-10395*I)*c^6)/k + (41580*c^7)/(k*k0), 0, (-135135*(140*c^9 - (99*I)*c^8*k0 - 24*c^7*k0^2 + (2*I)*c^6*k0^3))/(4*k*k0)}, 7, 11, 1] diff --git a/besseltransforms/6-1-6 b/besseltransforms/6-1-6 deleted file mode 100644 index 76c8354..0000000 --- a/besseltransforms/6-1-6 +++ /dev/null @@ -1,2 +0,0 @@ -((k^6 - 6*k^4*(-3 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^2 + 16*k^2*(3 - 2*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^4 - 32*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^6)/(k^6*Sqrt[1 + k^2/(c - I*k0)^2]*(c - I*k0)) - (6*(k^6 - 6*k^4*(-3 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^2 + 16*k^2*(3 - 2*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^4 - 32*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^6))/(k^6*Sqrt[1 + k^2/(2*c - I*k0)^2]*(2*c - I*k0)) + (15*(k^6 - 6*k^4*(-3 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^2 + 16*k^2*(3 - 2*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^4 - 32*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^6))/(k^6*Sqrt[1 + k^2/(3*c - I*k0)^2]*(3*c - I*k0)) - (20*(k^6 - 6*k^4*(-3 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^2 + 16*k^2*(3 - 2*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^4 - 32*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^6))/(k^6*Sqrt[1 + k^2/(4*c - I*k0)^2]*(4*c - I*k0)) + (15*(k^6 - 6*k^4*(-3 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^2 + 16*k^2*(3 - 2*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^4 - 32*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^6))/(k^6*Sqrt[1 + k^2/(5*c - I*k0)^2]*(5*c - I*k0)) - (6*(k^6 - 6*k^4*(-3 + Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^2 + 16*k^2*(3 - 2*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^4 - 32*(-1 + Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^6))/(k^6*Sqrt[1 + k^2/(6*c - I*k0)^2]*(6*c - I*k0)) + (k^6 - 6*k^4*(-3 + Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^2 + 16*k^2*(3 - 2*Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^4 - 32*(-1 + Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^6)/(k^6*Sqrt[1 + k^2/(7*c - I*k0)^2]*(7*c - I*k0)))/k0 -SeriesData[k, Infinity, {(10395*c^6)/(k*k0), 0, (-135135*(33*c^8 - (16*I)*c^7*k0 - 2*c^6*k0^2))/(4*k*k0), 0, (405405*(3047*c^10 - (2800*I)*c^9*k0 - 990*c^8*k0^2 + (160*I)*c^7*k0^3 + 10*c^6*k0^4))/(16*k*k0)}, 6, 11, 1] diff --git a/besseltransforms/6-1-7 b/besseltransforms/6-1-7 deleted file mode 100644 index f7222a7..0000000 --- a/besseltransforms/6-1-7 +++ /dev/null @@ -1,2 +0,0 @@ -((k^6*(-7 + Sqrt[1 + k^2/(c - I*k0)^2]) + 8*k^4*(-7 + 3*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^2 + 16*k^2*(-7 + 5*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^4 + 64*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^6)/(k^7*Sqrt[1 + k^2/(c - I*k0)^2]) - (6*(k^6*(-7 + Sqrt[1 + k^2/(2*c - I*k0)^2]) + 8*k^4*(-7 + 3*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^2 + 16*k^2*(-7 + 5*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^4 + 64*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^6))/(k^7*Sqrt[1 + k^2/(2*c - I*k0)^2]) + (15*(k^6*(-7 + Sqrt[1 + k^2/(3*c - I*k0)^2]) + 8*k^4*(-7 + 3*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^2 + 16*k^2*(-7 + 5*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^4 + 64*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^6))/(k^7*Sqrt[1 + k^2/(3*c - I*k0)^2]) - (20*(k^6*(-7 + Sqrt[1 + k^2/(4*c - I*k0)^2]) + 8*k^4*(-7 + 3*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^2 + 16*k^2*(-7 + 5*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^4 + 64*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^6))/(k^7*Sqrt[1 + k^2/(4*c - I*k0)^2]) + (15*(k^6*(-7 + Sqrt[1 + k^2/(5*c - I*k0)^2]) + 8*k^4*(-7 + 3*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^2 + 16*k^2*(-7 + 5*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^4 + 64*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^6))/(k^7*Sqrt[1 + k^2/(5*c - I*k0)^2]) - (6*(k^6*(-7 + Sqrt[1 + k^2/(6*c - I*k0)^2]) + 8*k^4*(-7 + 3*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^2 + 16*k^2*(-7 + 5*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^4 + 64*(-1 + Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^6))/(k^7*Sqrt[1 + k^2/(6*c - I*k0)^2]) + (k^6*(-7 + Sqrt[1 + k^2/(7*c - I*k0)^2]) + 8*k^4*(-7 + 3*Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^2 + 16*k^2*(-7 + 5*Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^4 + 64*(-1 + Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^6)/(k^7*Sqrt[1 + k^2/(7*c - I*k0)^2]))/k0 -SeriesData[k, Infinity, {(46080*c^6)/(k*k0), ((135135*I)*c^6)/k - (540540*c^7)/(k*k0), 0, (675675*(140*c^9 - (99*I)*c^8*k0 - 24*c^7*k0^2 + (2*I)*c^6*k0^3))/(4*k*k0)}, 6, 11, 1] diff --git a/besseltransforms/6-2-0 b/besseltransforms/6-2-0 deleted file mode 100644 index c39b980..0000000 --- a/besseltransforms/6-2-0 +++ /dev/null @@ -1,2 +0,0 @@ - -Simplify::time: Time spent on a transformation exceeded 300. seconds, and the transformation was aborted. Increasing the value of TimeConstraint option may improve the result of simplification. diff --git a/besseltransforms/6-2-1 b/besseltransforms/6-2-1 deleted file mode 100644 index 5293800..0000000 --- a/besseltransforms/6-2-1 +++ /dev/null @@ -1,2 +0,0 @@ -(-12*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0) + 30*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0) - 40*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0) + 30*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0) - 12*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0) + 2*(-1 + Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0) + k*Sqrt[Pi]*(Piecewise[{{0, k^2/k0^2 <= 1}}, (2*Sqrt[k^2 - k0^2])/(k*Sqrt[Pi])] + I*Piecewise[{{(2*k0)/(k*Sqrt[Pi]), k0^2/k^2 < 1}, {(2*(k0 - Sqrt[-k^2 + k0^2]))/(k*Sqrt[Pi]), k0^2/k^2 > 1}}, 0]))/(2*k*k0^2) -Piecewise[{{SeriesData[k, Infinity, {(45*c^6)/k0^2, 0, (1575*c^6)/2 - (29925*c^8)/(4*k0^2) + ((4725*I)*c^7)/k0, 0, (6615*(1087*c^10 - (1260*I)*c^9*k0 - 570*c^8*k0^2 + (120*I)*c^7*k0^3 + 10*c^6*k0^4))/(16*k0^2)}, 6, 11, 1], (k0 <= 0 && k^2/k0^2 > 1) || k0 > 0}}, SeriesData[k, Infinity, {-k0^(-2), 0, 1/2, 0, ((3*c*(c - I*k0)^3)/4 - (15*c*(2*c - I*k0)^3)/4 + (15*c*(3*c - I*k0)^3)/2 - (15*c*(4*c - I*k0)^3)/2 + (15*c*(5*c - I*k0)^3)/4 - (3*c*(6*c - I*k0)^3)/4 - (3*I)/4*(c - I*k0)^3*k0 + (15*I)/8*(2*c - I*k0)^3*k0 - (5*I)/2*(3*c - I*k0)^3*k0 + (15*I)/8*(4*c - I*k0)^3*k0 - (3*I)/4*(5*c - I*k0)^3*k0 + I/8*(6*c - I*k0)^3*k0)/k0^2, 0, ((-3*c*(c - I*k0)^5)/8 + (15*c*(2*c - I*k0)^5)/8 - (15*c*(3*c - I*k0)^5)/4 + (15*c*(4*c - I*k0)^5)/4 - (15*c*(5*c - I*k0)^5)/8 + (3*c*(6*c - I*k0)^5)/8 + (3*I)/8*(c - I*k0)^5*k0 - (15*I)/16*(2*c - I*k0)^5*k0 + (5*I)/4*(3*c - I*k0)^5*k0 - (15*I)/16*(4*c - I*k0)^5*k0 + (3*I)/8*(5*c - I*k0)^5*k0 - I/16*(6*c - I*k0)^5*k0)/k0^2, 0, ((15*c*(c - I*k0)^7)/64 - (75*c*(2*c - I*k0)^7)/64 + (75*c*(3*c - I*k0)^7)/32 - (75*c*(4*c - I*k0)^7)/32 + (75*c*(5*c - I*k0)^7)/64 - (15*c*(6*c - I*k0)^7)/64 - (15*I)/64*(c - I*k0)^7*k0 + (75*I)/128*(2*c - I*k0)^7*k0 - (25*I)/32*(3*c - I*k0)^7*k0 + (75*I)/128*(4*c - I*k0)^7*k0 - (15*I)/64*(5*c - I*k0)^7*k0 + (5*I)/128*(6*c - I*k0)^7*k0)/k0^2, 0, ((-21*c*(c - I*k0)^9)/128 + (105*c*(2*c - I*k0)^9)/128 - (105*c*(3*c - I*k0)^9)/64 + (105*c*(4*c - I*k0)^9)/64 - (105*c*(5*c - I*k0)^9)/128 + (21*c*(6*c - I*k0)^9)/128 + (21*I)/128*(c - I*k0)^9*k0 - (105*I)/256*(2*c - I*k0)^9*k0 + (35*I)/64*(3*c - I*k0)^9*k0 - (105*I)/256*(4*c - I*k0)^9*k0 + (21*I)/128*(5*c - I*k0)^9*k0 - (7*I)/256*(6*c - I*k0)^9*k0)/k0^2}, 0, 11, 1]] diff --git a/besseltransforms/6-2-2 b/besseltransforms/6-2-2 deleted file mode 100644 index 4f80592..0000000 --- a/besseltransforms/6-2-2 +++ /dev/null @@ -1,2 +0,0 @@ -(-k^2 + 12*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^2 - 30*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^2 + 40*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^2 - 30*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^2 + 12*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^2 - 2*(-1 + Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^2 + k^2*Sqrt[Pi]*(I*Piecewise[{{0, k^2/k0^2 <= 1}}, (2*k0*Sqrt[k^2 - k0^2])/(k^2*Sqrt[Pi])] + Piecewise[{{(k^2 + 2*k0*(-k0 + Sqrt[-k^2 + k0^2]))/(k^2*Sqrt[Pi]), k^2/k0^2 < 1}, {(1 - (2*k0^2)/k^2)/Sqrt[Pi], k^2/k0^2 > 1}}, 0]))/(2*k^2*k0^2) -SeriesData[k, Infinity, {(-945*c^7)/k0^2 + ((315*I)*c^6)/k0, 0, (4725*(63*c^9 - (57*I)*c^8*k0 - 18*c^7*k0^2 + (2*I)*c^6*k0^3))/(4*k0^2)}, 7, 11, 1] diff --git a/besseltransforms/6-2-3 b/besseltransforms/6-2-3 deleted file mode 100644 index f51020a..0000000 --- a/besseltransforms/6-2-3 +++ /dev/null @@ -1,2 +0,0 @@ -(k^2*(-3 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0) + 4*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^3 - 6*k^2*(-3 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0) - 24*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^3 + 15*k^2*(-3 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0) + 60*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^3 - 20*k^2*(-3 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0) - 80*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^3 + 15*k^2*(-3 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0) + 60*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^3 - 6*k^2*(-3 + Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0) - 24*(-1 + Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^3 + k^2*(-3 + Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0) + 4*(-1 + Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^3)/(3*k^3*k0^2) -SeriesData[k, Infinity, {(-105*c^6)/k0^2, 0, (-2835*c^6)/2 + (93555*c^8)/(4*k0^2) - ((11340*I)*c^7)/k0, 0, (5145525*c^8)/8 - (31673565*c^10)/(16*k0^2) + ((1819125*I)*c^9)/k0 - (103950*I)*c^7*k0 - (51975*c^6*k0^2)/8}, 6, 11, 1] diff --git a/besseltransforms/6-2-4 b/besseltransforms/6-2-4 deleted file mode 100644 index 17c1dae..0000000 --- a/besseltransforms/6-2-4 +++ /dev/null @@ -1,2 +0,0 @@ -(1/2 - 6*(1/4 - ((-2 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^2)/k^2 - (2*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^4)/k^4) + 15*(1/4 - ((-2 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^2)/k^2 - (2*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^4)/k^4) - 20*(1/4 - ((-2 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^2)/k^2 - (2*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^4)/k^4) + 15*(1/4 - ((-2 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^2)/k^2 - (2*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^4)/k^4) - 6*(1/4 - ((-2 + Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^2)/k^2 - (2*(-1 + Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^4)/k^4) - ((-2 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^2)/k^2 - (2*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^4)/k^4 - ((-2 + Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^2)/k^2 - (2*(-1 + Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^4)/k^4)/k0^2 -SeriesData[k, Infinity, {(3780*c^7)/k0^2 - ((945*I)*c^6)/k0, 0, 62370*c^7 - (363825*c^9)/k0^2 + ((1029105*I)/4*c^8)/k0 - (10395*I)/2*c^6*k0}, 7, 11, 1] diff --git a/besseltransforms/6-2-5 b/besseltransforms/6-2-5 deleted file mode 100644 index f92ff20..0000000 --- a/besseltransforms/6-2-5 +++ /dev/null @@ -1,2 +0,0 @@ -((k^4*(-5 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0) + 4*k^2*(-5 + 3*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^3 + 16*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^5)/(5*k^5) - (6*(k^4*(-5 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0) + 4*k^2*(-5 + 3*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^3 + 16*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^5))/(5*k^5) + (3*(k^4*(-5 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0) + 4*k^2*(-5 + 3*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^3 + 16*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^5))/k^5 - (4*(k^4*(-5 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0) + 4*k^2*(-5 + 3*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^3 + 16*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^5))/k^5 + (3*(k^4*(-5 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0) + 4*k^2*(-5 + 3*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^3 + 16*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^5))/k^5 - (6*(k^4*(-5 + Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0) + 4*k^2*(-5 + 3*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^3 + 16*(-1 + Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^5))/(5*k^5) + (k^4*(-5 + Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0) + 4*k^2*(-5 + 3*Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^3 + 16*(-1 + Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^5)/(5*k^5))/k0^2 -SeriesData[k, Infinity, {(945*c^6)/k0^2, 0, (10395*c^6)/2 - (343035*c^8)/(4*k0^2) + ((41580*I)*c^7)/k0, 0, (-13378365*c^8)/8 + (82351269*c^10)/(16*k0^2) - ((4729725*I)*c^9)/k0 + (270270*I)*c^7*k0 + (135135*c^6*k0^2)/8}, 6, 11, 1] diff --git a/besseltransforms/6-2-6 b/besseltransforms/6-2-6 deleted file mode 100644 index 3b96abb..0000000 --- a/besseltransforms/6-2-6 +++ /dev/null @@ -1,2 +0,0 @@ -((k^6 - 6*k^4*(-3 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^2 + 16*k^2*(3 - 2*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^4 - 32*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^6)/(6*k^6) - (k^6 - 6*k^4*(-3 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^2 + 16*k^2*(3 - 2*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^4 - 32*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^6)/k^6 + (5*(k^6 - 6*k^4*(-3 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^2 + 16*k^2*(3 - 2*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^4 - 32*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^6))/(2*k^6) - (10*(k^6 - 6*k^4*(-3 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^2 + 16*k^2*(3 - 2*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^4 - 32*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^6))/(3*k^6) + (5*(k^6 - 6*k^4*(-3 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^2 + 16*k^2*(3 - 2*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^4 - 32*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^6))/(2*k^6) - (k^6 - 6*k^4*(-3 + Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^2 + 16*k^2*(3 - 2*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^4 - 32*(-1 + Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^6)/k^6 + (k^6 - 6*k^4*(-3 + Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^2 + 16*k^2*(3 - 2*Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^4 - 32*(-1 + Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^6)/(6*k^6))/k0^2 -SeriesData[k, Infinity, {(3840*c^6)/k0^2, (-41580*c^7)/k0^2 + ((10395*I)*c^6)/k0, 0, -270270*c^7 + (1576575*c^9)/k0^2 - ((4459455*I)/4*c^8)/k0 + (45045*I)/2*c^6*k0}, 6, 11, 1] diff --git a/besseltransforms/6-2-7 b/besseltransforms/6-2-7 deleted file mode 100644 index 3231c56..0000000 --- a/besseltransforms/6-2-7 +++ /dev/null @@ -1,2 +0,0 @@ -((k^6*(-7 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0) + 8*k^4*(-7 + 3*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^3 + 16*k^2*(-7 + 5*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^5 + 64*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^7)/(7*k^7) - (6*(k^6*(-7 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0) + 8*k^4*(-7 + 3*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^3 + 16*k^2*(-7 + 5*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^5 + 64*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^7))/(7*k^7) + (15*(k^6*(-7 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0) + 8*k^4*(-7 + 3*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^3 + 16*k^2*(-7 + 5*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^5 + 64*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^7))/(7*k^7) - (20*(k^6*(-7 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0) + 8*k^4*(-7 + 3*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^3 + 16*k^2*(-7 + 5*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^5 + 64*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^7))/(7*k^7) + (15*(k^6*(-7 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0) + 8*k^4*(-7 + 3*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^3 + 16*k^2*(-7 + 5*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^5 + 64*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^7))/(7*k^7) - (6*(k^6*(-7 + Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0) + 8*k^4*(-7 + 3*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^3 + 16*k^2*(-7 + 5*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^5 + 64*(-1 + Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^7))/(7*k^7) + (k^6*(-7 + Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0) + 8*k^4*(-7 + 3*Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^3 + 16*k^2*(-7 + 5*Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^5 + 64*(-1 + Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^7)/(7*k^7))/k0^2 -SeriesData[k, Infinity, {(10395*c^6)/k0^2, (-184320*c^7)/k0^2 + ((46080*I)*c^6)/k0, (-135135*c^6)/2 + (4459455*c^8)/(4*k0^2) - ((540540*I)*c^7)/k0, 0, (66891825*c^8)/8 - (411756345*c^10)/(16*k0^2) + ((23648625*I)*c^9)/k0 - (1351350*I)*c^7*k0 - (675675*c^6*k0^2)/8}, 6, 11, 1] diff --git a/besseltransforms/6-3-0 b/besseltransforms/6-3-0 deleted file mode 100644 index c39b980..0000000 --- a/besseltransforms/6-3-0 +++ /dev/null @@ -1,2 +0,0 @@ - -Simplify::time: Time spent on a transformation exceeded 300. seconds, and the transformation was aborted. Increasing the value of TimeConstraint option may improve the result of simplification. diff --git a/besseltransforms/6-3-1 b/besseltransforms/6-3-1 deleted file mode 100644 index c39b980..0000000 --- a/besseltransforms/6-3-1 +++ /dev/null @@ -1,2 +0,0 @@ - -Simplify::time: Time spent on a transformation exceeded 300. seconds, and the transformation was aborted. Increasing the value of TimeConstraint option may improve the result of simplification. diff --git a/besseltransforms/6-3-2 b/besseltransforms/6-3-2 deleted file mode 100644 index d31d17d..0000000 --- a/besseltransforms/6-3-2 +++ /dev/null @@ -1,2 +0,0 @@ -((3 - 2*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0) - (2*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^3)/k^2 + (5*(-3 + 2*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0))/2 + (5*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^3)/k^2 + (10*(3 - 2*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0))/3 - (20*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^3)/(3*k^2) + (5*(-3 + 2*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0))/2 + (5*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^3)/k^2 + (3 - 2*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0) - (2*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^3)/k^2 + ((-3 + 2*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0))/6 + ((-1 + Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^3)/(3*k^2) + (k0*Sqrt[Pi]*(Piecewise[{{0, k^2/k0^2 <= 1}}, (4*(k^2 - k0^2)^(3/2))/(3*k^2*k0*Sqrt[Pi])] + I*Piecewise[{{(-2*(2*k0*(k0 - Sqrt[-k^2 + k0^2]) + k^2*(-3 + (2*Sqrt[-k^2 + k0^2])/k0)))/(3*k^2*Sqrt[Pi]), k^2/k0^2 < 1}, {(2*(1 - (2*k0^2)/(3*k^2)))/Sqrt[Pi], k^2/k0^2 > 1}}, 0]))/4)/k0^3 -SeriesData[k, Infinity, {(-15*c^6)/k0^3, 0, (315*(19*c^8 - (12*I)*c^7*k0 - 2*c^6*k0^2))/(4*k0^3), 0, (-945*(1087*c^10 - (1260*I)*c^9*k0 - 570*c^8*k0^2 + (120*I)*c^7*k0^3 + 10*c^6*k0^4))/(16*k0^3)}, 5, 11, 1] diff --git a/besseltransforms/6-3-3 b/besseltransforms/6-3-3 deleted file mode 100644 index 44cb237..0000000 --- a/besseltransforms/6-3-3 +++ /dev/null @@ -1,2 +0,0 @@ -((3*k^4 + 4*k^2*(3 - 2*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^2 - 8*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^4)/(24*k^3) - (3*k^4 + 4*k^2*(3 - 2*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^2 - 8*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^4)/(4*k^3) + (5*(3*k^4 + 4*k^2*(3 - 2*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^2 - 8*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^4))/(8*k^3) - (5*(3*k^4 + 4*k^2*(3 - 2*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^2 - 8*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^4))/(6*k^3) + (5*(3*k^4 + 4*k^2*(3 - 2*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^2 - 8*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^4))/(8*k^3) - (3*k^4 + 4*k^2*(3 - 2*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^2 - 8*(-1 + Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^4)/(4*k^3) + (3*k^4 + 4*k^2*(3 - 2*Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^2 - 8*(-1 + Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^4)/(24*k^3))/k0^3 -SeriesData[k, Infinity, {(420*c^7)/k0^3 - ((105*I)*c^6)/k0^2, 0, (-945*I)/2*c^6 - (33075*c^9)/k0^3 + ((93555*I)/4*c^8)/k0^2 + (5670*c^7)/k0, 0, (10395*(2716*c^11 - (3047*I)*c^10*k0 - 1400*c^9*k0^2 + (330*I)*c^8*k0^3 + 40*c^7*k0^4 - (2*I)*c^6*k0^5))/(16*k0^3)}, 6, 11, 1] diff --git a/besseltransforms/6-3-4 b/besseltransforms/6-3-4 deleted file mode 100644 index 63608ab..0000000 --- a/besseltransforms/6-3-4 +++ /dev/null @@ -1,2 +0,0 @@ -((k^4*(-15 + 4*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0) + 4*k^2*(-10 + 7*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^3 + 24*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^5)/(60*k^4) - (k^4*(-15 + 4*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0) + 4*k^2*(-10 + 7*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^3 + 24*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^5)/(10*k^4) + (k^4*(-15 + 4*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0) + 4*k^2*(-10 + 7*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^3 + 24*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^5)/(4*k^4) - (k^4*(-15 + 4*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0) + 4*k^2*(-10 + 7*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^3 + 24*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^5)/(3*k^4) + (k^4*(-15 + 4*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0) + 4*k^2*(-10 + 7*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^3 + 24*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^5)/(4*k^4) - (k^4*(-15 + 4*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0) + 4*k^2*(-10 + 7*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^3 + 24*(-1 + Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^5)/(10*k^4) + (k^4*(-15 + 4*Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0) + 4*k^2*(-10 + 7*Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^3 + 24*(-1 + Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^5)/(60*k^4))/k0^3 -SeriesData[k, Infinity, {(105*c^6)/k0^3, 0, (-945*(33*c^8 - (16*I)*c^7*k0 - 2*c^6*k0^2))/(4*k0^3), 0, (20790*I)*c^7 + (6334713*c^10)/(16*k0^3) - ((363825*I)*c^9)/k0^2 - (1029105*c^8)/(8*k0) + (10395*c^6*k0)/8}, 5, 11, 1] diff --git a/besseltransforms/6-3-5 b/besseltransforms/6-3-5 deleted file mode 100644 index f14412a..0000000 --- a/besseltransforms/6-3-5 +++ /dev/null @@ -1,2 +0,0 @@ -((5*k^6 + 12*k^4*(5 - 2*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^2 + 8*k^2*(15 - 11*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^4 - 64*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^6)/(120*k^5) - (5*k^6 + 12*k^4*(5 - 2*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^2 + 8*k^2*(15 - 11*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^4 - 64*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^6)/(20*k^5) + (5*k^6 + 12*k^4*(5 - 2*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^2 + 8*k^2*(15 - 11*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^4 - 64*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^6)/(8*k^5) - (5*k^6 + 12*k^4*(5 - 2*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^2 + 8*k^2*(15 - 11*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^4 - 64*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^6)/(6*k^5) + (5*k^6 + 12*k^4*(5 - 2*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^2 + 8*k^2*(15 - 11*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^4 - 64*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^6)/(8*k^5) - (5*k^6 + 12*k^4*(5 - 2*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^2 + 8*k^2*(15 - 11*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^4 - 64*(-1 + Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^6)/(20*k^5) + (5*k^6 + 12*k^4*(5 - 2*Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^2 + 8*k^2*(15 - 11*Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^4 - 64*(-1 + Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^6)/(120*k^5))/k0^3 -SeriesData[k, Infinity, {(384*c^6)/k0^3, (-3780*c^7)/k0^3 + ((945*I)*c^6)/k0^2, 0, (3465*I)/2*c^6 + (121275*c^9)/k0^3 - ((343035*I)/4*c^8)/k0^2 - (20790*c^7)/k0, 0, (-27027*(2716*c^11 - (3047*I)*c^10*k0 - 1400*c^9*k0^2 + (330*I)*c^8*k0^3 + 40*c^7*k0^4 - (2*I)*c^6*k0^5))/(16*k0^3)}, 5, 11, 1] diff --git a/besseltransforms/6-3-6 b/besseltransforms/6-3-6 deleted file mode 100644 index 416d8ec..0000000 --- a/besseltransforms/6-3-6 +++ /dev/null @@ -1,2 +0,0 @@ -((k^6*(-35 + 6*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0) + 6*k^4*(-35 + 17*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^3 + 16*k^2*(-21 + 16*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^5 + 160*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^7)/(210*k^6) - (k^6*(-35 + 6*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0) + 6*k^4*(-35 + 17*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^3 + 16*k^2*(-21 + 16*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^5 + 160*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^7)/(35*k^6) + (k^6*(-35 + 6*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0) + 6*k^4*(-35 + 17*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^3 + 16*k^2*(-21 + 16*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^5 + 160*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^7)/(14*k^6) - (2*(k^6*(-35 + 6*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0) + 6*k^4*(-35 + 17*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^3 + 16*k^2*(-21 + 16*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^5 + 160*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^7))/(21*k^6) + (k^6*(-35 + 6*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0) + 6*k^4*(-35 + 17*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^3 + 16*k^2*(-21 + 16*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^5 + 160*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^7)/(14*k^6) - (k^6*(-35 + 6*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0) + 6*k^4*(-35 + 17*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^3 + 16*k^2*(-21 + 16*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^5 + 160*(-1 + Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^7)/(35*k^6) + (k^6*(-35 + 6*Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0) + 6*k^4*(-35 + 17*Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^3 + 16*k^2*(-21 + 16*Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^5 + 160*(-1 + Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^7)/(210*k^6))/k0^3 -SeriesData[k, Infinity, {(945*c^6)/k0^3, (-15360*c^7)/k0^3 + ((3840*I)*c^6)/k0^2, (10395*(33*c^8 - (16*I)*c^7*k0 - 2*c^6*k0^2))/(4*k0^3), 0, (-90090*I)*c^7 - (27450423*c^10)/(16*k0^3) + ((1576575*I)*c^9)/k0^2 + (4459455*c^8)/(8*k0) - (45045*c^6*k0)/8}, 5, 11, 1] diff --git a/besseltransforms/6-3-7 b/besseltransforms/6-3-7 deleted file mode 100644 index 3527f20..0000000 --- a/besseltransforms/6-3-7 +++ /dev/null @@ -1,2 +0,0 @@ -((7*k^8 + 24*k^6*(7 - 2*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^2 + 16*k^4*(42 - 23*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^4 + 64*k^2*(14 - 11*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^6 - 384*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^8)/(336*k^7) - (7*k^8 + 24*k^6*(7 - 2*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^2 + 16*k^4*(42 - 23*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^4 + 64*k^2*(14 - 11*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^6 - 384*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^8)/(56*k^7) + (5*(7*k^8 + 24*k^6*(7 - 2*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^2 + 16*k^4*(42 - 23*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^4 + 64*k^2*(14 - 11*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^6 - 384*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^8))/(112*k^7) - (5*(7*k^8 + 24*k^6*(7 - 2*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^2 + 16*k^4*(42 - 23*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^4 + 64*k^2*(14 - 11*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^6 - 384*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^8))/(84*k^7) + (5*(7*k^8 + 24*k^6*(7 - 2*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^2 + 16*k^4*(42 - 23*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^4 + 64*k^2*(14 - 11*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^6 - 384*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^8))/(112*k^7) - (7*k^8 + 24*k^6*(7 - 2*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^2 + 16*k^4*(42 - 23*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^4 + 64*k^2*(14 - 11*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^6 - 384*(-1 + Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^8)/(56*k^7) + (7*k^8 + 24*k^6*(7 - 2*Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^2 + 16*k^4*(42 - 23*Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^4 + 64*k^2*(14 - 11*Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^6 - 384*(-1 + Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^8)/(336*k^7))/k0^3 -SeriesData[k, Infinity, {(1920*c^6)/k0^3, (-41580*c^7)/k0^3 + ((10395*I)*c^6)/k0^2, (380160*c^8)/k0^3 - ((184320*I)*c^7)/k0^2 - (23040*c^6)/k0, (-45045*I)/2*c^6 - (1576575*c^9)/k0^3 + ((4459455*I)/4*c^8)/k0^2 + (270270*c^7)/k0, 0, (135135*(2716*c^11 - (3047*I)*c^10*k0 - 1400*c^9*k0^2 + (330*I)*c^8*k0^3 + 40*c^7*k0^4 - (2*I)*c^6*k0^5))/(16*k0^3)}, 5, 11, 1] diff --git a/besseltransforms/6-4-0 b/besseltransforms/6-4-0 deleted file mode 100644 index dbda98f..0000000 --- a/besseltransforms/6-4-0 +++ /dev/null @@ -1,9 +0,0 @@ -Integrate[(E^(-(c*x) + I*k0*x)*(1 - E^(-(c*x)))^6*BesselJ[0, k*x])/(k0^4*x^3), {x, 0, Infinity}, Assumptions -> n == 0 && q == 4 && κ == 6 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0] - - -7 c x + I k0 x Pi -6 c x + I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi -7 c x + I k0 x Pi -6 c x + I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi -7 c x + I k0 x Pi -6 c x + I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi -7 c x + I k0 x Pi -6 c x + I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi -7 c x + I k0 x 2 Pi -6 c x + I k0 x 2 Pi -5 c x + I k0 x 2 Pi -4 c x + I k0 x 2 Pi -3 c x + I k0 x 2 Pi -2 c x + I k0 x 2 Pi -(c x) + I k0 x 2 Pi -7 c x + I k0 x Pi -6 c x + I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi -7 c x + I k0 x Pi -6 c x + I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi -7 c x + I k0 x Pi -6 c x + I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi -7 c x + I k0 x Pi -6 c x + I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi -7 c x + I k0 x Pi -6 c x + I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi - 13043905875 E Cos[-- - k x] 39131717625 E Cos[-- - k x] 195658588125 E Cos[-- - k x] 65219529375 E Cos[-- - k x] 195658588125 E Cos[-- - k x] 39131717625 E Cos[-- - k x] 13043905875 E Cos[-- - k x] 2401245 E Cos[-- - k x] 7203735 E Cos[-- - k x] 36018675 E Cos[-- - k x] 12006225 E Cos[-- - k x] 36018675 E Cos[-- - k x] 7203735 E Cos[-- - k x] 2401245 E Cos[-- - k x] 3675 E Cos[-- - k x] 11025 E Cos[-- - k x] 55125 E Cos[-- - k x] 18375 E Cos[-- - k x] 55125 E Cos[-- - k x] 11025 E Cos[-- - k x] 3675 E Cos[-- - k x] 9 E Cos[-- - k x] 27 E Cos[-- - k x] 135 E Cos[-- - k x] 45 E Cos[-- - k x] 135 E Cos[-- - k x] 27 E Cos[-- - k x] 9 E Cos[-- - k x] E Sqrt[--] Cos[-- - k x] 6 E Sqrt[--] Cos[-- - k x] 15 E Sqrt[--] Cos[-- - k x] 20 E Sqrt[--] Cos[-- - k x] 15 E Sqrt[--] Cos[-- - k x] 6 E Sqrt[--] Cos[-- - k x] E Sqrt[--] Cos[-- - k x] 418854310875 E Sin[-- - k x] 1256562932625 E Sin[-- - k x] 6282814663125 E Sin[-- - k x] 2094271554375 E Sin[-- - k x] 6282814663125 E Sin[-- - k x] 1256562932625 E Sin[-- - k x] 418854310875 E Sin[-- - k x] 57972915 E Sin[-- - k x] 173918745 E Sin[-- - k x] 869593725 E Sin[-- - k x] 289864575 E Sin[-- - k x] 869593725 E Sin[-- - k x] 173918745 E Sin[-- - k x] 57972915 E Sin[-- - k x] 59535 E Sin[-- - k x] 178605 E Sin[-- - k x] 893025 E Sin[-- - k x] 297675 E Sin[-- - k x] 893025 E Sin[-- - k x] 178605 E Sin[-- - k x] 59535 E Sin[-- - k x] 75 E Sin[-- - k x] 225 E Sin[-- - k x] 1125 E Sin[-- - k x] 375 E Sin[-- - k x] 1125 E Sin[-- - k x] 225 E Sin[-- - k x] 75 E Sin[-- - k x] E Sin[-- - k x] 3 E Sin[-- - k x] 15 E Sin[-- - k x] 5 E Sin[-- - k x] 15 E Sin[-- - k x] 3 E Sin[-- - k x] E Sin[-- - k x] - 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 Pi 4 Pi 4 Pi 4 Pi 4 Pi 4 Pi 4 Pi 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 -Integrate::idiv: Integral of ------------------------------------------ - ------------------------------------------ + ------------------------------------------- - ------------------------------------------ + ------------------------------------------- - ------------------------------------------ + ------------------------------------------ - -------------------------------------- + -------------------------------------- - --------------------------------------- + --------------------------------------- - --------------------------------------- + -------------------------------------- - -------------------------------------- + ----------------------------------- - ------------------------------------ + ------------------------------------ - ------------------------------------ + ------------------------------------ - ------------------------------------ + ----------------------------------- - -------------------------------- + --------------------------------- - ---------------------------------- + --------------------------------- - ---------------------------------- + --------------------------------- - -------------------------------- + --------------------------------------- - ----------------------------------------- + ------------------------------------------ - ------------------------------------------ + ------------------------------------------ - ----------------------------------------- + --------------------------------------- - ------------------------------------------- + -------------------------------------------- - -------------------------------------------- + -------------------------------------------- - -------------------------------------------- + -------------------------------------------- - ------------------------------------------- + --------------------------------------- - ---------------------------------------- + ---------------------------------------- - ---------------------------------------- + ---------------------------------------- - ---------------------------------------- + --------------------------------------- - ------------------------------------ + ------------------------------------- - ------------------------------------- + ------------------------------------- - ------------------------------------- + ------------------------------------- - ------------------------------------ + --------------------------------- - ---------------------------------- + ----------------------------------- - ---------------------------------- + ----------------------------------- - ---------------------------------- + --------------------------------- - ------------------------------ + -------------------------------- - --------------------------------- + -------------------------------- - --------------------------------- + -------------------------------- - ------------------------------ does not converge on {0, Infinity}. - 17/2 4 23/2 17/2 4 23/2 17/2 4 23/2 17/2 4 23/2 17/2 4 23/2 17/2 4 23/2 17/2 4 23/2 13/2 4 19/2 13/2 4 19/2 13/2 4 19/2 13/2 4 19/2 13/2 4 19/2 13/2 4 19/2 13/2 4 19/2 9/2 4 15/2 9/2 4 15/2 9/2 4 15/2 9/2 4 15/2 9/2 4 15/2 9/2 4 15/2 9/2 4 15/2 5/2 4 11/2 5/2 4 11/2 5/2 4 11/2 5/2 4 11/2 5/2 4 11/2 5/2 4 11/2 5/2 4 11/2 4 7/2 4 7/2 4 7/2 4 7/2 4 7/2 4 7/2 4 7/2 19/2 4 25/2 19/2 4 25/2 19/2 4 25/2 19/2 4 25/2 19/2 4 25/2 19/2 4 25/2 19/2 4 25/2 15/2 4 21/2 15/2 4 21/2 15/2 4 21/2 15/2 4 21/2 15/2 4 21/2 15/2 4 21/2 15/2 4 21/2 11/2 4 17/2 11/2 4 17/2 11/2 4 17/2 11/2 4 17/2 11/2 4 17/2 11/2 4 17/2 11/2 4 17/2 7/2 4 13/2 7/2 4 13/2 7/2 4 13/2 7/2 4 13/2 7/2 4 13/2 7/2 4 13/2 7/2 4 13/2 3/2 4 9/2 3/2 4 9/2 3/2 4 9/2 3/2 4 9/2 3/2 4 9/2 3/2 4 9/2 3/2 4 9/2 - 1073741824 k k0 Sqrt[2 Pi] x 536870912 k k0 Sqrt[2 Pi] x 1073741824 k k0 Sqrt[2 Pi] x 268435456 k k0 Sqrt[2 Pi] x 1073741824 k k0 Sqrt[2 Pi] x 536870912 k k0 Sqrt[2 Pi] x 1073741824 k k0 Sqrt[2 Pi] x 2097152 k k0 Sqrt[2 Pi] x 1048576 k k0 Sqrt[2 Pi] x 2097152 k k0 Sqrt[2 Pi] x 524288 k k0 Sqrt[2 Pi] x 2097152 k k0 Sqrt[2 Pi] x 1048576 k k0 Sqrt[2 Pi] x 2097152 k k0 Sqrt[2 Pi] x 16384 k k0 Sqrt[2 Pi] x 8192 k k0 Sqrt[2 Pi] x 16384 k k0 Sqrt[2 Pi] x 4096 k k0 Sqrt[2 Pi] x 16384 k k0 Sqrt[2 Pi] x 8192 k k0 Sqrt[2 Pi] x 16384 k k0 Sqrt[2 Pi] x 64 k k0 Sqrt[2 Pi] x 32 k k0 Sqrt[2 Pi] x 64 k k0 Sqrt[2 Pi] x 16 k k0 Sqrt[2 Pi] x 64 k k0 Sqrt[2 Pi] x 32 k k0 Sqrt[2 Pi] x 64 k k0 Sqrt[2 Pi] x Sqrt[k] k0 x Sqrt[k] k0 x Sqrt[k] k0 x Sqrt[k] k0 x Sqrt[k] k0 x Sqrt[k] k0 x Sqrt[k] k0 x 8589934592 k k0 Sqrt[2 Pi] x 4294967296 k k0 Sqrt[2 Pi] x 8589934592 k k0 Sqrt[2 Pi] x 2147483648 k k0 Sqrt[2 Pi] x 8589934592 k k0 Sqrt[2 Pi] x 4294967296 k k0 Sqrt[2 Pi] x 8589934592 k k0 Sqrt[2 Pi] x 16777216 k k0 Sqrt[2 Pi] x 8388608 k k0 Sqrt[2 Pi] x 16777216 k k0 Sqrt[2 Pi] x 4194304 k k0 Sqrt[2 Pi] x 16777216 k k0 Sqrt[2 Pi] x 8388608 k k0 Sqrt[2 Pi] x 16777216 k k0 Sqrt[2 Pi] x 131072 k k0 Sqrt[2 Pi] x 65536 k k0 Sqrt[2 Pi] x 131072 k k0 Sqrt[2 Pi] x 32768 k k0 Sqrt[2 Pi] x 131072 k k0 Sqrt[2 Pi] x 65536 k k0 Sqrt[2 Pi] x 131072 k k0 Sqrt[2 Pi] x 512 k k0 Sqrt[2 Pi] x 256 k k0 Sqrt[2 Pi] x 512 k k0 Sqrt[2 Pi] x 128 k k0 Sqrt[2 Pi] x 512 k k0 Sqrt[2 Pi] x 256 k k0 Sqrt[2 Pi] x 512 k k0 Sqrt[2 Pi] x 4 k k0 Sqrt[2 Pi] x 2 k k0 Sqrt[2 Pi] x 4 k k0 Sqrt[2 Pi] x k k0 Sqrt[2 Pi] x 4 k k0 Sqrt[2 Pi] x 2 k k0 Sqrt[2 Pi] x 4 k k0 Sqrt[2 Pi] x -Series[Integrate[(E^(-(c*x) + I*k0*x)*(1 - E^(-(c*x)))^6*BesselJ[0, k*x])/(k0^4*x^3), {x, 0, Infinity}, Assumptions -> n == 0 && q == 4 && κ == 6 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0], {k, Infinity, 10}] diff --git a/besseltransforms/6-4-1 b/besseltransforms/6-4-1 deleted file mode 100644 index d12b458..0000000 --- a/besseltransforms/6-4-1 +++ /dev/null @@ -1,9 +0,0 @@ -Integrate[(E^(-(c*x) + I*k0*x)*(1 - E^(-(c*x)))^6*BesselJ[1, k*x])/(k0^4*x^3), {x, 0, Infinity}, Assumptions -> n == 1 && q == 4 && κ == 6 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0] - - -7 c x + I k0 x c x 6 2 2 4 4 6 6 8 8 Pi 2 2 4 4 6 6 8 8 Pi - -(E (-1 + E ) (8 k x (-14783093325 + 1452971520 k x - 309657600 k x + 251658240 k x + 2147483648 k x ) Cos[-- + k x] - 3 (156043762875 - 11416204800 k x + 1589575680 k x - 587202560 k x + 2147483648 k x ) Sin[-- + k x])) - 4 4 -Integrate::idiv: Integral of ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ does not converge on {0, Infinity}. - 19/2 4 25/2 - 8589934592 k k0 Sqrt[2 Pi] x -Series[Integrate[(E^(-(c*x) + I*k0*x)*(1 - E^(-(c*x)))^6*BesselJ[1, k*x])/(k0^4*x^3), {x, 0, Infinity}, Assumptions -> n == 1 && q == 4 && κ == 6 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0], {k, Infinity, 10}] diff --git a/besseltransforms/6-4-2 b/besseltransforms/6-4-2 deleted file mode 100644 index 9dea599..0000000 --- a/besseltransforms/6-4-2 +++ /dev/null @@ -1,9 +0,0 @@ -Integrate[(E^(-(c*x) + I*k0*x)*(1 - E^(-(c*x)))^6*BesselJ[2, k*x])/(k0^4*x^3), {x, 0, Infinity}, Assumptions -> n == 2 && q == 4 && κ == 6 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0] - - -7 c x + I k0 x Pi -6 c x + I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi -7 c x + I k0 x Pi -6 c x + I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi -7 c x + I k0 x Pi -6 c x + I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi -7 c x + I k0 x Pi -6 c x + I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi -7 c x + I k0 x 2 Pi -6 c x + I k0 x 2 Pi -5 c x + I k0 x 2 Pi -4 c x + I k0 x 2 Pi -3 c x + I k0 x 2 Pi -2 c x + I k0 x 2 Pi -(c x) + I k0 x 2 Pi -7 c x + I k0 x Pi -6 c x + I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi -7 c x + I k0 x Pi -6 c x + I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi -7 c x + I k0 x Pi -6 c x + I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi -7 c x + I k0 x Pi -6 c x + I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi -7 c x + I k0 x Pi -6 c x + I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi - -21606059475 E Cos[-- - k x] 64818178425 E Cos[-- - k x] 324090892125 E Cos[-- - k x] 108030297375 E Cos[-- - k x] 324090892125 E Cos[-- - k x] 64818178425 E Cos[-- - k x] 21606059475 E Cos[-- - k x] 4729725 E Cos[-- - k x] 14189175 E Cos[-- - k x] 70945875 E Cos[-- - k x] 23648625 E Cos[-- - k x] 70945875 E Cos[-- - k x] 14189175 E Cos[-- - k x] 4729725 E Cos[-- - k x] 10395 E Cos[-- - k x] 31185 E Cos[-- - k x] 155925 E Cos[-- - k x] 51975 E Cos[-- - k x] 155925 E Cos[-- - k x] 31185 E Cos[-- - k x] 10395 E Cos[-- - k x] 105 E Cos[-- - k x] 315 E Cos[-- - k x] 1575 E Cos[-- - k x] 525 E Cos[-- - k x] 1575 E Cos[-- - k x] 315 E Cos[-- - k x] 105 E Cos[-- - k x] E Sqrt[--] Cos[-- - k x] 6 E Sqrt[--] Cos[-- - k x] 15 E Sqrt[--] Cos[-- - k x] 20 E Sqrt[--] Cos[-- - k x] 15 E Sqrt[--] Cos[-- - k x] 6 E Sqrt[--] Cos[-- - k x] E Sqrt[--] Cos[-- - k x] 655383804075 E Sin[-- - k x] 1966151412225 E Sin[-- - k x] 9830757061125 E Sin[-- - k x] 3276919020375 E Sin[-- - k x] 9830757061125 E Sin[-- - k x] 1966151412225 E Sin[-- - k x] 655383804075 E Sin[-- - k x] 103378275 E Sin[-- - k x] 310134825 E Sin[-- - k x] 1550674125 E Sin[-- - k x] 516891375 E Sin[-- - k x] 1550674125 E Sin[-- - k x] 310134825 E Sin[-- - k x] 103378275 E Sin[-- - k x] 135135 E Sin[-- - k x] 405405 E Sin[-- - k x] 2027025 E Sin[-- - k x] 675675 E Sin[-- - k x] 2027025 E Sin[-- - k x] 405405 E Sin[-- - k x] 135135 E Sin[-- - k x] 315 E Sin[-- - k x] 945 E Sin[-- - k x] 4725 E Sin[-- - k x] 1575 E Sin[-- - k x] 4725 E Sin[-- - k x] 945 E Sin[-- - k x] 315 E Sin[-- - k x] 15 E Sin[-- - k x] 45 E Sin[-- - k x] 225 E Sin[-- - k x] 75 E Sin[-- - k x] 225 E Sin[-- - k x] 45 E Sin[-- - k x] 15 E Sin[-- - k x] - 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 Pi 4 Pi 4 Pi 4 Pi 4 Pi 4 Pi 4 Pi 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 -Integrate::idiv: Integral of ------------------------------------------- + ------------------------------------------ - ------------------------------------------- + ------------------------------------------- - ------------------------------------------- + ------------------------------------------ - ------------------------------------------ + -------------------------------------- - --------------------------------------- + --------------------------------------- - --------------------------------------- + --------------------------------------- - --------------------------------------- + -------------------------------------- - ------------------------------------ + ------------------------------------ - ------------------------------------- + ------------------------------------ - ------------------------------------- + ------------------------------------ - ------------------------------------ + ---------------------------------- - ---------------------------------- + ----------------------------------- - ---------------------------------- + ----------------------------------- - ---------------------------------- + ---------------------------------- - --------------------------------------- + ----------------------------------------- - ------------------------------------------ + ------------------------------------------ - ------------------------------------------ + ----------------------------------------- - --------------------------------------- + ------------------------------------------- - -------------------------------------------- + -------------------------------------------- - -------------------------------------------- + -------------------------------------------- - -------------------------------------------- + ------------------------------------------- - ---------------------------------------- + ---------------------------------------- - ----------------------------------------- + ---------------------------------------- - ----------------------------------------- + ---------------------------------------- - ---------------------------------------- + ------------------------------------- - ------------------------------------- + -------------------------------------- - ------------------------------------- + -------------------------------------- - ------------------------------------- + ------------------------------------- - ---------------------------------- + ---------------------------------- - ----------------------------------- + ----------------------------------- - ----------------------------------- + ---------------------------------- - ---------------------------------- - --------------------------------- + --------------------------------- - ---------------------------------- + --------------------------------- - ---------------------------------- + --------------------------------- - --------------------------------- does not converge on {0, Infinity}. - 17/2 4 23/2 17/2 4 23/2 17/2 4 23/2 17/2 4 23/2 17/2 4 23/2 17/2 4 23/2 17/2 4 23/2 13/2 4 19/2 13/2 4 19/2 13/2 4 19/2 13/2 4 19/2 13/2 4 19/2 13/2 4 19/2 13/2 4 19/2 9/2 4 15/2 9/2 4 15/2 9/2 4 15/2 9/2 4 15/2 9/2 4 15/2 9/2 4 15/2 9/2 4 15/2 5/2 4 11/2 5/2 4 11/2 5/2 4 11/2 5/2 4 11/2 5/2 4 11/2 5/2 4 11/2 5/2 4 11/2 4 7/2 4 7/2 4 7/2 4 7/2 4 7/2 4 7/2 4 7/2 19/2 4 25/2 19/2 4 25/2 19/2 4 25/2 19/2 4 25/2 19/2 4 25/2 19/2 4 25/2 19/2 4 25/2 15/2 4 21/2 15/2 4 21/2 15/2 4 21/2 15/2 4 21/2 15/2 4 21/2 15/2 4 21/2 15/2 4 21/2 11/2 4 17/2 11/2 4 17/2 11/2 4 17/2 11/2 4 17/2 11/2 4 17/2 11/2 4 17/2 11/2 4 17/2 7/2 4 13/2 7/2 4 13/2 7/2 4 13/2 7/2 4 13/2 7/2 4 13/2 7/2 4 13/2 7/2 4 13/2 3/2 4 9/2 3/2 4 9/2 3/2 4 9/2 3/2 4 9/2 3/2 4 9/2 3/2 4 9/2 3/2 4 9/2 - 1073741824 k k0 Sqrt[2 Pi] x 536870912 k k0 Sqrt[2 Pi] x 1073741824 k k0 Sqrt[2 Pi] x 268435456 k k0 Sqrt[2 Pi] x 1073741824 k k0 Sqrt[2 Pi] x 536870912 k k0 Sqrt[2 Pi] x 1073741824 k k0 Sqrt[2 Pi] x 2097152 k k0 Sqrt[2 Pi] x 1048576 k k0 Sqrt[2 Pi] x 2097152 k k0 Sqrt[2 Pi] x 524288 k k0 Sqrt[2 Pi] x 2097152 k k0 Sqrt[2 Pi] x 1048576 k k0 Sqrt[2 Pi] x 2097152 k k0 Sqrt[2 Pi] x 16384 k k0 Sqrt[2 Pi] x 8192 k k0 Sqrt[2 Pi] x 16384 k k0 Sqrt[2 Pi] x 4096 k k0 Sqrt[2 Pi] x 16384 k k0 Sqrt[2 Pi] x 8192 k k0 Sqrt[2 Pi] x 16384 k k0 Sqrt[2 Pi] x 64 k k0 Sqrt[2 Pi] x 32 k k0 Sqrt[2 Pi] x 64 k k0 Sqrt[2 Pi] x 16 k k0 Sqrt[2 Pi] x 64 k k0 Sqrt[2 Pi] x 32 k k0 Sqrt[2 Pi] x 64 k k0 Sqrt[2 Pi] x Sqrt[k] k0 x Sqrt[k] k0 x Sqrt[k] k0 x Sqrt[k] k0 x Sqrt[k] k0 x Sqrt[k] k0 x Sqrt[k] k0 x 8589934592 k k0 Sqrt[2 Pi] x 4294967296 k k0 Sqrt[2 Pi] x 8589934592 k k0 Sqrt[2 Pi] x 2147483648 k k0 Sqrt[2 Pi] x 8589934592 k k0 Sqrt[2 Pi] x 4294967296 k k0 Sqrt[2 Pi] x 8589934592 k k0 Sqrt[2 Pi] x 16777216 k k0 Sqrt[2 Pi] x 8388608 k k0 Sqrt[2 Pi] x 16777216 k k0 Sqrt[2 Pi] x 4194304 k k0 Sqrt[2 Pi] x 16777216 k k0 Sqrt[2 Pi] x 8388608 k k0 Sqrt[2 Pi] x 16777216 k k0 Sqrt[2 Pi] x 131072 k k0 Sqrt[2 Pi] x 65536 k k0 Sqrt[2 Pi] x 131072 k k0 Sqrt[2 Pi] x 32768 k k0 Sqrt[2 Pi] x 131072 k k0 Sqrt[2 Pi] x 65536 k k0 Sqrt[2 Pi] x 131072 k k0 Sqrt[2 Pi] x 512 k k0 Sqrt[2 Pi] x 256 k k0 Sqrt[2 Pi] x 512 k k0 Sqrt[2 Pi] x 128 k k0 Sqrt[2 Pi] x 512 k k0 Sqrt[2 Pi] x 256 k k0 Sqrt[2 Pi] x 512 k k0 Sqrt[2 Pi] x 4 k k0 Sqrt[2 Pi] x 2 k k0 Sqrt[2 Pi] x 4 k k0 Sqrt[2 Pi] x k k0 Sqrt[2 Pi] x 4 k k0 Sqrt[2 Pi] x 2 k k0 Sqrt[2 Pi] x 4 k k0 Sqrt[2 Pi] x -Series[Integrate[(E^(-(c*x) + I*k0*x)*(1 - E^(-(c*x)))^6*BesselJ[2, k*x])/(k0^4*x^3), {x, 0, Infinity}, Assumptions -> n == 2 && q == 4 && κ == 6 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0], {k, Infinity, 10}] diff --git a/besseltransforms/6-4-3 b/besseltransforms/6-4-3 deleted file mode 100644 index d520464..0000000 --- a/besseltransforms/6-4-3 +++ /dev/null @@ -1,2 +0,0 @@ -((k^4*(-15 + 8*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0) + 4*k^2*(-5 + 4*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^3 + 8*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^5)/(120*k^3) - (k^4*(-15 + 8*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0) + 4*k^2*(-5 + 4*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^3 + 8*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^5)/(20*k^3) + (k^4*(-15 + 8*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0) + 4*k^2*(-5 + 4*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^3 + 8*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^5)/(8*k^3) - (k^4*(-15 + 8*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0) + 4*k^2*(-5 + 4*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^3 + 8*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^5)/(6*k^3) + (k^4*(-15 + 8*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0) + 4*k^2*(-5 + 4*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^3 + 8*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^5)/(8*k^3) - (k^4*(-15 + 8*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0) + 4*k^2*(-5 + 4*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^3 + 8*(-1 + Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^5)/(20*k^3) + (k^4*(-15 + 8*Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0) + 4*k^2*(-5 + 4*Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^3 + 8*(-1 + Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^5)/(120*k^3))/k0^4 -SeriesData[k, Infinity, {(15*c^6)/k0^4, 0, (-105*(33*c^8 - (16*I)*c^7*k0 - 2*c^6*k0^2))/(4*k0^4), 0, (189*(3047*c^10 - (2800*I)*c^9*k0 - 990*c^8*k0^2 + (160*I)*c^7*k0^3 + 10*c^6*k0^4))/(16*k0^4), 0, (-165*(259792*c^12 - (342216*I)*c^11*k0 - 191961*c^10*k0^2 + (58800*I)*c^9*k0^3 + 10395*c^8*k0^4 - (1008*I)*c^7*k0^5 - 42*c^6*k0^6))/(32*k0^4)}, 4, 11, 1] diff --git a/besseltransforms/6-4-4 b/besseltransforms/6-4-4 deleted file mode 100644 index 367e6eb..0000000 --- a/besseltransforms/6-4-4 +++ /dev/null @@ -1,2 +0,0 @@ -((5*k^6 + 2*k^4*(15 - 8*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^2 + 8*k^2*(5 - 4*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^4 - 16*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^6)/(240*k^4) - (5*k^6 + 2*k^4*(15 - 8*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^2 + 8*k^2*(5 - 4*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^4 - 16*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^6)/(40*k^4) + (5*k^6 + 2*k^4*(15 - 8*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^2 + 8*k^2*(5 - 4*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^4 - 16*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^6)/(16*k^4) - (5*k^6 + 2*k^4*(15 - 8*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^2 + 8*k^2*(5 - 4*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^4 - 16*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^6)/(12*k^4) + (5*k^6 + 2*k^4*(15 - 8*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^2 + 8*k^2*(5 - 4*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^4 - 16*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^6)/(16*k^4) - (5*k^6 + 2*k^4*(15 - 8*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^2 + 8*k^2*(5 - 4*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^4 - 16*(-1 + Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^6)/(40*k^4) + (5*k^6 + 2*k^4*(15 - 8*Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^2 + 8*k^2*(5 - 4*Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^4 - 16*(-1 + Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^6)/(240*k^4))/k0^4 -SeriesData[k, Infinity, {(48*c^6)/k0^4, (-420*c^7)/k0^4 + ((105*I)*c^6)/k0^3, 0, (315*(140*c^9 - (99*I)*c^8*k0 - 24*c^7*k0^2 + (2*I)*c^6*k0^3))/(4*k0^4), 0, (-2079*(2716*c^11 - (3047*I)*c^10*k0 - 1400*c^9*k0^2 + (330*I)*c^8*k0^3 + 40*c^7*k0^4 - (2*I)*c^6*k0^5))/(16*k0^4)}, 4, 11, 1] diff --git a/besseltransforms/6-4-5 b/besseltransforms/6-4-5 deleted file mode 100644 index 2b982d5..0000000 --- a/besseltransforms/6-4-5 +++ /dev/null @@ -1,2 +0,0 @@ -((k^6*(-35 + 8*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0) + 20*k^4*(-7 + 4*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^3 + 8*k^2*(-21 + 17*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^5 + 64*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^7)/(840*k^5) - (k^6*(-35 + 8*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0) + 20*k^4*(-7 + 4*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^3 + 8*k^2*(-21 + 17*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^5 + 64*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^7)/(140*k^5) + (k^6*(-35 + 8*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0) + 20*k^4*(-7 + 4*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^3 + 8*k^2*(-21 + 17*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^5 + 64*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^7)/(56*k^5) - (k^6*(-35 + 8*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0) + 20*k^4*(-7 + 4*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^3 + 8*k^2*(-21 + 17*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^5 + 64*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^7)/(42*k^5) + (k^6*(-35 + 8*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0) + 20*k^4*(-7 + 4*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^3 + 8*k^2*(-21 + 17*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^5 + 64*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^7)/(56*k^5) - (k^6*(-35 + 8*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0) + 20*k^4*(-7 + 4*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^3 + 8*k^2*(-21 + 17*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^5 + 64*(-1 + Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^7)/(140*k^5) + (k^6*(-35 + 8*Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0) + 20*k^4*(-7 + 4*Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^3 + 8*k^2*(-21 + 17*Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^5 + 64*(-1 + Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^7)/(840*k^5))/k0^4 -SeriesData[k, Infinity, {(105*c^6)/k0^4, (-1536*c^7)/k0^4 + ((384*I)*c^6)/k0^3, (945*(33*c^8 - (16*I)*c^7*k0 - 2*c^6*k0^2))/(4*k0^4), 0, (-693*(3047*c^10 - (2800*I)*c^9*k0 - 990*c^8*k0^2 + (160*I)*c^7*k0^3 + 10*c^6*k0^4))/(16*k0^4), 0, (429*(259792*c^12 - (342216*I)*c^11*k0 - 191961*c^10*k0^2 + (58800*I)*c^9*k0^3 + 10395*c^8*k0^4 - (1008*I)*c^7*k0^5 - 42*c^6*k0^6))/(32*k0^4)}, 4, 11, 1] diff --git a/besseltransforms/6-4-6 b/besseltransforms/6-4-6 deleted file mode 100644 index ed31408..0000000 --- a/besseltransforms/6-4-6 +++ /dev/null @@ -1,2 +0,0 @@ -((35*k^8 + 16*k^6*(35 - 12*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^2 + 16*k^4*(105 - 64*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^4 + 64*k^2*(28 - 23*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^6 - 640*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^8)/(6720*k^6) - (35*k^8 + 16*k^6*(35 - 12*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^2 + 16*k^4*(105 - 64*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^4 + 64*k^2*(28 - 23*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^6 - 640*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^8)/(1120*k^6) + (35*k^8 + 16*k^6*(35 - 12*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^2 + 16*k^4*(105 - 64*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^4 + 64*k^2*(28 - 23*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^6 - 640*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^8)/(448*k^6) - (35*k^8 + 16*k^6*(35 - 12*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^2 + 16*k^4*(105 - 64*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^4 + 64*k^2*(28 - 23*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^6 - 640*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^8)/(336*k^6) + (35*k^8 + 16*k^6*(35 - 12*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^2 + 16*k^4*(105 - 64*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^4 + 64*k^2*(28 - 23*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^6 - 640*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^8)/(448*k^6) - (35*k^8 + 16*k^6*(35 - 12*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^2 + 16*k^4*(105 - 64*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^4 + 64*k^2*(28 - 23*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^6 - 640*(-1 + Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^8)/(1120*k^6) + (35*k^8 + 16*k^6*(35 - 12*Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^2 + 16*k^4*(105 - 64*Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^4 + 64*k^2*(28 - 23*Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^6 - 640*(-1 + Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^8)/(6720*k^6))/k0^4 -SeriesData[k, Infinity, {(192*c^6)/k0^4, (-3780*c^7)/k0^4 + ((945*I)*c^6)/k0^3, (31680*c^8)/k0^4 - ((15360*I)*c^7)/k0^3 - (1920*c^6)/k0^2, (-3465*(140*c^9 - (99*I)*c^8*k0 - 24*c^7*k0^2 + (2*I)*c^6*k0^3))/(4*k0^4), 0, (9009*(2716*c^11 - (3047*I)*c^10*k0 - 1400*c^9*k0^2 + (330*I)*c^8*k0^3 + 40*c^7*k0^4 - (2*I)*c^6*k0^5))/(16*k0^4)}, 4, 11, 1] diff --git a/besseltransforms/6-4-7 b/besseltransforms/6-4-7 deleted file mode 100644 index f9a4830..0000000 --- a/besseltransforms/6-4-7 +++ /dev/null @@ -1,2 +0,0 @@ -((k^8*(-105 + 16*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0) + 8*k^6*(-105 + 44*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^3 + 144*k^4*(-14 + 9*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^5 + 320*k^2*(-6 + 5*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^7 + 640*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^9)/(5040*k^7) - (k^8*(-105 + 16*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0) + 8*k^6*(-105 + 44*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^3 + 144*k^4*(-14 + 9*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^5 + 320*k^2*(-6 + 5*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^7 + 640*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^9)/(840*k^7) + (k^8*(-105 + 16*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0) + 8*k^6*(-105 + 44*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^3 + 144*k^4*(-14 + 9*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^5 + 320*k^2*(-6 + 5*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^7 + 640*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^9)/(336*k^7) - (k^8*(-105 + 16*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0) + 8*k^6*(-105 + 44*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^3 + 144*k^4*(-14 + 9*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^5 + 320*k^2*(-6 + 5*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^7 + 640*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^9)/(252*k^7) + (k^8*(-105 + 16*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0) + 8*k^6*(-105 + 44*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^3 + 144*k^4*(-14 + 9*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^5 + 320*k^2*(-6 + 5*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^7 + 640*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^9)/(336*k^7) - (k^8*(-105 + 16*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0) + 8*k^6*(-105 + 44*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^3 + 144*k^4*(-14 + 9*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^5 + 320*k^2*(-6 + 5*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^7 + 640*(-1 + Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^9)/(840*k^7) + (k^8*(-105 + 16*Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0) + 8*k^6*(-105 + 44*Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^3 + 144*k^4*(-14 + 9*Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^5 + 320*k^2*(-6 + 5*Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^7 + 640*(-1 + Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^9)/(5040*k^7))/k0^4 -SeriesData[k, Infinity, {(315*c^6)/k0^4, (-7680*c^7)/k0^4 + ((1920*I)*c^6)/k0^3, (10395*(33*c^8 - (16*I)*c^7*k0 - 2*c^6*k0^2))/(4*k0^4), (-537600*c^9)/k0^4 + ((380160*I)*c^8)/k0^3 + (92160*c^7)/k0^2 - ((7680*I)*c^6)/k0, (9009*(3047*c^10 - (2800*I)*c^9*k0 - 990*c^8*k0^2 + (160*I)*c^7*k0^3 + 10*c^6*k0^4))/(16*k0^4), 0, (-2145*(259792*c^12 - (342216*I)*c^11*k0 - 191961*c^10*k0^2 + (58800*I)*c^9*k0^3 + 10395*c^8*k0^4 - (1008*I)*c^7*k0^5 - 42*c^6*k0^6))/(32*k0^4)}, 4, 11, 1] diff --git a/besseltransforms/6-5-0 b/besseltransforms/6-5-0 deleted file mode 100644 index 4116622..0000000 --- a/besseltransforms/6-5-0 +++ /dev/null @@ -1,9 +0,0 @@ -Integrate[(E^(-(c*x) + I*k0*x)*(1 - E^(-(c*x)))^6*BesselJ[0, k*x])/(k0^5*x^4), {x, 0, Infinity}, Assumptions -> n == 0 && q == 5 && κ == 6 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0] - - -7 c x + I k0 x Pi -6 c x + I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi -7 c x + I k0 x Pi -6 c x + I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi -7 c x + I k0 x Pi -6 c x + I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi -7 c x + I k0 x Pi -6 c x + I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi -7 c x + I k0 x 2 Pi -6 c x + I k0 x 2 Pi -5 c x + I k0 x 2 Pi -4 c x + I k0 x 2 Pi -3 c x + I k0 x 2 Pi -2 c x + I k0 x 2 Pi -(c x) + I k0 x 2 Pi -7 c x + I k0 x Pi -6 c x + I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi -7 c x + I k0 x Pi -6 c x + I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi -7 c x + I k0 x Pi -6 c x + I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi -7 c x + I k0 x Pi -6 c x + I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi -7 c x + I k0 x Pi -6 c x + I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi - 13043905875 E Cos[-- - k x] 39131717625 E Cos[-- - k x] 195658588125 E Cos[-- - k x] 65219529375 E Cos[-- - k x] 195658588125 E Cos[-- - k x] 39131717625 E Cos[-- - k x] 13043905875 E Cos[-- - k x] 2401245 E Cos[-- - k x] 7203735 E Cos[-- - k x] 36018675 E Cos[-- - k x] 12006225 E Cos[-- - k x] 36018675 E Cos[-- - k x] 7203735 E Cos[-- - k x] 2401245 E Cos[-- - k x] 3675 E Cos[-- - k x] 11025 E Cos[-- - k x] 55125 E Cos[-- - k x] 18375 E Cos[-- - k x] 55125 E Cos[-- - k x] 11025 E Cos[-- - k x] 3675 E Cos[-- - k x] 9 E Cos[-- - k x] 27 E Cos[-- - k x] 135 E Cos[-- - k x] 45 E Cos[-- - k x] 135 E Cos[-- - k x] 27 E Cos[-- - k x] 9 E Cos[-- - k x] E Sqrt[--] Cos[-- - k x] 6 E Sqrt[--] Cos[-- - k x] 15 E Sqrt[--] Cos[-- - k x] 20 E Sqrt[--] Cos[-- - k x] 15 E Sqrt[--] Cos[-- - k x] 6 E Sqrt[--] Cos[-- - k x] E Sqrt[--] Cos[-- - k x] 418854310875 E Sin[-- - k x] 1256562932625 E Sin[-- - k x] 6282814663125 E Sin[-- - k x] 2094271554375 E Sin[-- - k x] 6282814663125 E Sin[-- - k x] 1256562932625 E Sin[-- - k x] 418854310875 E Sin[-- - k x] 57972915 E Sin[-- - k x] 173918745 E Sin[-- - k x] 869593725 E Sin[-- - k x] 289864575 E Sin[-- - k x] 869593725 E Sin[-- - k x] 173918745 E Sin[-- - k x] 57972915 E Sin[-- - k x] 59535 E Sin[-- - k x] 178605 E Sin[-- - k x] 893025 E Sin[-- - k x] 297675 E Sin[-- - k x] 893025 E Sin[-- - k x] 178605 E Sin[-- - k x] 59535 E Sin[-- - k x] 75 E Sin[-- - k x] 225 E Sin[-- - k x] 1125 E Sin[-- - k x] 375 E Sin[-- - k x] 1125 E Sin[-- - k x] 225 E Sin[-- - k x] 75 E Sin[-- - k x] E Sin[-- - k x] 3 E Sin[-- - k x] 15 E Sin[-- - k x] 5 E Sin[-- - k x] 15 E Sin[-- - k x] 3 E Sin[-- - k x] E Sin[-- - k x] - 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 Pi 4 Pi 4 Pi 4 Pi 4 Pi 4 Pi 4 Pi 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 -Integrate::idiv: Integral of ------------------------------------------ - ------------------------------------------ + ------------------------------------------- - ------------------------------------------ + ------------------------------------------- - ------------------------------------------ + ------------------------------------------ - -------------------------------------- + -------------------------------------- - --------------------------------------- + --------------------------------------- - --------------------------------------- + -------------------------------------- - -------------------------------------- + ----------------------------------- - ------------------------------------ + ------------------------------------ - ------------------------------------ + ------------------------------------ - ------------------------------------ + ----------------------------------- - -------------------------------- + --------------------------------- - ---------------------------------- + --------------------------------- - ---------------------------------- + --------------------------------- - -------------------------------- + --------------------------------------- - ----------------------------------------- + ------------------------------------------ - ------------------------------------------ + ------------------------------------------ - ----------------------------------------- + --------------------------------------- - ------------------------------------------- + -------------------------------------------- - -------------------------------------------- + -------------------------------------------- - -------------------------------------------- + -------------------------------------------- - ------------------------------------------- + --------------------------------------- - ---------------------------------------- + ---------------------------------------- - ---------------------------------------- + ---------------------------------------- - ---------------------------------------- + --------------------------------------- - ------------------------------------ + ------------------------------------- - ------------------------------------- + ------------------------------------- - ------------------------------------- + ------------------------------------- - ------------------------------------ + --------------------------------- - ---------------------------------- + ----------------------------------- - ---------------------------------- + ----------------------------------- - ---------------------------------- + --------------------------------- - ------------------------------ + -------------------------------- - --------------------------------- + -------------------------------- - --------------------------------- + -------------------------------- - ------------------------------ does not converge on {0, Infinity}. - 17/2 5 25/2 17/2 5 25/2 17/2 5 25/2 17/2 5 25/2 17/2 5 25/2 17/2 5 25/2 17/2 5 25/2 13/2 5 21/2 13/2 5 21/2 13/2 5 21/2 13/2 5 21/2 13/2 5 21/2 13/2 5 21/2 13/2 5 21/2 9/2 5 17/2 9/2 5 17/2 9/2 5 17/2 9/2 5 17/2 9/2 5 17/2 9/2 5 17/2 9/2 5 17/2 5/2 5 13/2 5/2 5 13/2 5/2 5 13/2 5/2 5 13/2 5/2 5 13/2 5/2 5 13/2 5/2 5 13/2 5 9/2 5 9/2 5 9/2 5 9/2 5 9/2 5 9/2 5 9/2 19/2 5 27/2 19/2 5 27/2 19/2 5 27/2 19/2 5 27/2 19/2 5 27/2 19/2 5 27/2 19/2 5 27/2 15/2 5 23/2 15/2 5 23/2 15/2 5 23/2 15/2 5 23/2 15/2 5 23/2 15/2 5 23/2 15/2 5 23/2 11/2 5 19/2 11/2 5 19/2 11/2 5 19/2 11/2 5 19/2 11/2 5 19/2 11/2 5 19/2 11/2 5 19/2 7/2 5 15/2 7/2 5 15/2 7/2 5 15/2 7/2 5 15/2 7/2 5 15/2 7/2 5 15/2 7/2 5 15/2 3/2 5 11/2 3/2 5 11/2 3/2 5 11/2 3/2 5 11/2 3/2 5 11/2 3/2 5 11/2 3/2 5 11/2 - 1073741824 k k0 Sqrt[2 Pi] x 536870912 k k0 Sqrt[2 Pi] x 1073741824 k k0 Sqrt[2 Pi] x 268435456 k k0 Sqrt[2 Pi] x 1073741824 k k0 Sqrt[2 Pi] x 536870912 k k0 Sqrt[2 Pi] x 1073741824 k k0 Sqrt[2 Pi] x 2097152 k k0 Sqrt[2 Pi] x 1048576 k k0 Sqrt[2 Pi] x 2097152 k k0 Sqrt[2 Pi] x 524288 k k0 Sqrt[2 Pi] x 2097152 k k0 Sqrt[2 Pi] x 1048576 k k0 Sqrt[2 Pi] x 2097152 k k0 Sqrt[2 Pi] x 16384 k k0 Sqrt[2 Pi] x 8192 k k0 Sqrt[2 Pi] x 16384 k k0 Sqrt[2 Pi] x 4096 k k0 Sqrt[2 Pi] x 16384 k k0 Sqrt[2 Pi] x 8192 k k0 Sqrt[2 Pi] x 16384 k k0 Sqrt[2 Pi] x 64 k k0 Sqrt[2 Pi] x 32 k k0 Sqrt[2 Pi] x 64 k k0 Sqrt[2 Pi] x 16 k k0 Sqrt[2 Pi] x 64 k k0 Sqrt[2 Pi] x 32 k k0 Sqrt[2 Pi] x 64 k k0 Sqrt[2 Pi] x Sqrt[k] k0 x Sqrt[k] k0 x Sqrt[k] k0 x Sqrt[k] k0 x Sqrt[k] k0 x Sqrt[k] k0 x Sqrt[k] k0 x 8589934592 k k0 Sqrt[2 Pi] x 4294967296 k k0 Sqrt[2 Pi] x 8589934592 k k0 Sqrt[2 Pi] x 2147483648 k k0 Sqrt[2 Pi] x 8589934592 k k0 Sqrt[2 Pi] x 4294967296 k k0 Sqrt[2 Pi] x 8589934592 k k0 Sqrt[2 Pi] x 16777216 k k0 Sqrt[2 Pi] x 8388608 k k0 Sqrt[2 Pi] x 16777216 k k0 Sqrt[2 Pi] x 4194304 k k0 Sqrt[2 Pi] x 16777216 k k0 Sqrt[2 Pi] x 8388608 k k0 Sqrt[2 Pi] x 16777216 k k0 Sqrt[2 Pi] x 131072 k k0 Sqrt[2 Pi] x 65536 k k0 Sqrt[2 Pi] x 131072 k k0 Sqrt[2 Pi] x 32768 k k0 Sqrt[2 Pi] x 131072 k k0 Sqrt[2 Pi] x 65536 k k0 Sqrt[2 Pi] x 131072 k k0 Sqrt[2 Pi] x 512 k k0 Sqrt[2 Pi] x 256 k k0 Sqrt[2 Pi] x 512 k k0 Sqrt[2 Pi] x 128 k k0 Sqrt[2 Pi] x 512 k k0 Sqrt[2 Pi] x 256 k k0 Sqrt[2 Pi] x 512 k k0 Sqrt[2 Pi] x 4 k k0 Sqrt[2 Pi] x 2 k k0 Sqrt[2 Pi] x 4 k k0 Sqrt[2 Pi] x k k0 Sqrt[2 Pi] x 4 k k0 Sqrt[2 Pi] x 2 k k0 Sqrt[2 Pi] x 4 k k0 Sqrt[2 Pi] x -Series[Integrate[(E^(-(c*x) + I*k0*x)*(1 - E^(-(c*x)))^6*BesselJ[0, k*x])/(k0^5*x^4), {x, 0, Infinity}, Assumptions -> n == 0 && q == 5 && κ == 6 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0], {k, Infinity, 10}] diff --git a/besseltransforms/6-5-1 b/besseltransforms/6-5-1 deleted file mode 100644 index 8e2366b..0000000 --- a/besseltransforms/6-5-1 +++ /dev/null @@ -1,9 +0,0 @@ -Integrate[(E^(-(c*x) + I*k0*x)*(1 - E^(-(c*x)))^6*BesselJ[1, k*x])/(k0^5*x^4), {x, 0, Infinity}, Assumptions -> n == 1 && q == 5 && κ == 6 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0] - - -7 c x + I k0 x c x 6 2 2 4 4 6 6 8 8 Pi 2 2 4 4 6 6 8 8 Pi - -(E (-1 + E ) (8 k x (-14783093325 + 1452971520 k x - 309657600 k x + 251658240 k x + 2147483648 k x ) Cos[-- + k x] - 3 (156043762875 - 11416204800 k x + 1589575680 k x - 587202560 k x + 2147483648 k x ) Sin[-- + k x])) - 4 4 -Integrate::idiv: Integral of ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ does not converge on {0, Infinity}. - 19/2 5 27/2 - 8589934592 k k0 Sqrt[2 Pi] x -Series[Integrate[(E^(-(c*x) + I*k0*x)*(1 - E^(-(c*x)))^6*BesselJ[1, k*x])/(k0^5*x^4), {x, 0, Infinity}, Assumptions -> n == 1 && q == 5 && κ == 6 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0], {k, Infinity, 10}] diff --git a/besseltransforms/6-5-2 b/besseltransforms/6-5-2 deleted file mode 100644 index be33b7d..0000000 --- a/besseltransforms/6-5-2 +++ /dev/null @@ -1,9 +0,0 @@ -Integrate[(E^(-(c*x) + I*k0*x)*(1 - E^(-(c*x)))^6*BesselJ[2, k*x])/(k0^5*x^4), {x, 0, Infinity}, Assumptions -> n == 2 && q == 5 && κ == 6 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0] - - -7 c x + I k0 x Pi -6 c x + I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi -7 c x + I k0 x Pi -6 c x + I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi -7 c x + I k0 x Pi -6 c x + I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi -7 c x + I k0 x Pi -6 c x + I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi -7 c x + I k0 x 2 Pi -6 c x + I k0 x 2 Pi -5 c x + I k0 x 2 Pi -4 c x + I k0 x 2 Pi -3 c x + I k0 x 2 Pi -2 c x + I k0 x 2 Pi -(c x) + I k0 x 2 Pi -7 c x + I k0 x Pi -6 c x + I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi -7 c x + I k0 x Pi -6 c x + I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi -7 c x + I k0 x Pi -6 c x + I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi -7 c x + I k0 x Pi -6 c x + I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi -7 c x + I k0 x Pi -6 c x + I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi - -21606059475 E Cos[-- - k x] 64818178425 E Cos[-- - k x] 324090892125 E Cos[-- - k x] 108030297375 E Cos[-- - k x] 324090892125 E Cos[-- - k x] 64818178425 E Cos[-- - k x] 21606059475 E Cos[-- - k x] 4729725 E Cos[-- - k x] 14189175 E Cos[-- - k x] 70945875 E Cos[-- - k x] 23648625 E Cos[-- - k x] 70945875 E Cos[-- - k x] 14189175 E Cos[-- - k x] 4729725 E Cos[-- - k x] 10395 E Cos[-- - k x] 31185 E Cos[-- - k x] 155925 E Cos[-- - k x] 51975 E Cos[-- - k x] 155925 E Cos[-- - k x] 31185 E Cos[-- - k x] 10395 E Cos[-- - k x] 105 E Cos[-- - k x] 315 E Cos[-- - k x] 1575 E Cos[-- - k x] 525 E Cos[-- - k x] 1575 E Cos[-- - k x] 315 E Cos[-- - k x] 105 E Cos[-- - k x] E Sqrt[--] Cos[-- - k x] 6 E Sqrt[--] Cos[-- - k x] 15 E Sqrt[--] Cos[-- - k x] 20 E Sqrt[--] Cos[-- - k x] 15 E Sqrt[--] Cos[-- - k x] 6 E Sqrt[--] Cos[-- - k x] E Sqrt[--] Cos[-- - k x] 655383804075 E Sin[-- - k x] 1966151412225 E Sin[-- - k x] 9830757061125 E Sin[-- - k x] 3276919020375 E Sin[-- - k x] 9830757061125 E Sin[-- - k x] 1966151412225 E Sin[-- - k x] 655383804075 E Sin[-- - k x] 103378275 E Sin[-- - k x] 310134825 E Sin[-- - k x] 1550674125 E Sin[-- - k x] 516891375 E Sin[-- - k x] 1550674125 E Sin[-- - k x] 310134825 E Sin[-- - k x] 103378275 E Sin[-- - k x] 135135 E Sin[-- - k x] 405405 E Sin[-- - k x] 2027025 E Sin[-- - k x] 675675 E Sin[-- - k x] 2027025 E Sin[-- - k x] 405405 E Sin[-- - k x] 135135 E Sin[-- - k x] 315 E Sin[-- - k x] 945 E Sin[-- - k x] 4725 E Sin[-- - k x] 1575 E Sin[-- - k x] 4725 E Sin[-- - k x] 945 E Sin[-- - k x] 315 E Sin[-- - k x] 15 E Sin[-- - k x] 45 E Sin[-- - k x] 225 E Sin[-- - k x] 75 E Sin[-- - k x] 225 E Sin[-- - k x] 45 E Sin[-- - k x] 15 E Sin[-- - k x] - 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 Pi 4 Pi 4 Pi 4 Pi 4 Pi 4 Pi 4 Pi 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 -Integrate::idiv: Integral of ------------------------------------------- + ------------------------------------------ - ------------------------------------------- + ------------------------------------------- - ------------------------------------------- + ------------------------------------------ - ------------------------------------------ + -------------------------------------- - --------------------------------------- + --------------------------------------- - --------------------------------------- + --------------------------------------- - --------------------------------------- + -------------------------------------- - ------------------------------------ + ------------------------------------ - ------------------------------------- + ------------------------------------ - ------------------------------------- + ------------------------------------ - ------------------------------------ + ---------------------------------- - ---------------------------------- + ----------------------------------- - ---------------------------------- + ----------------------------------- - ---------------------------------- + ---------------------------------- - --------------------------------------- + ----------------------------------------- - ------------------------------------------ + ------------------------------------------ - ------------------------------------------ + ----------------------------------------- - --------------------------------------- + ------------------------------------------- - -------------------------------------------- + -------------------------------------------- - -------------------------------------------- + -------------------------------------------- - -------------------------------------------- + ------------------------------------------- - ---------------------------------------- + ---------------------------------------- - ----------------------------------------- + ---------------------------------------- - ----------------------------------------- + ---------------------------------------- - ---------------------------------------- + ------------------------------------- - ------------------------------------- + -------------------------------------- - ------------------------------------- + -------------------------------------- - ------------------------------------- + ------------------------------------- - ---------------------------------- + ---------------------------------- - ----------------------------------- + ----------------------------------- - ----------------------------------- + ---------------------------------- - ---------------------------------- - --------------------------------- + --------------------------------- - ---------------------------------- + --------------------------------- - ---------------------------------- + --------------------------------- - --------------------------------- does not converge on {0, Infinity}. - 17/2 5 25/2 17/2 5 25/2 17/2 5 25/2 17/2 5 25/2 17/2 5 25/2 17/2 5 25/2 17/2 5 25/2 13/2 5 21/2 13/2 5 21/2 13/2 5 21/2 13/2 5 21/2 13/2 5 21/2 13/2 5 21/2 13/2 5 21/2 9/2 5 17/2 9/2 5 17/2 9/2 5 17/2 9/2 5 17/2 9/2 5 17/2 9/2 5 17/2 9/2 5 17/2 5/2 5 13/2 5/2 5 13/2 5/2 5 13/2 5/2 5 13/2 5/2 5 13/2 5/2 5 13/2 5/2 5 13/2 5 9/2 5 9/2 5 9/2 5 9/2 5 9/2 5 9/2 5 9/2 19/2 5 27/2 19/2 5 27/2 19/2 5 27/2 19/2 5 27/2 19/2 5 27/2 19/2 5 27/2 19/2 5 27/2 15/2 5 23/2 15/2 5 23/2 15/2 5 23/2 15/2 5 23/2 15/2 5 23/2 15/2 5 23/2 15/2 5 23/2 11/2 5 19/2 11/2 5 19/2 11/2 5 19/2 11/2 5 19/2 11/2 5 19/2 11/2 5 19/2 11/2 5 19/2 7/2 5 15/2 7/2 5 15/2 7/2 5 15/2 7/2 5 15/2 7/2 5 15/2 7/2 5 15/2 7/2 5 15/2 3/2 5 11/2 3/2 5 11/2 3/2 5 11/2 3/2 5 11/2 3/2 5 11/2 3/2 5 11/2 3/2 5 11/2 - 1073741824 k k0 Sqrt[2 Pi] x 536870912 k k0 Sqrt[2 Pi] x 1073741824 k k0 Sqrt[2 Pi] x 268435456 k k0 Sqrt[2 Pi] x 1073741824 k k0 Sqrt[2 Pi] x 536870912 k k0 Sqrt[2 Pi] x 1073741824 k k0 Sqrt[2 Pi] x 2097152 k k0 Sqrt[2 Pi] x 1048576 k k0 Sqrt[2 Pi] x 2097152 k k0 Sqrt[2 Pi] x 524288 k k0 Sqrt[2 Pi] x 2097152 k k0 Sqrt[2 Pi] x 1048576 k k0 Sqrt[2 Pi] x 2097152 k k0 Sqrt[2 Pi] x 16384 k k0 Sqrt[2 Pi] x 8192 k k0 Sqrt[2 Pi] x 16384 k k0 Sqrt[2 Pi] x 4096 k k0 Sqrt[2 Pi] x 16384 k k0 Sqrt[2 Pi] x 8192 k k0 Sqrt[2 Pi] x 16384 k k0 Sqrt[2 Pi] x 64 k k0 Sqrt[2 Pi] x 32 k k0 Sqrt[2 Pi] x 64 k k0 Sqrt[2 Pi] x 16 k k0 Sqrt[2 Pi] x 64 k k0 Sqrt[2 Pi] x 32 k k0 Sqrt[2 Pi] x 64 k k0 Sqrt[2 Pi] x Sqrt[k] k0 x Sqrt[k] k0 x Sqrt[k] k0 x Sqrt[k] k0 x Sqrt[k] k0 x Sqrt[k] k0 x Sqrt[k] k0 x 8589934592 k k0 Sqrt[2 Pi] x 4294967296 k k0 Sqrt[2 Pi] x 8589934592 k k0 Sqrt[2 Pi] x 2147483648 k k0 Sqrt[2 Pi] x 8589934592 k k0 Sqrt[2 Pi] x 4294967296 k k0 Sqrt[2 Pi] x 8589934592 k k0 Sqrt[2 Pi] x 16777216 k k0 Sqrt[2 Pi] x 8388608 k k0 Sqrt[2 Pi] x 16777216 k k0 Sqrt[2 Pi] x 4194304 k k0 Sqrt[2 Pi] x 16777216 k k0 Sqrt[2 Pi] x 8388608 k k0 Sqrt[2 Pi] x 16777216 k k0 Sqrt[2 Pi] x 131072 k k0 Sqrt[2 Pi] x 65536 k k0 Sqrt[2 Pi] x 131072 k k0 Sqrt[2 Pi] x 32768 k k0 Sqrt[2 Pi] x 131072 k k0 Sqrt[2 Pi] x 65536 k k0 Sqrt[2 Pi] x 131072 k k0 Sqrt[2 Pi] x 512 k k0 Sqrt[2 Pi] x 256 k k0 Sqrt[2 Pi] x 512 k k0 Sqrt[2 Pi] x 128 k k0 Sqrt[2 Pi] x 512 k k0 Sqrt[2 Pi] x 256 k k0 Sqrt[2 Pi] x 512 k k0 Sqrt[2 Pi] x 4 k k0 Sqrt[2 Pi] x 2 k k0 Sqrt[2 Pi] x 4 k k0 Sqrt[2 Pi] x k k0 Sqrt[2 Pi] x 4 k k0 Sqrt[2 Pi] x 2 k k0 Sqrt[2 Pi] x 4 k k0 Sqrt[2 Pi] x -Series[Integrate[(E^(-(c*x) + I*k0*x)*(1 - E^(-(c*x)))^6*BesselJ[2, k*x])/(k0^5*x^4), {x, 0, Infinity}, Assumptions -> n == 2 && q == 5 && κ == 6 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0], {k, Infinity, 10}] diff --git a/besseltransforms/6-5-3 b/besseltransforms/6-5-3 deleted file mode 100644 index 47f6455..0000000 --- a/besseltransforms/6-5-3 +++ /dev/null @@ -1,9 +0,0 @@ -Integrate[(E^(-(c*x) + I*k0*x)*(1 - E^(-(c*x)))^6*BesselJ[3, k*x])/(k0^5*x^4), {x, 0, Infinity}, Assumptions -> n == 3 && q == 5 && κ == 6 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0] - - -7 c x + I k0 x Pi -6 c x + I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi -7 c x + I k0 x Pi -6 c x + I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi -7 c x + I k0 x Pi -6 c x + I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi -7 c x + I k0 x Pi -6 c x + I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi -7 c x + I k0 x 2 Pi -6 c x + I k0 x 2 Pi -5 c x + I k0 x 2 Pi -4 c x + I k0 x 2 Pi -3 c x + I k0 x 2 Pi -2 c x + I k0 x 2 Pi -(c x) + I k0 x 2 Pi -7 c x + I k0 x Pi -6 c x + I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi -7 c x + I k0 x Pi -6 c x + I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi -7 c x + I k0 x Pi -6 c x + I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi -7 c x + I k0 x Pi -6 c x + I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi -7 c x + I k0 x Pi -6 c x + I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi - -41247931725 E Cos[-- + k x] 123743795175 E Cos[-- + k x] 618718975875 E Cos[-- + k x] 206239658625 E Cos[-- + k x] 618718975875 E Cos[-- + k x] 123743795175 E Cos[-- + k x] 41247931725 E Cos[-- + k x] 11486475 E Cos[-- + k x] 34459425 E Cos[-- + k x] 172297125 E Cos[-- + k x] 57432375 E Cos[-- + k x] 172297125 E Cos[-- + k x] 34459425 E Cos[-- + k x] 11486475 E Cos[-- + k x] 45045 E Cos[-- + k x] 135135 E Cos[-- + k x] 675675 E Cos[-- + k x] 225225 E Cos[-- + k x] 675675 E Cos[-- + k x] 135135 E Cos[-- + k x] 45045 E Cos[-- + k x] 945 E Cos[-- + k x] 2835 E Cos[-- + k x] 14175 E Cos[-- + k x] 4725 E Cos[-- + k x] 14175 E Cos[-- + k x] 2835 E Cos[-- + k x] 945 E Cos[-- + k x] E Sqrt[--] Cos[-- + k x] 6 E Sqrt[--] Cos[-- + k x] 15 E Sqrt[--] Cos[-- + k x] 20 E Sqrt[--] Cos[-- + k x] 15 E Sqrt[--] Cos[-- + k x] 6 E Sqrt[--] Cos[-- + k x] E Sqrt[--] Cos[-- + k x] 1159525191825 E Sin[-- + k x] 3478575575475 E Sin[-- + k x] 17392877877375 E Sin[-- + k x] 5797625959125 E Sin[-- + k x] 17392877877375 E Sin[-- + k x] 3478575575475 E Sin[-- + k x] 1159525191825 E Sin[-- + k x] 218243025 E Sin[-- + k x] 654729075 E Sin[-- + k x] 3273645375 E Sin[-- + k x] 1091215125 E Sin[-- + k x] 3273645375 E Sin[-- + k x] 654729075 E Sin[-- + k x] 218243025 E Sin[-- + k x] 405405 E Sin[-- + k x] 1216215 E Sin[-- + k x] 6081075 E Sin[-- + k x] 2027025 E Sin[-- + k x] 6081075 E Sin[-- + k x] 1216215 E Sin[-- + k x] 405405 E Sin[-- + k x] 3465 E Sin[-- + k x] 10395 E Sin[-- + k x] 51975 E Sin[-- + k x] 17325 E Sin[-- + k x] 51975 E Sin[-- + k x] 10395 E Sin[-- + k x] 3465 E Sin[-- + k x] 35 E Sin[-- + k x] 105 E Sin[-- + k x] 525 E Sin[-- + k x] 175 E Sin[-- + k x] 525 E Sin[-- + k x] 105 E Sin[-- + k x] 35 E Sin[-- + k x] - 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 Pi 4 Pi 4 Pi 4 Pi 4 Pi 4 Pi 4 Pi 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 -Integrate::idiv: Integral of ------------------------------------------- + ------------------------------------------- - ------------------------------------------- + ------------------------------------------- - ------------------------------------------- + ------------------------------------------- - ------------------------------------------ + --------------------------------------- - --------------------------------------- + ---------------------------------------- - --------------------------------------- + ---------------------------------------- - --------------------------------------- + --------------------------------------- - ------------------------------------ + ------------------------------------- - ------------------------------------- + ------------------------------------- - ------------------------------------- + ------------------------------------- - ------------------------------------ - ---------------------------------- + ----------------------------------- - ------------------------------------ + ----------------------------------- - ------------------------------------ + ----------------------------------- - ---------------------------------- + --------------------------------------- - ----------------------------------------- + ------------------------------------------ - ------------------------------------------ + ------------------------------------------ - ----------------------------------------- + --------------------------------------- - -------------------------------------------- + -------------------------------------------- - --------------------------------------------- + -------------------------------------------- - --------------------------------------------- + -------------------------------------------- - -------------------------------------------- + ---------------------------------------- - ---------------------------------------- + ----------------------------------------- - ----------------------------------------- + ----------------------------------------- - ---------------------------------------- + ---------------------------------------- - ------------------------------------- + -------------------------------------- - -------------------------------------- + -------------------------------------- - -------------------------------------- + -------------------------------------- - ------------------------------------- + ----------------------------------- - ------------------------------------ + ------------------------------------ - ------------------------------------ + ------------------------------------ - ------------------------------------ + ----------------------------------- - --------------------------------- + ---------------------------------- - ---------------------------------- + ---------------------------------- - ---------------------------------- + ---------------------------------- - --------------------------------- does not converge on {0, Infinity}. - 17/2 5 25/2 17/2 5 25/2 17/2 5 25/2 17/2 5 25/2 17/2 5 25/2 17/2 5 25/2 17/2 5 25/2 13/2 5 21/2 13/2 5 21/2 13/2 5 21/2 13/2 5 21/2 13/2 5 21/2 13/2 5 21/2 13/2 5 21/2 9/2 5 17/2 9/2 5 17/2 9/2 5 17/2 9/2 5 17/2 9/2 5 17/2 9/2 5 17/2 9/2 5 17/2 5/2 5 13/2 5/2 5 13/2 5/2 5 13/2 5/2 5 13/2 5/2 5 13/2 5/2 5 13/2 5/2 5 13/2 5 9/2 5 9/2 5 9/2 5 9/2 5 9/2 5 9/2 5 9/2 19/2 5 27/2 19/2 5 27/2 19/2 5 27/2 19/2 5 27/2 19/2 5 27/2 19/2 5 27/2 19/2 5 27/2 15/2 5 23/2 15/2 5 23/2 15/2 5 23/2 15/2 5 23/2 15/2 5 23/2 15/2 5 23/2 15/2 5 23/2 11/2 5 19/2 11/2 5 19/2 11/2 5 19/2 11/2 5 19/2 11/2 5 19/2 11/2 5 19/2 11/2 5 19/2 7/2 5 15/2 7/2 5 15/2 7/2 5 15/2 7/2 5 15/2 7/2 5 15/2 7/2 5 15/2 7/2 5 15/2 3/2 5 11/2 3/2 5 11/2 3/2 5 11/2 3/2 5 11/2 3/2 5 11/2 3/2 5 11/2 3/2 5 11/2 - 1073741824 k k0 Sqrt[2 Pi] x 536870912 k k0 Sqrt[2 Pi] x 1073741824 k k0 Sqrt[2 Pi] x 268435456 k k0 Sqrt[2 Pi] x 1073741824 k k0 Sqrt[2 Pi] x 536870912 k k0 Sqrt[2 Pi] x 1073741824 k k0 Sqrt[2 Pi] x 2097152 k k0 Sqrt[2 Pi] x 1048576 k k0 Sqrt[2 Pi] x 2097152 k k0 Sqrt[2 Pi] x 524288 k k0 Sqrt[2 Pi] x 2097152 k k0 Sqrt[2 Pi] x 1048576 k k0 Sqrt[2 Pi] x 2097152 k k0 Sqrt[2 Pi] x 16384 k k0 Sqrt[2 Pi] x 8192 k k0 Sqrt[2 Pi] x 16384 k k0 Sqrt[2 Pi] x 4096 k k0 Sqrt[2 Pi] x 16384 k k0 Sqrt[2 Pi] x 8192 k k0 Sqrt[2 Pi] x 16384 k k0 Sqrt[2 Pi] x 64 k k0 Sqrt[2 Pi] x 32 k k0 Sqrt[2 Pi] x 64 k k0 Sqrt[2 Pi] x 16 k k0 Sqrt[2 Pi] x 64 k k0 Sqrt[2 Pi] x 32 k k0 Sqrt[2 Pi] x 64 k k0 Sqrt[2 Pi] x Sqrt[k] k0 x Sqrt[k] k0 x Sqrt[k] k0 x Sqrt[k] k0 x Sqrt[k] k0 x Sqrt[k] k0 x Sqrt[k] k0 x 8589934592 k k0 Sqrt[2 Pi] x 4294967296 k k0 Sqrt[2 Pi] x 8589934592 k k0 Sqrt[2 Pi] x 2147483648 k k0 Sqrt[2 Pi] x 8589934592 k k0 Sqrt[2 Pi] x 4294967296 k k0 Sqrt[2 Pi] x 8589934592 k k0 Sqrt[2 Pi] x 16777216 k k0 Sqrt[2 Pi] x 8388608 k k0 Sqrt[2 Pi] x 16777216 k k0 Sqrt[2 Pi] x 4194304 k k0 Sqrt[2 Pi] x 16777216 k k0 Sqrt[2 Pi] x 8388608 k k0 Sqrt[2 Pi] x 16777216 k k0 Sqrt[2 Pi] x 131072 k k0 Sqrt[2 Pi] x 65536 k k0 Sqrt[2 Pi] x 131072 k k0 Sqrt[2 Pi] x 32768 k k0 Sqrt[2 Pi] x 131072 k k0 Sqrt[2 Pi] x 65536 k k0 Sqrt[2 Pi] x 131072 k k0 Sqrt[2 Pi] x 512 k k0 Sqrt[2 Pi] x 256 k k0 Sqrt[2 Pi] x 512 k k0 Sqrt[2 Pi] x 128 k k0 Sqrt[2 Pi] x 512 k k0 Sqrt[2 Pi] x 256 k k0 Sqrt[2 Pi] x 512 k k0 Sqrt[2 Pi] x 4 k k0 Sqrt[2 Pi] x 2 k k0 Sqrt[2 Pi] x 4 k k0 Sqrt[2 Pi] x k k0 Sqrt[2 Pi] x 4 k k0 Sqrt[2 Pi] x 2 k k0 Sqrt[2 Pi] x 4 k k0 Sqrt[2 Pi] x -Series[Integrate[(E^(-(c*x) + I*k0*x)*(1 - E^(-(c*x)))^6*BesselJ[3, k*x])/(k0^5*x^4), {x, 0, Infinity}, Assumptions -> n == 3 && q == 5 && κ == 6 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0], {k, Infinity, 10}] diff --git a/besseltransforms/6-5-4 b/besseltransforms/6-5-4 deleted file mode 100644 index b475d54..0000000 --- a/besseltransforms/6-5-4 +++ /dev/null @@ -1,2 +0,0 @@ -((k^6*(-35 + 16*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0) + 2*k^4*(-35 + 24*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^3 + 8*k^2*(-7 + 6*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^5 + 16*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^7)/(1680*k^4) - (k^6*(-35 + 16*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0) + 2*k^4*(-35 + 24*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^3 + 8*k^2*(-7 + 6*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^5 + 16*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^7)/(280*k^4) + (k^6*(-35 + 16*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0) + 2*k^4*(-35 + 24*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^3 + 8*k^2*(-7 + 6*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^5 + 16*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^7)/(112*k^4) - (k^6*(-35 + 16*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0) + 2*k^4*(-35 + 24*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^3 + 8*k^2*(-7 + 6*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^5 + 16*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^7)/(84*k^4) + (k^6*(-35 + 16*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0) + 2*k^4*(-35 + 24*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^3 + 8*k^2*(-7 + 6*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^5 + 16*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^7)/(112*k^4) - (k^6*(-35 + 16*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0) + 2*k^4*(-35 + 24*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^3 + 8*k^2*(-7 + 6*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^5 + 16*(-1 + Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^7)/(280*k^4) + (k^6*(-35 + 16*Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0) + 2*k^4*(-35 + 24*Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^3 + 8*k^2*(-7 + 6*Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^5 + 16*(-1 + Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^7)/(1680*k^4))/k0^5 -SeriesData[k, Infinity, {(15*c^6)/k0^5, (-192*c^7)/k0^5 + ((48*I)*c^6)/k0^4, (105*(33*c^8 - (16*I)*c^7*k0 - 2*c^6*k0^2))/(4*k0^5), 0, (-63*(3047*c^10 - (2800*I)*c^9*k0 - 990*c^8*k0^2 + (160*I)*c^7*k0^3 + 10*c^6*k0^4))/(16*k0^5), 0, (33*(259792*c^12 - (342216*I)*c^11*k0 - 191961*c^10*k0^2 + (58800*I)*c^9*k0^3 + 10395*c^8*k0^4 - (1008*I)*c^7*k0^5 - 42*c^6*k0^6))/(32*k0^5)}, 3, 11, 1] diff --git a/besseltransforms/6-5-5 b/besseltransforms/6-5-5 deleted file mode 100644 index 033cb55..0000000 --- a/besseltransforms/6-5-5 +++ /dev/null @@ -1,2 +0,0 @@ -((35*k^8 + 8*k^6*(35 - 16*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^2 + 16*k^4*(35 - 24*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^4 + 64*k^2*(7 - 6*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^6 - 128*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^8)/(13440*k^5) - (35*k^8 + 8*k^6*(35 - 16*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^2 + 16*k^4*(35 - 24*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^4 + 64*k^2*(7 - 6*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^6 - 128*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^8)/(2240*k^5) + (35*k^8 + 8*k^6*(35 - 16*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^2 + 16*k^4*(35 - 24*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^4 + 64*k^2*(7 - 6*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^6 - 128*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^8)/(896*k^5) - (35*k^8 + 8*k^6*(35 - 16*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^2 + 16*k^4*(35 - 24*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^4 + 64*k^2*(7 - 6*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^6 - 128*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^8)/(672*k^5) + (35*k^8 + 8*k^6*(35 - 16*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^2 + 16*k^4*(35 - 24*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^4 + 64*k^2*(7 - 6*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^6 - 128*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^8)/(896*k^5) - (35*k^8 + 8*k^6*(35 - 16*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^2 + 16*k^4*(35 - 24*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^4 + 64*k^2*(7 - 6*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^6 - 128*(-1 + Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^8)/(2240*k^5) + (35*k^8 + 8*k^6*(35 - 16*Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^2 + 16*k^4*(35 - 24*Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^4 + 64*k^2*(7 - 6*Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^6 - 128*(-1 + Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^8)/(13440*k^5))/k0^5 -SeriesData[k, Infinity, {(24*c^6)/k0^5, (-420*c^7)/k0^5 + ((105*I)*c^6)/k0^4, (3168*c^8)/k0^5 - ((1536*I)*c^7)/k0^4 - (192*c^6)/k0^3, (-315*(140*c^9 - (99*I)*c^8*k0 - 24*c^7*k0^2 + (2*I)*c^6*k0^3))/(4*k0^5), 0, (693*(2716*c^11 - (3047*I)*c^10*k0 - 1400*c^9*k0^2 + (330*I)*c^8*k0^3 + 40*c^7*k0^4 - (2*I)*c^6*k0^5))/(16*k0^5), 0, (-429*(172480*c^13 - (259792*I)*c^12*k0 - 171108*c^11*k0^2 + (63987*I)*c^10*k0^3 + 14700*c^9*k0^4 - (2079*I)*c^8*k0^5 - 168*c^7*k0^6 + (6*I)*c^6*k0^7))/(32*k0^5)}, 3, 11, 1] diff --git a/besseltransforms/6-5-6 b/besseltransforms/6-5-6 deleted file mode 100644 index 8a55259..0000000 --- a/besseltransforms/6-5-6 +++ /dev/null @@ -1,2 +0,0 @@ -((k^8*(-315 + 64*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0) + 16*k^6*(-105 + 52*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^3 + 48*k^4*(-63 + 44*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^5 + 64*k^2*(-36 + 31*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^7 + 640*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^9)/(60480*k^6) - (k^8*(-315 + 64*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0) + 16*k^6*(-105 + 52*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^3 + 48*k^4*(-63 + 44*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^5 + 64*k^2*(-36 + 31*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^7 + 640*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^9)/(10080*k^6) + (k^8*(-315 + 64*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0) + 16*k^6*(-105 + 52*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^3 + 48*k^4*(-63 + 44*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^5 + 64*k^2*(-36 + 31*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^7 + 640*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^9)/(4032*k^6) - (k^8*(-315 + 64*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0) + 16*k^6*(-105 + 52*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^3 + 48*k^4*(-63 + 44*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^5 + 64*k^2*(-36 + 31*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^7 + 640*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^9)/(3024*k^6) + (k^8*(-315 + 64*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0) + 16*k^6*(-105 + 52*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^3 + 48*k^4*(-63 + 44*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^5 + 64*k^2*(-36 + 31*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^7 + 640*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^9)/(4032*k^6) - (k^8*(-315 + 64*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0) + 16*k^6*(-105 + 52*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^3 + 48*k^4*(-63 + 44*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^5 + 64*k^2*(-36 + 31*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^7 + 640*(-1 + Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^9)/(10080*k^6) + (k^8*(-315 + 64*Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0) + 16*k^6*(-105 + 52*Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^3 + 48*k^4*(-63 + 44*Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^5 + 64*k^2*(-36 + 31*Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^7 + 640*(-1 + Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^9)/(60480*k^6))/k0^5 -SeriesData[k, Infinity, {(35*c^6)/k0^5, (-768*c^7)/k0^5 + ((192*I)*c^6)/k0^4, (945*(33*c^8 - (16*I)*c^7*k0 - 2*c^6*k0^2))/(4*k0^5), (-44800*c^9)/k0^5 + ((31680*I)*c^8)/k0^4 + (7680*c^7)/k0^3 - ((640*I)*c^6)/k0^2, (693*(3047*c^10 - (2800*I)*c^9*k0 - 990*c^8*k0^2 + (160*I)*c^7*k0^3 + 10*c^6*k0^4))/(16*k0^5), 0, (-143*(259792*c^12 - (342216*I)*c^11*k0 - 191961*c^10*k0^2 + (58800*I)*c^9*k0^3 + 10395*c^8*k0^4 - (1008*I)*c^7*k0^5 - 42*c^6*k0^6))/(32*k0^5)}, 3, 11, 1] diff --git a/besseltransforms/6-5-7 b/besseltransforms/6-5-7 deleted file mode 100644 index 2f390fa..0000000 --- a/besseltransforms/6-5-7 +++ /dev/null @@ -1,2 +0,0 @@ -((21*k^10 + 4*k^8*(105 - 32*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^2 + 112*k^6*(15 - 8*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^4 + 384*k^4*(7 - 5*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^6 + 128*k^2*(15 - 13*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^8 - 512*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^10)/(40320*k^7) - (21*k^10 + 4*k^8*(105 - 32*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^2 + 112*k^6*(15 - 8*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^4 + 384*k^4*(7 - 5*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^6 + 128*k^2*(15 - 13*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^8 - 512*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^10)/(6720*k^7) + (21*k^10 + 4*k^8*(105 - 32*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^2 + 112*k^6*(15 - 8*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^4 + 384*k^4*(7 - 5*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^6 + 128*k^2*(15 - 13*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^8 - 512*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^10)/(2688*k^7) - (21*k^10 + 4*k^8*(105 - 32*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^2 + 112*k^6*(15 - 8*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^4 + 384*k^4*(7 - 5*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^6 + 128*k^2*(15 - 13*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^8 - 512*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^10)/(2016*k^7) + (21*k^10 + 4*k^8*(105 - 32*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^2 + 112*k^6*(15 - 8*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^4 + 384*k^4*(7 - 5*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^6 + 128*k^2*(15 - 13*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^8 - 512*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^10)/(2688*k^7) - (21*k^10 + 4*k^8*(105 - 32*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^2 + 112*k^6*(15 - 8*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^4 + 384*k^4*(7 - 5*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^6 + 128*k^2*(15 - 13*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^8 - 512*(-1 + Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^10)/(6720*k^7) + (21*k^10 + 4*k^8*(105 - 32*Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^2 + 112*k^6*(15 - 8*Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^4 + 384*k^4*(7 - 5*Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^6 + 128*k^2*(15 - 13*Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^8 - 512*(-1 + Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^10)/(40320*k^7))/k0^5 -SeriesData[k, Infinity, {(48*c^6)/k0^5, (-1260*c^7)/k0^5 + ((315*I)*c^6)/k0^4, (15840*c^8)/k0^5 - ((7680*I)*c^7)/k0^4 - (960*c^6)/k0^3, (-3465*(140*c^9 - (99*I)*c^8*k0 - 24*c^7*k0^2 + (2*I)*c^6*k0^3))/(4*k0^5), (585024*c^10)/k0^5 - ((537600*I)*c^9)/k0^4 - (190080*c^8)/k0^3 + ((30720*I)*c^7)/k0^2 + (1920*c^6)/k0, (-9009*(2716*c^11 - (3047*I)*c^10*k0 - 1400*c^9*k0^2 + (330*I)*c^8*k0^3 + 40*c^7*k0^4 - (2*I)*c^6*k0^5))/(16*k0^5), 0, (2145*(172480*c^13 - (259792*I)*c^12*k0 - 171108*c^11*k0^2 + (63987*I)*c^10*k0^3 + 14700*c^9*k0^4 - (2079*I)*c^8*k0^5 - 168*c^7*k0^6 + (6*I)*c^6*k0^7))/(32*k0^5)}, 3, 11, 1] diff --git a/besseltransforms/7-1-0.REMOVED.git-id b/besseltransforms/7-1-0.REMOVED.git-id deleted file mode 100644 index ac74957..0000000 --- a/besseltransforms/7-1-0.REMOVED.git-id +++ /dev/null @@ -1 +0,0 @@ -ae505b9d4c1eeaa06af2c14fbf57097d2e776630 \ No newline at end of file diff --git a/besseltransforms/7-1-1.REMOVED.git-id b/besseltransforms/7-1-1.REMOVED.git-id deleted file mode 100644 index a28c3cd..0000000 --- a/besseltransforms/7-1-1.REMOVED.git-id +++ /dev/null @@ -1 +0,0 @@ -2ba9a09f1db5bc6a45dd3b7edebf70f39529b350 \ No newline at end of file diff --git a/besseltransforms/7-1-2.REMOVED.git-id b/besseltransforms/7-1-2.REMOVED.git-id deleted file mode 100644 index 5b7552f..0000000 --- a/besseltransforms/7-1-2.REMOVED.git-id +++ /dev/null @@ -1 +0,0 @@ -ffac63299c303e912d85a312d47d1b59b898daf7 \ No newline at end of file diff --git a/besseltransforms/7-1-3 b/besseltransforms/7-1-3 deleted file mode 100644 index f4c5a4c..0000000 --- a/besseltransforms/7-1-3 +++ /dev/null @@ -1,2 +0,0 @@ -((k^2*(-3 + Sqrt[1 + k^2/(c - I*k0)^2]) + 4*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^2)/(k^3*Sqrt[1 + k^2/(c - I*k0)^2]) - (7*(k^2*(-3 + Sqrt[1 + k^2/(2*c - I*k0)^2]) + 4*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^2))/(k^3*Sqrt[1 + k^2/(2*c - I*k0)^2]) + (21*(k^2*(-3 + Sqrt[1 + k^2/(3*c - I*k0)^2]) + 4*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^2))/(k^3*Sqrt[1 + k^2/(3*c - I*k0)^2]) - (35*(k^2*(-3 + Sqrt[1 + k^2/(4*c - I*k0)^2]) + 4*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^2))/(k^3*Sqrt[1 + k^2/(4*c - I*k0)^2]) + (35*(k^2*(-3 + Sqrt[1 + k^2/(5*c - I*k0)^2]) + 4*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^2))/(k^3*Sqrt[1 + k^2/(5*c - I*k0)^2]) - (21*(k^2*(-3 + Sqrt[1 + k^2/(6*c - I*k0)^2]) + 4*(-1 + Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^2))/(k^3*Sqrt[1 + k^2/(6*c - I*k0)^2]) + (7*(k^2*(-3 + Sqrt[1 + k^2/(7*c - I*k0)^2]) + 4*(-1 + Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^2))/(k^3*Sqrt[1 + k^2/(7*c - I*k0)^2]) - (k^2*(-3 + Sqrt[1 + k^2/(8*c - I*k0)^2]) + 4*(-1 + Sqrt[1 + k^2/(8*c - I*k0)^2])*(8*c - I*k0)^2)/(k^3*Sqrt[1 + k^2/(8*c - I*k0)^2]))/k0 -SeriesData[k, Infinity, {(2835*c^7)/(k*k0), 0, (-51975*(125*c^9 - (54*I)*c^8*k0 - 6*c^7*k0^2))/(4*k*k0)}, 7, 11, 1] diff --git a/besseltransforms/7-1-4 b/besseltransforms/7-1-4 deleted file mode 100644 index 123b36b..0000000 --- a/besseltransforms/7-1-4 +++ /dev/null @@ -1,2 +0,0 @@ -((k^4 - 4*k^2*(-2 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^2 - 8*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^4)/(k^4*Sqrt[1 + k^2/(c - I*k0)^2]*(c - I*k0)) - (7*(k^4 - 4*k^2*(-2 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^2 - 8*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^4))/(k^4*Sqrt[1 + k^2/(2*c - I*k0)^2]*(2*c - I*k0)) + (21*(k^4 - 4*k^2*(-2 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^2 - 8*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^4))/(k^4*Sqrt[1 + k^2/(3*c - I*k0)^2]*(3*c - I*k0)) - (35*(k^4 - 4*k^2*(-2 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^2 - 8*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^4))/(k^4*Sqrt[1 + k^2/(4*c - I*k0)^2]*(4*c - I*k0)) + (35*(k^4 - 4*k^2*(-2 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^2 - 8*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^4))/(k^4*Sqrt[1 + k^2/(5*c - I*k0)^2]*(5*c - I*k0)) - (21*(k^4 - 4*k^2*(-2 + Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^2 - 8*(-1 + Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^4))/(k^4*Sqrt[1 + k^2/(6*c - I*k0)^2]*(6*c - I*k0)) + (7*(k^4 - 4*k^2*(-2 + Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^2 - 8*(-1 + Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^4))/(k^4*Sqrt[1 + k^2/(7*c - I*k0)^2]*(7*c - I*k0)) - (k^4 - 4*k^2*(-2 + Sqrt[1 + k^2/(8*c - I*k0)^2])*(8*c - I*k0)^2 - 8*(-1 + Sqrt[1 + k^2/(8*c - I*k0)^2])*(8*c - I*k0)^4)/(k^4*Sqrt[1 + k^2/(8*c - I*k0)^2]*(8*c - I*k0)))/k0 -SeriesData[k, Infinity, {((31185*I)*c^7)/k - (280665*c^8)/(2*k*k0), 0, (675675*(198*c^10 - (125*I)*c^9*k0 - 27*c^8*k0^2 + (2*I)*c^7*k0^3))/(4*k*k0)}, 8, 11, 1] diff --git a/besseltransforms/7-1-5 b/besseltransforms/7-1-5 deleted file mode 100644 index 4ff1e02..0000000 --- a/besseltransforms/7-1-5 +++ /dev/null @@ -1,2 +0,0 @@ -((k^4*(-5 + Sqrt[1 + k^2/(c - I*k0)^2]) + 4*k^2*(-5 + 3*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^2 + 16*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^4)/(k^5*Sqrt[1 + k^2/(c - I*k0)^2]) - (7*(k^4*(-5 + Sqrt[1 + k^2/(2*c - I*k0)^2]) + 4*k^2*(-5 + 3*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^2 + 16*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^4))/(k^5*Sqrt[1 + k^2/(2*c - I*k0)^2]) + (21*(k^4*(-5 + Sqrt[1 + k^2/(3*c - I*k0)^2]) + 4*k^2*(-5 + 3*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^2 + 16*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^4))/(k^5*Sqrt[1 + k^2/(3*c - I*k0)^2]) - (35*(k^4*(-5 + Sqrt[1 + k^2/(4*c - I*k0)^2]) + 4*k^2*(-5 + 3*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^2 + 16*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^4))/(k^5*Sqrt[1 + k^2/(4*c - I*k0)^2]) + (35*(k^4*(-5 + Sqrt[1 + k^2/(5*c - I*k0)^2]) + 4*k^2*(-5 + 3*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^2 + 16*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^4))/(k^5*Sqrt[1 + k^2/(5*c - I*k0)^2]) - (21*(k^4*(-5 + Sqrt[1 + k^2/(6*c - I*k0)^2]) + 4*k^2*(-5 + 3*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^2 + 16*(-1 + Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^4))/(k^5*Sqrt[1 + k^2/(6*c - I*k0)^2]) + (7*(k^4*(-5 + Sqrt[1 + k^2/(7*c - I*k0)^2]) + 4*k^2*(-5 + 3*Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^2 + 16*(-1 + Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^4))/(k^5*Sqrt[1 + k^2/(7*c - I*k0)^2]) - (k^4*(-5 + Sqrt[1 + k^2/(8*c - I*k0)^2]) + 4*k^2*(-5 + 3*Sqrt[1 + k^2/(8*c - I*k0)^2])*(8*c - I*k0)^2 + 16*(-1 + Sqrt[1 + k^2/(8*c - I*k0)^2])*(8*c - I*k0)^4)/(k^5*Sqrt[1 + k^2/(8*c - I*k0)^2]))/k0 -SeriesData[k, Infinity, {(-10395*c^7)/(k*k0), 0, (135135*(125*c^9 - (54*I)*c^8*k0 - 6*c^7*k0^2))/(4*k*k0)}, 7, 11, 1] diff --git a/besseltransforms/7-1-6 b/besseltransforms/7-1-6 deleted file mode 100644 index b5b3a5e..0000000 --- a/besseltransforms/7-1-6 +++ /dev/null @@ -1,2 +0,0 @@ -((k^6 - 6*k^4*(-3 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^2 + 16*k^2*(3 - 2*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^4 - 32*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^6)/(k^6*Sqrt[1 + k^2/(c - I*k0)^2]*(c - I*k0)) - (7*(k^6 - 6*k^4*(-3 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^2 + 16*k^2*(3 - 2*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^4 - 32*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^6))/(k^6*Sqrt[1 + k^2/(2*c - I*k0)^2]*(2*c - I*k0)) + (21*(k^6 - 6*k^4*(-3 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^2 + 16*k^2*(3 - 2*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^4 - 32*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^6))/(k^6*Sqrt[1 + k^2/(3*c - I*k0)^2]*(3*c - I*k0)) - (35*(k^6 - 6*k^4*(-3 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^2 + 16*k^2*(3 - 2*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^4 - 32*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^6))/(k^6*Sqrt[1 + k^2/(4*c - I*k0)^2]*(4*c - I*k0)) + (35*(k^6 - 6*k^4*(-3 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^2 + 16*k^2*(3 - 2*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^4 - 32*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^6))/(k^6*Sqrt[1 + k^2/(5*c - I*k0)^2]*(5*c - I*k0)) - (21*(k^6 - 6*k^4*(-3 + Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^2 + 16*k^2*(3 - 2*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^4 - 32*(-1 + Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^6))/(k^6*Sqrt[1 + k^2/(6*c - I*k0)^2]*(6*c - I*k0)) + (7*(k^6 - 6*k^4*(-3 + Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^2 + 16*k^2*(3 - 2*Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^4 - 32*(-1 + Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^6))/(k^6*Sqrt[1 + k^2/(7*c - I*k0)^2]*(7*c - I*k0)) - (k^6 - 6*k^4*(-3 + Sqrt[1 + k^2/(8*c - I*k0)^2])*(8*c - I*k0)^2 + 16*k^2*(3 - 2*Sqrt[1 + k^2/(8*c - I*k0)^2])*(8*c - I*k0)^4 - 32*(-1 + Sqrt[1 + k^2/(8*c - I*k0)^2])*(8*c - I*k0)^6)/(k^6*Sqrt[1 + k^2/(8*c - I*k0)^2]*(8*c - I*k0)))/k0 -SeriesData[k, Infinity, {((-135135*I)*c^7)/k + (1216215*c^8)/(2*k*k0), 0, (-2027025*(198*c^10 - (125*I)*c^9*k0 - 27*c^8*k0^2 + (2*I)*c^7*k0^3))/(4*k*k0)}, 8, 11, 1] diff --git a/besseltransforms/7-1-7 b/besseltransforms/7-1-7 deleted file mode 100644 index 003aedb..0000000 --- a/besseltransforms/7-1-7 +++ /dev/null @@ -1,2 +0,0 @@ -((k^6*(-7 + Sqrt[1 + k^2/(c - I*k0)^2]) + 8*k^4*(-7 + 3*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^2 + 16*k^2*(-7 + 5*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^4 + 64*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^6)/(k^7*Sqrt[1 + k^2/(c - I*k0)^2]) - (7*(k^6*(-7 + Sqrt[1 + k^2/(2*c - I*k0)^2]) + 8*k^4*(-7 + 3*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^2 + 16*k^2*(-7 + 5*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^4 + 64*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^6))/(k^7*Sqrt[1 + k^2/(2*c - I*k0)^2]) + (21*(k^6*(-7 + Sqrt[1 + k^2/(3*c - I*k0)^2]) + 8*k^4*(-7 + 3*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^2 + 16*k^2*(-7 + 5*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^4 + 64*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^6))/(k^7*Sqrt[1 + k^2/(3*c - I*k0)^2]) - (35*(k^6*(-7 + Sqrt[1 + k^2/(4*c - I*k0)^2]) + 8*k^4*(-7 + 3*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^2 + 16*k^2*(-7 + 5*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^4 + 64*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^6))/(k^7*Sqrt[1 + k^2/(4*c - I*k0)^2]) + (35*(k^6*(-7 + Sqrt[1 + k^2/(5*c - I*k0)^2]) + 8*k^4*(-7 + 3*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^2 + 16*k^2*(-7 + 5*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^4 + 64*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^6))/(k^7*Sqrt[1 + k^2/(5*c - I*k0)^2]) - (21*(k^6*(-7 + Sqrt[1 + k^2/(6*c - I*k0)^2]) + 8*k^4*(-7 + 3*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^2 + 16*k^2*(-7 + 5*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^4 + 64*(-1 + Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^6))/(k^7*Sqrt[1 + k^2/(6*c - I*k0)^2]) + (7*(k^6*(-7 + Sqrt[1 + k^2/(7*c - I*k0)^2]) + 8*k^4*(-7 + 3*Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^2 + 16*k^2*(-7 + 5*Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^4 + 64*(-1 + Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^6))/(k^7*Sqrt[1 + k^2/(7*c - I*k0)^2]) - (k^6*(-7 + Sqrt[1 + k^2/(8*c - I*k0)^2]) + 8*k^4*(-7 + 3*Sqrt[1 + k^2/(8*c - I*k0)^2])*(8*c - I*k0)^2 + 16*k^2*(-7 + 5*Sqrt[1 + k^2/(8*c - I*k0)^2])*(8*c - I*k0)^4 + 64*(-1 + Sqrt[1 + k^2/(8*c - I*k0)^2])*(8*c - I*k0)^6)/(k^7*Sqrt[1 + k^2/(8*c - I*k0)^2]))/k0 -SeriesData[k, Infinity, {(135135*c^7)/(k*k0), 0, (-675675*(125*c^9 - (54*I)*c^8*k0 - 6*c^7*k0^2))/(4*k*k0)}, 7, 11, 1] diff --git a/besseltransforms/7-2-0 b/besseltransforms/7-2-0 deleted file mode 100644 index c39b980..0000000 --- a/besseltransforms/7-2-0 +++ /dev/null @@ -1,2 +0,0 @@ - -Simplify::time: Time spent on a transformation exceeded 300. seconds, and the transformation was aborted. Increasing the value of TimeConstraint option may improve the result of simplification. diff --git a/besseltransforms/7-2-1 b/besseltransforms/7-2-1 deleted file mode 100644 index f4300bc..0000000 --- a/besseltransforms/7-2-1 +++ /dev/null @@ -1,2 +0,0 @@ -(-14*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0) + 42*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0) - 70*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0) + 70*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0) - 42*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0) + 14*(-1 + Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0) - 2*(-1 + Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0) + k*Sqrt[Pi]*(Piecewise[{{0, k^2/k0^2 <= 1}}, (2*Sqrt[k^2 - k0^2])/(k*Sqrt[Pi])] + I*Piecewise[{{(2*k0)/(k*Sqrt[Pi]), k0^2/k^2 < 1}, {(2*(k0 - Sqrt[-k^2 + k0^2]))/(k*Sqrt[Pi]), k0^2/k^2 > 1}}, 0]))/(2*k*k0^2) -Piecewise[{{SeriesData[k, Infinity, {(11025*c^8)/(2*k0^2) - ((1575*I)*c^7)/k0, 0, (-33075*(98*c^10 - (77*I)*c^9*k0 - 21*c^8*k0^2 + (2*I)*c^7*k0^3))/(4*k0^2)}, 8, 11, 1], (k0 <= 0 && k^2/k0^2 > 1) || k0 > 0}}, SeriesData[k, Infinity, {-k0^(-2), 0, 1/2, 0, ((7*c*(c - I*k0)^3)/8 - (21*c*(2*c - I*k0)^3)/4 + (105*c*(3*c - I*k0)^3)/8 - (35*c*(4*c - I*k0)^3)/2 + (105*c*(5*c - I*k0)^3)/8 - (21*c*(6*c - I*k0)^3)/4 + (7*c*(7*c - I*k0)^3)/8 - (7*I)/8*(c - I*k0)^3*k0 + (21*I)/8*(2*c - I*k0)^3*k0 - (35*I)/8*(3*c - I*k0)^3*k0 + (35*I)/8*(4*c - I*k0)^3*k0 - (21*I)/8*(5*c - I*k0)^3*k0 + (7*I)/8*(6*c - I*k0)^3*k0 - I/8*(7*c - I*k0)^3*k0)/k0^2, 0, ((-7*c*(c - I*k0)^5)/16 + (21*c*(2*c - I*k0)^5)/8 - (105*c*(3*c - I*k0)^5)/16 + (35*c*(4*c - I*k0)^5)/4 - (105*c*(5*c - I*k0)^5)/16 + (21*c*(6*c - I*k0)^5)/8 - (7*c*(7*c - I*k0)^5)/16 + (7*I)/16*(c - I*k0)^5*k0 - (21*I)/16*(2*c - I*k0)^5*k0 + (35*I)/16*(3*c - I*k0)^5*k0 - (35*I)/16*(4*c - I*k0)^5*k0 + (21*I)/16*(5*c - I*k0)^5*k0 - (7*I)/16*(6*c - I*k0)^5*k0 + I/16*(7*c - I*k0)^5*k0)/k0^2, 0, ((35*c*(c - I*k0)^7)/128 - (105*c*(2*c - I*k0)^7)/64 + (525*c*(3*c - I*k0)^7)/128 - (175*c*(4*c - I*k0)^7)/32 + (525*c*(5*c - I*k0)^7)/128 - (105*c*(6*c - I*k0)^7)/64 + (35*c*(7*c - I*k0)^7)/128 - (35*I)/128*(c - I*k0)^7*k0 + (105*I)/128*(2*c - I*k0)^7*k0 - (175*I)/128*(3*c - I*k0)^7*k0 + (175*I)/128*(4*c - I*k0)^7*k0 - (105*I)/128*(5*c - I*k0)^7*k0 + (35*I)/128*(6*c - I*k0)^7*k0 - (5*I)/128*(7*c - I*k0)^7*k0)/k0^2, 0, ((-49*c*(c - I*k0)^9)/256 + (147*c*(2*c - I*k0)^9)/128 - (735*c*(3*c - I*k0)^9)/256 + (245*c*(4*c - I*k0)^9)/64 - (735*c*(5*c - I*k0)^9)/256 + (147*c*(6*c - I*k0)^9)/128 - (49*c*(7*c - I*k0)^9)/256 + (49*I)/256*(c - I*k0)^9*k0 - (147*I)/256*(2*c - I*k0)^9*k0 + (245*I)/256*(3*c - I*k0)^9*k0 - (245*I)/256*(4*c - I*k0)^9*k0 + (147*I)/256*(5*c - I*k0)^9*k0 - (49*I)/256*(6*c - I*k0)^9*k0 + (7*I)/256*(7*c - I*k0)^9*k0)/k0^2}, 0, 11, 1]] diff --git a/besseltransforms/7-2-2 b/besseltransforms/7-2-2 deleted file mode 100644 index ee8e04c..0000000 --- a/besseltransforms/7-2-2 +++ /dev/null @@ -1,2 +0,0 @@ -(-k^2 + 14*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^2 - 42*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^2 + 70*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^2 - 70*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^2 + 42*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^2 - 14*(-1 + Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^2 + 2*(-1 + Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^2 + k^2*Sqrt[Pi]*(I*Piecewise[{{0, k^2/k0^2 <= 1}}, (2*k0*Sqrt[k^2 - k0^2])/(k^2*Sqrt[Pi])] + Piecewise[{{(k^2 + 2*k0*(-k0 + Sqrt[-k^2 + k0^2]))/(k^2*Sqrt[Pi]), k^2/k0^2 < 1}, {(1 - (2*k0^2)/k^2)/Sqrt[Pi], k^2/k0^2 > 1}}, 0]))/(2*k^2*k0^2) -SeriesData[k, Infinity, {(315*c^7)/k0^2, 0, (-4725*(77*c^9 - (42*I)*c^8*k0 - 6*c^7*k0^2))/(4*k0^2)}, 7, 11, 1] diff --git a/besseltransforms/7-2-3 b/besseltransforms/7-2-3 deleted file mode 100644 index a23033b..0000000 --- a/besseltransforms/7-2-3 +++ /dev/null @@ -1,2 +0,0 @@ -(k^2*(-3 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0) + 4*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^3 - 7*k^2*(-3 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0) - 28*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^3 + 21*k^2*(-3 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0) + 84*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^3 - 35*k^2*(-3 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0) - 140*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^3 + 35*k^2*(-3 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0) + 140*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^3 - 21*k^2*(-3 + Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0) - 84*(-1 + Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^3 + 7*k^2*(-3 + Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0) + 28*(-1 + Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^3 - k^2*(-3 + Sqrt[1 + k^2/(8*c - I*k0)^2])*(8*c - I*k0) - 4*(-1 + Sqrt[1 + k^2/(8*c - I*k0)^2])*(8*c - I*k0)^3)/(3*k^3*k0^2) -SeriesData[k, Infinity, {(-25515*c^8)/(2*k0^2) + ((2835*I)*c^7)/k0, 0, (51975*(198*c^10 - (125*I)*c^9*k0 - 27*c^8*k0^2 + (2*I)*c^7*k0^3))/(4*k0^2)}, 8, 11, 1] diff --git a/besseltransforms/7-2-4 b/besseltransforms/7-2-4 deleted file mode 100644 index 8f2cb62..0000000 --- a/besseltransforms/7-2-4 +++ /dev/null @@ -1,2 +0,0 @@ -(-(k^2*(-2 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^2) - 2*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^4 + 7*k^2*(-2 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^2 + 14*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^4 - 21*k^2*(-2 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^2 - 42*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^4 + 35*k^2*(-2 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^2 + 70*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^4 - 35*k^2*(-2 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^2 - 70*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^4 + 21*k^2*(-2 + Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^2 + 42*(-1 + Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^4 - 7*k^2*(-2 + Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^2 - 14*(-1 + Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^4 + k^2*(-2 + Sqrt[1 + k^2/(8*c - I*k0)^2])*(8*c - I*k0)^2 + 2*(-1 + Sqrt[1 + k^2/(8*c - I*k0)^2])*(8*c - I*k0)^4)/(k^4*k0^2) -SeriesData[k, Infinity, {(-945*c^7)/k0^2, 0, (10395*(125*c^9 - (54*I)*c^8*k0 - 6*c^7*k0^2))/(4*k0^2)}, 7, 11, 1] diff --git a/besseltransforms/7-2-5 b/besseltransforms/7-2-5 deleted file mode 100644 index b995fe1..0000000 --- a/besseltransforms/7-2-5 +++ /dev/null @@ -1,2 +0,0 @@ -((k^4*(-5 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0) + 4*k^2*(-5 + 3*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^3 + 16*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^5)/(5*k^5) - (7*(k^4*(-5 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0) + 4*k^2*(-5 + 3*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^3 + 16*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^5))/(5*k^5) + (21*(k^4*(-5 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0) + 4*k^2*(-5 + 3*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^3 + 16*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^5))/(5*k^5) - (7*(k^4*(-5 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0) + 4*k^2*(-5 + 3*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^3 + 16*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^5))/k^5 + (7*(k^4*(-5 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0) + 4*k^2*(-5 + 3*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^3 + 16*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^5))/k^5 - (21*(k^4*(-5 + Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0) + 4*k^2*(-5 + 3*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^3 + 16*(-1 + Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^5))/(5*k^5) + (7*(k^4*(-5 + Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0) + 4*k^2*(-5 + 3*Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^3 + 16*(-1 + Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^5))/(5*k^5) - (k^4*(-5 + Sqrt[1 + k^2/(8*c - I*k0)^2])*(8*c - I*k0) + 4*k^2*(-5 + 3*Sqrt[1 + k^2/(8*c - I*k0)^2])*(8*c - I*k0)^3 + 16*(-1 + Sqrt[1 + k^2/(8*c - I*k0)^2])*(8*c - I*k0)^5)/(5*k^5))/k0^2 -SeriesData[k, Infinity, {(93555*c^8)/(2*k0^2) - ((10395*I)*c^7)/k0, 0, (-135135*(198*c^10 - (125*I)*c^9*k0 - 27*c^8*k0^2 + (2*I)*c^7*k0^3))/(4*k0^2)}, 8, 11, 1] diff --git a/besseltransforms/7-2-6 b/besseltransforms/7-2-6 deleted file mode 100644 index 2c3c7f5..0000000 --- a/besseltransforms/7-2-6 +++ /dev/null @@ -1,2 +0,0 @@ -((k^6 - 6*k^4*(-3 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^2 + 16*k^2*(3 - 2*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^4 - 32*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^6)/(6*k^6) - (7*(k^6 - 6*k^4*(-3 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^2 + 16*k^2*(3 - 2*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^4 - 32*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^6))/(6*k^6) + (7*(k^6 - 6*k^4*(-3 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^2 + 16*k^2*(3 - 2*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^4 - 32*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^6))/(2*k^6) - (35*(k^6 - 6*k^4*(-3 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^2 + 16*k^2*(3 - 2*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^4 - 32*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^6))/(6*k^6) + (35*(k^6 - 6*k^4*(-3 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^2 + 16*k^2*(3 - 2*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^4 - 32*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^6))/(6*k^6) - (7*(k^6 - 6*k^4*(-3 + Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^2 + 16*k^2*(3 - 2*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^4 - 32*(-1 + Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^6))/(2*k^6) + (7*(k^6 - 6*k^4*(-3 + Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^2 + 16*k^2*(3 - 2*Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^4 - 32*(-1 + Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^6))/(6*k^6) - (k^6 - 6*k^4*(-3 + Sqrt[1 + k^2/(8*c - I*k0)^2])*(8*c - I*k0)^2 + 16*k^2*(3 - 2*Sqrt[1 + k^2/(8*c - I*k0)^2])*(8*c - I*k0)^4 - 32*(-1 + Sqrt[1 + k^2/(8*c - I*k0)^2])*(8*c - I*k0)^6)/(6*k^6))/k0^2 -SeriesData[k, Infinity, {(10395*c^7)/k0^2, 0, (-45045*(125*c^9 - (54*I)*c^8*k0 - 6*c^7*k0^2))/(4*k0^2)}, 7, 11, 1] diff --git a/besseltransforms/7-2-7 b/besseltransforms/7-2-7 deleted file mode 100644 index 08204f7..0000000 --- a/besseltransforms/7-2-7 +++ /dev/null @@ -1,2 +0,0 @@ -((k^6*(-7 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0) + 8*k^4*(-7 + 3*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^3 + 16*k^2*(-7 + 5*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^5 + 64*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^7)/(7*k^7) - (k^6*(-7 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0) + 8*k^4*(-7 + 3*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^3 + 16*k^2*(-7 + 5*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^5 + 64*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^7)/k^7 + (3*(k^6*(-7 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0) + 8*k^4*(-7 + 3*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^3 + 16*k^2*(-7 + 5*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^5 + 64*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^7))/k^7 - (5*(k^6*(-7 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0) + 8*k^4*(-7 + 3*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^3 + 16*k^2*(-7 + 5*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^5 + 64*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^7))/k^7 + (5*(k^6*(-7 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0) + 8*k^4*(-7 + 3*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^3 + 16*k^2*(-7 + 5*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^5 + 64*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^7))/k^7 - (3*(k^6*(-7 + Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0) + 8*k^4*(-7 + 3*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^3 + 16*k^2*(-7 + 5*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^5 + 64*(-1 + Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^7))/k^7 + (k^6*(-7 + Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0) + 8*k^4*(-7 + 3*Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^3 + 16*k^2*(-7 + 5*Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^5 + 64*(-1 + Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^7)/k^7 - (k^6*(-7 + Sqrt[1 + k^2/(8*c - I*k0)^2])*(8*c - I*k0) + 8*k^4*(-7 + 3*Sqrt[1 + k^2/(8*c - I*k0)^2])*(8*c - I*k0)^3 + 16*k^2*(-7 + 5*Sqrt[1 + k^2/(8*c - I*k0)^2])*(8*c - I*k0)^5 + 64*(-1 + Sqrt[1 + k^2/(8*c - I*k0)^2])*(8*c - I*k0)^7)/(7*k^7))/k0^2 -SeriesData[k, Infinity, {(46080*c^7)/k0^2, (-1216215*c^8)/(2*k0^2) + ((135135*I)*c^7)/k0, 0, (675675*(198*c^10 - (125*I)*c^9*k0 - 27*c^8*k0^2 + (2*I)*c^7*k0^3))/(4*k0^2)}, 7, 11, 1] diff --git a/besseltransforms/7-3-0 b/besseltransforms/7-3-0 deleted file mode 100644 index c39b980..0000000 --- a/besseltransforms/7-3-0 +++ /dev/null @@ -1,2 +0,0 @@ - -Simplify::time: Time spent on a transformation exceeded 300. seconds, and the transformation was aborted. Increasing the value of TimeConstraint option may improve the result of simplification. diff --git a/besseltransforms/7-3-1 b/besseltransforms/7-3-1 deleted file mode 100644 index c39b980..0000000 --- a/besseltransforms/7-3-1 +++ /dev/null @@ -1,2 +0,0 @@ - -Simplify::time: Time spent on a transformation exceeded 300. seconds, and the transformation was aborted. Increasing the value of TimeConstraint option may improve the result of simplification. diff --git a/besseltransforms/7-3-2 b/besseltransforms/7-3-2 deleted file mode 100644 index 7e0c894..0000000 --- a/besseltransforms/7-3-2 +++ /dev/null @@ -1,2 +0,0 @@ -(14*k^2*(3 - 2*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0) - 28*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^3 + 42*k^2*(-3 + 2*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0) + 84*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^3 + 70*k^2*(3 - 2*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0) - 140*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^3 + 70*k^2*(-3 + 2*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0) + 140*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^3 + 42*k^2*(3 - 2*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0) - 84*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^3 + 14*k^2*(-3 + 2*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0) + 28*(-1 + Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^3 + 2*k^2*(3 - 2*Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0) - 4*(-1 + Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^3 + 3*k^2*k0*Sqrt[Pi]*(Piecewise[{{0, k^2/k0^2 <= 1}}, (4*(k^2 - k0^2)^(3/2))/(3*k^2*k0*Sqrt[Pi])] + I*Piecewise[{{(-2*(2*k0*(k0 - Sqrt[-k^2 + k0^2]) + k^2*(-3 + (2*Sqrt[-k^2 + k0^2])/k0)))/(3*k^2*Sqrt[Pi]), k^2/k0^2 < 1}, {(2*(1 - (2*k0^2)/(3*k^2)))/Sqrt[Pi], k^2/k0^2 > 1}}, 0]))/(12*k^2*k0^3) -SeriesData[k, Infinity, {(-2205*c^8)/(2*k0^3) + ((315*I)*c^7)/k0^2, 0, (4725*(98*c^10 - (77*I)*c^9*k0 - 21*c^8*k0^2 + (2*I)*c^7*k0^3))/(4*k0^3)}, 7, 11, 1] diff --git a/besseltransforms/7-3-3 b/besseltransforms/7-3-3 deleted file mode 100644 index 00bb32f..0000000 --- a/besseltransforms/7-3-3 +++ /dev/null @@ -1,2 +0,0 @@ -((3*k^4 + 4*k^2*(3 - 2*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^2 - 8*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^4)/(24*k^3) - (7*(3*k^4 + 4*k^2*(3 - 2*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^2 - 8*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^4))/(24*k^3) + (7*(3*k^4 + 4*k^2*(3 - 2*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^2 - 8*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^4))/(8*k^3) - (35*(3*k^4 + 4*k^2*(3 - 2*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^2 - 8*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^4))/(24*k^3) + (35*(3*k^4 + 4*k^2*(3 - 2*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^2 - 8*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^4))/(24*k^3) - (7*(3*k^4 + 4*k^2*(3 - 2*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^2 - 8*(-1 + Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^4))/(8*k^3) + (7*(3*k^4 + 4*k^2*(3 - 2*Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^2 - 8*(-1 + Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^4))/(24*k^3) - (3*k^4 + 4*k^2*(3 - 2*Sqrt[1 + k^2/(8*c - I*k0)^2])*(8*c - I*k0)^2 - 8*(-1 + Sqrt[1 + k^2/(8*c - I*k0)^2])*(8*c - I*k0)^4)/(24*k^3))/k0^3 -SeriesData[k, Infinity, {(-105*c^7)/k0^3, 0, (945*(125*c^9 - (54*I)*c^8*k0 - 6*c^7*k0^2))/(4*k0^3), 0, (-10395*(4819*c^11 - (3960*I)*c^10*k0 - 1250*c^9*k0^2 + (180*I)*c^8*k0^3 + 10*c^7*k0^4))/(16*k0^3)}, 6, 11, 1] diff --git a/besseltransforms/7-3-4 b/besseltransforms/7-3-4 deleted file mode 100644 index 1713d3f..0000000 --- a/besseltransforms/7-3-4 +++ /dev/null @@ -1,2 +0,0 @@ -((k^4*(-15 + 4*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0) + 4*k^2*(-10 + 7*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^3 + 24*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^5)/(60*k^4) - (7*(k^4*(-15 + 4*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0) + 4*k^2*(-10 + 7*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^3 + 24*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^5))/(60*k^4) + (7*(k^4*(-15 + 4*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0) + 4*k^2*(-10 + 7*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^3 + 24*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^5))/(20*k^4) - (7*(k^4*(-15 + 4*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0) + 4*k^2*(-10 + 7*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^3 + 24*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^5))/(12*k^4) + (7*(k^4*(-15 + 4*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0) + 4*k^2*(-10 + 7*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^3 + 24*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^5))/(12*k^4) - (7*(k^4*(-15 + 4*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0) + 4*k^2*(-10 + 7*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^3 + 24*(-1 + Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^5))/(20*k^4) + (7*(k^4*(-15 + 4*Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0) + 4*k^2*(-10 + 7*Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^3 + 24*(-1 + Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^5))/(60*k^4) - (k^4*(-15 + 4*Sqrt[1 + k^2/(8*c - I*k0)^2])*(8*c - I*k0) + 4*k^2*(-10 + 7*Sqrt[1 + k^2/(8*c - I*k0)^2])*(8*c - I*k0)^3 + 24*(-1 + Sqrt[1 + k^2/(8*c - I*k0)^2])*(8*c - I*k0)^5)/(60*k^4))/k0^3 -SeriesData[k, Infinity, {(8505*c^8)/(2*k0^3) - ((945*I)*c^7)/k0^2, 0, (-10395*(198*c^10 - (125*I)*c^9*k0 - 27*c^8*k0^2 + (2*I)*c^7*k0^3))/(4*k0^3)}, 7, 11, 1] diff --git a/besseltransforms/7-3-5 b/besseltransforms/7-3-5 deleted file mode 100644 index 65b066a..0000000 --- a/besseltransforms/7-3-5 +++ /dev/null @@ -1,2 +0,0 @@ -((5*k^6 + 12*k^4*(5 - 2*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^2 + 8*k^2*(15 - 11*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^4 - 64*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^6)/(120*k^5) - (7*(5*k^6 + 12*k^4*(5 - 2*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^2 + 8*k^2*(15 - 11*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^4 - 64*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^6))/(120*k^5) + (7*(5*k^6 + 12*k^4*(5 - 2*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^2 + 8*k^2*(15 - 11*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^4 - 64*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^6))/(40*k^5) - (7*(5*k^6 + 12*k^4*(5 - 2*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^2 + 8*k^2*(15 - 11*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^4 - 64*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^6))/(24*k^5) + (7*(5*k^6 + 12*k^4*(5 - 2*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^2 + 8*k^2*(15 - 11*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^4 - 64*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^6))/(24*k^5) - (7*(5*k^6 + 12*k^4*(5 - 2*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^2 + 8*k^2*(15 - 11*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^4 - 64*(-1 + Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^6))/(40*k^5) + (7*(5*k^6 + 12*k^4*(5 - 2*Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^2 + 8*k^2*(15 - 11*Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^4 - 64*(-1 + Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^6))/(120*k^5) - (5*k^6 + 12*k^4*(5 - 2*Sqrt[1 + k^2/(8*c - I*k0)^2])*(8*c - I*k0)^2 + 8*k^2*(15 - 11*Sqrt[1 + k^2/(8*c - I*k0)^2])*(8*c - I*k0)^4 - 64*(-1 + Sqrt[1 + k^2/(8*c - I*k0)^2])*(8*c - I*k0)^6)/(120*k^5))/k0^3 -SeriesData[k, Infinity, {(945*c^7)/k0^3, 0, (-3465*(125*c^9 - (54*I)*c^8*k0 - 6*c^7*k0^2))/(4*k0^3), 0, (27027*(4819*c^11 - (3960*I)*c^10*k0 - 1250*c^9*k0^2 + (180*I)*c^8*k0^3 + 10*c^7*k0^4))/(16*k0^3)}, 6, 11, 1] diff --git a/besseltransforms/7-3-6 b/besseltransforms/7-3-6 deleted file mode 100644 index 4ec742d..0000000 --- a/besseltransforms/7-3-6 +++ /dev/null @@ -1,2 +0,0 @@ -((k^6*(-35 + 6*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0) + 6*k^4*(-35 + 17*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^3 + 16*k^2*(-21 + 16*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^5 + 160*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^7)/(210*k^6) - (k^6*(-35 + 6*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0) + 6*k^4*(-35 + 17*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^3 + 16*k^2*(-21 + 16*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^5 + 160*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^7)/(30*k^6) + (k^6*(-35 + 6*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0) + 6*k^4*(-35 + 17*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^3 + 16*k^2*(-21 + 16*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^5 + 160*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^7)/(10*k^6) - (k^6*(-35 + 6*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0) + 6*k^4*(-35 + 17*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^3 + 16*k^2*(-21 + 16*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^5 + 160*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^7)/(6*k^6) + (k^6*(-35 + 6*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0) + 6*k^4*(-35 + 17*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^3 + 16*k^2*(-21 + 16*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^5 + 160*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^7)/(6*k^6) - (k^6*(-35 + 6*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0) + 6*k^4*(-35 + 17*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^3 + 16*k^2*(-21 + 16*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^5 + 160*(-1 + Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^7)/(10*k^6) + (k^6*(-35 + 6*Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0) + 6*k^4*(-35 + 17*Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^3 + 16*k^2*(-21 + 16*Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^5 + 160*(-1 + Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^7)/(30*k^6) - (k^6*(-35 + 6*Sqrt[1 + k^2/(8*c - I*k0)^2])*(8*c - I*k0) + 6*k^4*(-35 + 17*Sqrt[1 + k^2/(8*c - I*k0)^2])*(8*c - I*k0)^3 + 16*k^2*(-21 + 16*Sqrt[1 + k^2/(8*c - I*k0)^2])*(8*c - I*k0)^5 + 160*(-1 + Sqrt[1 + k^2/(8*c - I*k0)^2])*(8*c - I*k0)^7)/(210*k^6))/k0^3 -SeriesData[k, Infinity, {(3840*c^7)/k0^3, (-93555*c^8)/(2*k0^3) + ((10395*I)*c^7)/k0^2, 0, (45045*(198*c^10 - (125*I)*c^9*k0 - 27*c^8*k0^2 + (2*I)*c^7*k0^3))/(4*k0^3)}, 6, 11, 1] diff --git a/besseltransforms/7-3-7 b/besseltransforms/7-3-7 deleted file mode 100644 index 8d6266f..0000000 --- a/besseltransforms/7-3-7 +++ /dev/null @@ -1,2 +0,0 @@ -((7*k^8 + 24*k^6*(7 - 2*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^2 + 16*k^4*(42 - 23*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^4 + 64*k^2*(14 - 11*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^6 - 384*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^8)/(336*k^7) - (7*k^8 + 24*k^6*(7 - 2*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^2 + 16*k^4*(42 - 23*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^4 + 64*k^2*(14 - 11*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^6 - 384*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^8)/(48*k^7) + (7*k^8 + 24*k^6*(7 - 2*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^2 + 16*k^4*(42 - 23*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^4 + 64*k^2*(14 - 11*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^6 - 384*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^8)/(16*k^7) - (5*(7*k^8 + 24*k^6*(7 - 2*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^2 + 16*k^4*(42 - 23*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^4 + 64*k^2*(14 - 11*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^6 - 384*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^8))/(48*k^7) + (5*(7*k^8 + 24*k^6*(7 - 2*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^2 + 16*k^4*(42 - 23*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^4 + 64*k^2*(14 - 11*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^6 - 384*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^8))/(48*k^7) - (7*k^8 + 24*k^6*(7 - 2*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^2 + 16*k^4*(42 - 23*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^4 + 64*k^2*(14 - 11*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^6 - 384*(-1 + Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^8)/(16*k^7) + (7*k^8 + 24*k^6*(7 - 2*Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^2 + 16*k^4*(42 - 23*Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^4 + 64*k^2*(14 - 11*Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^6 - 384*(-1 + Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^8)/(48*k^7) - (7*k^8 + 24*k^6*(7 - 2*Sqrt[1 + k^2/(8*c - I*k0)^2])*(8*c - I*k0)^2 + 16*k^4*(42 - 23*Sqrt[1 + k^2/(8*c - I*k0)^2])*(8*c - I*k0)^4 + 64*k^2*(14 - 11*Sqrt[1 + k^2/(8*c - I*k0)^2])*(8*c - I*k0)^6 - 384*(-1 + Sqrt[1 + k^2/(8*c - I*k0)^2])*(8*c - I*k0)^8)/(336*k^7))/k0^3 -SeriesData[k, Infinity, {(10395*c^7)/k0^3, (-207360*c^8)/k0^3 + ((46080*I)*c^7)/k0^2, (45045*(125*c^9 - (54*I)*c^8*k0 - 6*c^7*k0^2))/(4*k0^3), 0, (-135135*(4819*c^11 - (3960*I)*c^10*k0 - 1250*c^9*k0^2 + (180*I)*c^8*k0^3 + 10*c^7*k0^4))/(16*k0^3)}, 6, 11, 1] diff --git a/besseltransforms/7-4-0 b/besseltransforms/7-4-0 deleted file mode 100644 index 38b67d7..0000000 --- a/besseltransforms/7-4-0 +++ /dev/null @@ -1,9 +0,0 @@ -Integrate[(E^(-(c*x) + I*k0*x)*(1 - E^(-(c*x)))^7*BesselJ[0, k*x])/(k0^4*x^3), {x, 0, Infinity}, Assumptions -> n == 0 && q == 4 && κ == 7 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0] - - -8 c x + I k0 x c x 7 2 2 4 4 6 6 8 8 Pi 2 2 4 4 6 6 8 8 - E (-1 + E ) ((-418854310875 + 29682132480 k x - 3901685760 k x + 1258291200 k x - 2147483648 k x ) Cos[-- + k x] + 4 Sqrt[2] k x (13043905875 - 1229437440 k x + 240844800 k x - 150994944 k x + 2147483648 k x ) (Cos[k x] + Sin[k x])) - 4 -Integrate::idiv: Integral of ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ does not converge on {0, Infinity}. - 19/2 4 25/2 - 8589934592 k k0 Sqrt[2 Pi] x -Series[Integrate[(E^(-(c*x) + I*k0*x)*(1 - E^(-(c*x)))^7*BesselJ[0, k*x])/(k0^4*x^3), {x, 0, Infinity}, Assumptions -> n == 0 && q == 4 && κ == 7 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0], {k, Infinity, 10}] diff --git a/besseltransforms/7-4-1 b/besseltransforms/7-4-1 deleted file mode 100644 index e1c52ce..0000000 --- a/besseltransforms/7-4-1 +++ /dev/null @@ -1,9 +0,0 @@ -Integrate[(E^(-(c*x) + I*k0*x)*(1 - E^(-(c*x)))^7*BesselJ[1, k*x])/(k0^4*x^3), {x, 0, Infinity}, Assumptions -> n == 1 && q == 4 && κ == 7 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0] - - -8 c x + I k0 x c x 7 2 2 4 4 6 6 8 8 Pi 2 2 4 4 6 6 8 8 Pi - -(E (-1 + E ) (8 k x (-14783093325 + 1452971520 k x - 309657600 k x + 251658240 k x + 2147483648 k x ) Cos[-- + k x] - 3 (156043762875 - 11416204800 k x + 1589575680 k x - 587202560 k x + 2147483648 k x ) Sin[-- + k x])) - 4 4 -Integrate::idiv: Integral of ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ does not converge on {0, Infinity}. - 19/2 4 25/2 - 8589934592 k k0 Sqrt[2 Pi] x -Series[Integrate[(E^(-(c*x) + I*k0*x)*(1 - E^(-(c*x)))^7*BesselJ[1, k*x])/(k0^4*x^3), {x, 0, Infinity}, Assumptions -> n == 1 && q == 4 && κ == 7 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0], {k, Infinity, 10}] diff --git a/besseltransforms/7-4-2 b/besseltransforms/7-4-2 deleted file mode 100644 index 58d2f5c..0000000 --- a/besseltransforms/7-4-2 +++ /dev/null @@ -1,9 +0,0 @@ -Integrate[(E^(-(c*x) + I*k0*x)*(1 - E^(-(c*x)))^7*BesselJ[2, k*x])/(k0^4*x^3), {x, 0, Infinity}, Assumptions -> n == 2 && q == 4 && κ == 7 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0] - - -8 c x + I k0 x c x 7 2 2 4 4 6 6 8 8 Pi 2 2 4 4 6 6 8 8 - -(E (-1 + E ) (15 (-43692253605 + 3528645120 k x - 590413824 k x + 352321536 k x + 2147483648 k x ) Cos[-- + k x] + 4 Sqrt[2] k x (21606059475 - 2421619200 k x + 681246720 k x - 1761607680 k x + 2147483648 k x ) (Cos[k x] + Sin[k x]))) - 4 -Integrate::idiv: Integral of --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- does not converge on {0, Infinity}. - 19/2 4 25/2 - 8589934592 k k0 Sqrt[2 Pi] x -Series[Integrate[(E^(-(c*x) + I*k0*x)*(1 - E^(-(c*x)))^7*BesselJ[2, k*x])/(k0^4*x^3), {x, 0, Infinity}, Assumptions -> n == 2 && q == 4 && κ == 7 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0], {k, Infinity, 10}] diff --git a/besseltransforms/7-4-3 b/besseltransforms/7-4-3 deleted file mode 100644 index 55566eb..0000000 --- a/besseltransforms/7-4-3 +++ /dev/null @@ -1,2 +0,0 @@ -((k^4*(-15 + 8*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0) + 4*k^2*(-5 + 4*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^3 + 8*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^5)/(120*k^3) - (7*(k^4*(-15 + 8*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0) + 4*k^2*(-5 + 4*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^3 + 8*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^5))/(120*k^3) + (7*(k^4*(-15 + 8*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0) + 4*k^2*(-5 + 4*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^3 + 8*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^5))/(40*k^3) - (7*(k^4*(-15 + 8*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0) + 4*k^2*(-5 + 4*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^3 + 8*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^5))/(24*k^3) + (7*(k^4*(-15 + 8*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0) + 4*k^2*(-5 + 4*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^3 + 8*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^5))/(24*k^3) - (7*(k^4*(-15 + 8*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0) + 4*k^2*(-5 + 4*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^3 + 8*(-1 + Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^5))/(40*k^3) + (7*(k^4*(-15 + 8*Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0) + 4*k^2*(-5 + 4*Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^3 + 8*(-1 + Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^5))/(120*k^3) - (k^4*(-15 + 8*Sqrt[1 + k^2/(8*c - I*k0)^2])*(8*c - I*k0) + 4*k^2*(-5 + 4*Sqrt[1 + k^2/(8*c - I*k0)^2])*(8*c - I*k0)^3 + 8*(-1 + Sqrt[1 + k^2/(8*c - I*k0)^2])*(8*c - I*k0)^5)/(120*k^3))/k0^4 -SeriesData[k, Infinity, {(945*c^8)/(2*k0^4) - ((105*I)*c^7)/k0^3, 0, (-945*(198*c^10 - (125*I)*c^9*k0 - 27*c^8*k0^2 + (2*I)*c^7*k0^3))/(4*k0^4), 0, (3465*(14391*c^12 - (14457*I)*c^11*k0 - 5940*c^10*k0^2 + (1250*I)*c^9*k0^3 + 135*c^8*k0^4 - (6*I)*c^7*k0^5))/(16*k0^4)}, 6, 11, 1] diff --git a/besseltransforms/7-4-4 b/besseltransforms/7-4-4 deleted file mode 100644 index 89e1c6c..0000000 --- a/besseltransforms/7-4-4 +++ /dev/null @@ -1,2 +0,0 @@ -((5*k^6 + 2*k^4*(15 - 8*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^2 + 8*k^2*(5 - 4*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^4 - 16*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^6)/(240*k^4) - (7*(5*k^6 + 2*k^4*(15 - 8*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^2 + 8*k^2*(5 - 4*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^4 - 16*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^6))/(240*k^4) + (7*(5*k^6 + 2*k^4*(15 - 8*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^2 + 8*k^2*(5 - 4*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^4 - 16*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^6))/(80*k^4) - (7*(5*k^6 + 2*k^4*(15 - 8*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^2 + 8*k^2*(5 - 4*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^4 - 16*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^6))/(48*k^4) + (7*(5*k^6 + 2*k^4*(15 - 8*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^2 + 8*k^2*(5 - 4*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^4 - 16*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^6))/(48*k^4) - (7*(5*k^6 + 2*k^4*(15 - 8*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^2 + 8*k^2*(5 - 4*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^4 - 16*(-1 + Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^6))/(80*k^4) + (7*(5*k^6 + 2*k^4*(15 - 8*Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^2 + 8*k^2*(5 - 4*Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^4 - 16*(-1 + Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^6))/(240*k^4) - (5*k^6 + 2*k^4*(15 - 8*Sqrt[1 + k^2/(8*c - I*k0)^2])*(8*c - I*k0)^2 + 8*k^2*(5 - 4*Sqrt[1 + k^2/(8*c - I*k0)^2])*(8*c - I*k0)^4 - 16*(-1 + Sqrt[1 + k^2/(8*c - I*k0)^2])*(8*c - I*k0)^6)/(240*k^4))/k0^4 -SeriesData[k, Infinity, {(105*c^7)/k0^4, 0, (-315*(125*c^9 - (54*I)*c^8*k0 - 6*c^7*k0^2))/(4*k0^4), 0, (2079*(4819*c^11 - (3960*I)*c^10*k0 - 1250*c^9*k0^2 + (180*I)*c^8*k0^3 + 10*c^7*k0^4))/(16*k0^4)}, 5, 11, 1] diff --git a/besseltransforms/7-4-5 b/besseltransforms/7-4-5 deleted file mode 100644 index 090ee13..0000000 --- a/besseltransforms/7-4-5 +++ /dev/null @@ -1,2 +0,0 @@ -((k^6*(-35 + 8*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0) + 20*k^4*(-7 + 4*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^3 + 8*k^2*(-21 + 17*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^5 + 64*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^7)/(840*k^5) - (k^6*(-35 + 8*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0) + 20*k^4*(-7 + 4*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^3 + 8*k^2*(-21 + 17*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^5 + 64*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^7)/(120*k^5) + (k^6*(-35 + 8*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0) + 20*k^4*(-7 + 4*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^3 + 8*k^2*(-21 + 17*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^5 + 64*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^7)/(40*k^5) - (k^6*(-35 + 8*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0) + 20*k^4*(-7 + 4*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^3 + 8*k^2*(-21 + 17*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^5 + 64*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^7)/(24*k^5) + (k^6*(-35 + 8*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0) + 20*k^4*(-7 + 4*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^3 + 8*k^2*(-21 + 17*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^5 + 64*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^7)/(24*k^5) - (k^6*(-35 + 8*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0) + 20*k^4*(-7 + 4*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^3 + 8*k^2*(-21 + 17*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^5 + 64*(-1 + Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^7)/(40*k^5) + (k^6*(-35 + 8*Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0) + 20*k^4*(-7 + 4*Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^3 + 8*k^2*(-21 + 17*Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^5 + 64*(-1 + Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^7)/(120*k^5) - (k^6*(-35 + 8*Sqrt[1 + k^2/(8*c - I*k0)^2])*(8*c - I*k0) + 20*k^4*(-7 + 4*Sqrt[1 + k^2/(8*c - I*k0)^2])*(8*c - I*k0)^3 + 8*k^2*(-21 + 17*Sqrt[1 + k^2/(8*c - I*k0)^2])*(8*c - I*k0)^5 + 64*(-1 + Sqrt[1 + k^2/(8*c - I*k0)^2])*(8*c - I*k0)^7)/(840*k^5))/k0^4 -SeriesData[k, Infinity, {(384*c^7)/k0^4, (-8505*c^8)/(2*k0^4) + ((945*I)*c^7)/k0^3, 0, (3465*(198*c^10 - (125*I)*c^9*k0 - 27*c^8*k0^2 + (2*I)*c^7*k0^3))/(4*k0^4), 0, (-9009*(14391*c^12 - (14457*I)*c^11*k0 - 5940*c^10*k0^2 + (1250*I)*c^9*k0^3 + 135*c^8*k0^4 - (6*I)*c^7*k0^5))/(16*k0^4)}, 5, 11, 1] diff --git a/besseltransforms/7-4-6 b/besseltransforms/7-4-6 deleted file mode 100644 index c8a5a4d..0000000 --- a/besseltransforms/7-4-6 +++ /dev/null @@ -1,2 +0,0 @@ -((35*k^8 + 16*k^6*(35 - 12*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^2 + 16*k^4*(105 - 64*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^4 + 64*k^2*(28 - 23*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^6 - 640*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^8)/(6720*k^6) - (35*k^8 + 16*k^6*(35 - 12*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^2 + 16*k^4*(105 - 64*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^4 + 64*k^2*(28 - 23*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^6 - 640*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^8)/(960*k^6) + (35*k^8 + 16*k^6*(35 - 12*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^2 + 16*k^4*(105 - 64*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^4 + 64*k^2*(28 - 23*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^6 - 640*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^8)/(320*k^6) - (35*k^8 + 16*k^6*(35 - 12*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^2 + 16*k^4*(105 - 64*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^4 + 64*k^2*(28 - 23*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^6 - 640*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^8)/(192*k^6) + (35*k^8 + 16*k^6*(35 - 12*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^2 + 16*k^4*(105 - 64*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^4 + 64*k^2*(28 - 23*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^6 - 640*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^8)/(192*k^6) - (35*k^8 + 16*k^6*(35 - 12*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^2 + 16*k^4*(105 - 64*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^4 + 64*k^2*(28 - 23*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^6 - 640*(-1 + Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^8)/(320*k^6) + (35*k^8 + 16*k^6*(35 - 12*Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^2 + 16*k^4*(105 - 64*Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^4 + 64*k^2*(28 - 23*Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^6 - 640*(-1 + Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^8)/(960*k^6) - (35*k^8 + 16*k^6*(35 - 12*Sqrt[1 + k^2/(8*c - I*k0)^2])*(8*c - I*k0)^2 + 16*k^4*(105 - 64*Sqrt[1 + k^2/(8*c - I*k0)^2])*(8*c - I*k0)^4 + 64*k^2*(28 - 23*Sqrt[1 + k^2/(8*c - I*k0)^2])*(8*c - I*k0)^6 - 640*(-1 + Sqrt[1 + k^2/(8*c - I*k0)^2])*(8*c - I*k0)^8)/(6720*k^6))/k0^4 -SeriesData[k, Infinity, {(945*c^7)/k0^4, (-17280*c^8)/k0^4 + ((3840*I)*c^7)/k0^3, (3465*(125*c^9 - (54*I)*c^8*k0 - 6*c^7*k0^2))/(4*k0^4), 0, (-9009*(4819*c^11 - (3960*I)*c^10*k0 - 1250*c^9*k0^2 + (180*I)*c^8*k0^3 + 10*c^7*k0^4))/(16*k0^4)}, 5, 11, 1] diff --git a/besseltransforms/7-4-7 b/besseltransforms/7-4-7 deleted file mode 100644 index 569ec89..0000000 --- a/besseltransforms/7-4-7 +++ /dev/null @@ -1,2 +0,0 @@ -((k^8*(-105 + 16*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0) + 8*k^6*(-105 + 44*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^3 + 144*k^4*(-14 + 9*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^5 + 320*k^2*(-6 + 5*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^7 + 640*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^9)/(5040*k^7) - (k^8*(-105 + 16*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0) + 8*k^6*(-105 + 44*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^3 + 144*k^4*(-14 + 9*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^5 + 320*k^2*(-6 + 5*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^7 + 640*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^9)/(720*k^7) + (k^8*(-105 + 16*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0) + 8*k^6*(-105 + 44*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^3 + 144*k^4*(-14 + 9*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^5 + 320*k^2*(-6 + 5*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^7 + 640*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^9)/(240*k^7) - (k^8*(-105 + 16*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0) + 8*k^6*(-105 + 44*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^3 + 144*k^4*(-14 + 9*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^5 + 320*k^2*(-6 + 5*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^7 + 640*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^9)/(144*k^7) + (k^8*(-105 + 16*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0) + 8*k^6*(-105 + 44*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^3 + 144*k^4*(-14 + 9*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^5 + 320*k^2*(-6 + 5*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^7 + 640*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^9)/(144*k^7) - (k^8*(-105 + 16*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0) + 8*k^6*(-105 + 44*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^3 + 144*k^4*(-14 + 9*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^5 + 320*k^2*(-6 + 5*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^7 + 640*(-1 + Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^9)/(240*k^7) + (k^8*(-105 + 16*Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0) + 8*k^6*(-105 + 44*Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^3 + 144*k^4*(-14 + 9*Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^5 + 320*k^2*(-6 + 5*Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^7 + 640*(-1 + Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^9)/(720*k^7) - (k^8*(-105 + 16*Sqrt[1 + k^2/(8*c - I*k0)^2])*(8*c - I*k0) + 8*k^6*(-105 + 44*Sqrt[1 + k^2/(8*c - I*k0)^2])*(8*c - I*k0)^3 + 144*k^4*(-14 + 9*Sqrt[1 + k^2/(8*c - I*k0)^2])*(8*c - I*k0)^5 + 320*k^2*(-6 + 5*Sqrt[1 + k^2/(8*c - I*k0)^2])*(8*c - I*k0)^7 + 640*(-1 + Sqrt[1 + k^2/(8*c - I*k0)^2])*(8*c - I*k0)^9)/(5040*k^7))/k0^4 -SeriesData[k, Infinity, {(1920*c^7)/k0^4, (-93555*c^8)/(2*k0^4) + ((10395*I)*c^7)/k0^3, (480000*c^9)/k0^4 - ((207360*I)*c^8)/k0^3 - (23040*c^7)/k0^2, (-45045*(198*c^10 - (125*I)*c^9*k0 - 27*c^8*k0^2 + (2*I)*c^7*k0^3))/(4*k0^4), 0, (45045*(14391*c^12 - (14457*I)*c^11*k0 - 5940*c^10*k0^2 + (1250*I)*c^9*k0^3 + 135*c^8*k0^4 - (6*I)*c^7*k0^5))/(16*k0^4)}, 5, 11, 1] diff --git a/besseltransforms/7-5-0 b/besseltransforms/7-5-0 deleted file mode 100644 index e69de29..0000000 diff --git a/besseltransforms/7-5-1 b/besseltransforms/7-5-1 deleted file mode 100644 index a0de589..0000000 --- a/besseltransforms/7-5-1 +++ /dev/null @@ -1,9 +0,0 @@ -Integrate[(E^(-(c*x) + I*k0*x)*(1 - E^(-(c*x)))^7*BesselJ[1, k*x])/(k0^5*x^4), {x, 0, Infinity}, Assumptions -> n == 1 && q == 5 && κ == 7 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0] - - -8 c x + I k0 x c x 7 2 2 4 4 6 6 8 8 Pi 2 2 4 4 6 6 8 8 Pi - -(E (-1 + E ) (8 k x (-14783093325 + 1452971520 k x - 309657600 k x + 251658240 k x + 2147483648 k x ) Cos[-- + k x] - 3 (156043762875 - 11416204800 k x + 1589575680 k x - 587202560 k x + 2147483648 k x ) Sin[-- + k x])) - 4 4 -Integrate::idiv: Integral of ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ does not converge on {0, Infinity}. - 19/2 5 27/2 - 8589934592 k k0 Sqrt[2 Pi] x -Series[Integrate[(E^(-(c*x) + I*k0*x)*(1 - E^(-(c*x)))^7*BesselJ[1, k*x])/(k0^5*x^4), {x, 0, Infinity}, Assumptions -> n == 1 && q == 5 && κ == 7 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0], {k, Infinity, 10}] diff --git a/besseltransforms/7-5-2 b/besseltransforms/7-5-2 deleted file mode 100644 index 1b22dae..0000000 --- a/besseltransforms/7-5-2 +++ /dev/null @@ -1,9 +0,0 @@ -Integrate[(E^(-(c*x) + I*k0*x)*(1 - E^(-(c*x)))^7*BesselJ[2, k*x])/(k0^5*x^4), {x, 0, Infinity}, Assumptions -> n == 2 && q == 5 && κ == 7 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0] - - -8 c x + I k0 x c x 7 2 2 4 4 6 6 8 8 Pi 2 2 4 4 6 6 8 8 - -(E (-1 + E ) (15 (-43692253605 + 3528645120 k x - 590413824 k x + 352321536 k x + 2147483648 k x ) Cos[-- + k x] + 4 Sqrt[2] k x (21606059475 - 2421619200 k x + 681246720 k x - 1761607680 k x + 2147483648 k x ) (Cos[k x] + Sin[k x]))) - 4 -Integrate::idiv: Integral of --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- does not converge on {0, Infinity}. - 19/2 5 27/2 - 8589934592 k k0 Sqrt[2 Pi] x -Series[Integrate[(E^(-(c*x) + I*k0*x)*(1 - E^(-(c*x)))^7*BesselJ[2, k*x])/(k0^5*x^4), {x, 0, Infinity}, Assumptions -> n == 2 && q == 5 && κ == 7 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0], {k, Infinity, 10}] diff --git a/besseltransforms/7-5-3 b/besseltransforms/7-5-3 deleted file mode 100644 index 772d6de..0000000 --- a/besseltransforms/7-5-3 +++ /dev/null @@ -1,10 +0,0 @@ -Integrate[(E^(-(c*x) + I*k0*x)*(1 - E^(-(c*x)))^7*BesselJ[3, k*x])/(k0^5*x^4), {x, 0, Infinity}, Assumptions -> n == 3 && q == 5 && κ == 7 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0] - - 2 2 4 4 6 6 8 8 - -8 c x + I k0 x c x 7 2 2 4 4 6 6 8 8 Pi 35 (33129291195 - 3192583680 k x + 759103488 k x - 1660944384 k x + 2147483648 k x ) (Cos[k x] + Sin[k x]) - E (-1 + E ) (8 k x (-41247931725 + 5881075200 k x - 2952069120 k x - 15854469120 k x + 2147483648 k x ) Cos[-- + k x] - -----------------------------------------------------------------------------------------------------------------) - 4 Sqrt[2] -Integrate::idiv: Integral of ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- does not converge on {0, Infinity}. - 19/2 5 27/2 - 8589934592 k k0 Sqrt[2 Pi] x -Series[Integrate[(E^(-(c*x) + I*k0*x)*(1 - E^(-(c*x)))^7*BesselJ[3, k*x])/(k0^5*x^4), {x, 0, Infinity}, Assumptions -> n == 3 && q == 5 && κ == 7 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0], {k, Infinity, 10}] diff --git a/besseltransforms/7-5-4 b/besseltransforms/7-5-4 deleted file mode 100644 index b8b1107..0000000 --- a/besseltransforms/7-5-4 +++ /dev/null @@ -1,2 +0,0 @@ -((k^6*(-35 + 16*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0) + 2*k^4*(-35 + 24*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^3 + 8*k^2*(-7 + 6*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^5 + 16*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^7)/(1680*k^4) - (k^6*(-35 + 16*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0) + 2*k^4*(-35 + 24*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^3 + 8*k^2*(-7 + 6*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^5 + 16*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^7)/(240*k^4) + (k^6*(-35 + 16*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0) + 2*k^4*(-35 + 24*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^3 + 8*k^2*(-7 + 6*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^5 + 16*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^7)/(80*k^4) - (k^6*(-35 + 16*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0) + 2*k^4*(-35 + 24*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^3 + 8*k^2*(-7 + 6*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^5 + 16*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^7)/(48*k^4) + (k^6*(-35 + 16*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0) + 2*k^4*(-35 + 24*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^3 + 8*k^2*(-7 + 6*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^5 + 16*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^7)/(48*k^4) - (k^6*(-35 + 16*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0) + 2*k^4*(-35 + 24*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^3 + 8*k^2*(-7 + 6*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^5 + 16*(-1 + Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^7)/(80*k^4) + (k^6*(-35 + 16*Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0) + 2*k^4*(-35 + 24*Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^3 + 8*k^2*(-7 + 6*Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^5 + 16*(-1 + Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^7)/(240*k^4) - (k^6*(-35 + 16*Sqrt[1 + k^2/(8*c - I*k0)^2])*(8*c - I*k0) + 2*k^4*(-35 + 24*Sqrt[1 + k^2/(8*c - I*k0)^2])*(8*c - I*k0)^3 + 8*k^2*(-7 + 6*Sqrt[1 + k^2/(8*c - I*k0)^2])*(8*c - I*k0)^5 + 16*(-1 + Sqrt[1 + k^2/(8*c - I*k0)^2])*(8*c - I*k0)^7)/(1680*k^4))/k0^5 -SeriesData[k, Infinity, {(48*c^7)/k0^5, (-945*c^8)/(2*k0^5) + ((105*I)*c^7)/k0^4, 0, (315*(198*c^10 - (125*I)*c^9*k0 - 27*c^8*k0^2 + (2*I)*c^7*k0^3))/(4*k0^5), 0, (-693*(14391*c^12 - (14457*I)*c^11*k0 - 5940*c^10*k0^2 + (1250*I)*c^9*k0^3 + 135*c^8*k0^4 - (6*I)*c^7*k0^5))/(16*k0^5)}, 4, 11, 1] diff --git a/besseltransforms/7-5-5 b/besseltransforms/7-5-5 deleted file mode 100644 index 997dca6..0000000 --- a/besseltransforms/7-5-5 +++ /dev/null @@ -1,2 +0,0 @@ -((35*k^8 + 8*k^6*(35 - 16*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^2 + 16*k^4*(35 - 24*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^4 + 64*k^2*(7 - 6*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^6 - 128*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^8)/(13440*k^5) - (35*k^8 + 8*k^6*(35 - 16*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^2 + 16*k^4*(35 - 24*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^4 + 64*k^2*(7 - 6*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^6 - 128*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^8)/(1920*k^5) + (35*k^8 + 8*k^6*(35 - 16*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^2 + 16*k^4*(35 - 24*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^4 + 64*k^2*(7 - 6*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^6 - 128*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^8)/(640*k^5) - (35*k^8 + 8*k^6*(35 - 16*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^2 + 16*k^4*(35 - 24*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^4 + 64*k^2*(7 - 6*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^6 - 128*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^8)/(384*k^5) + (35*k^8 + 8*k^6*(35 - 16*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^2 + 16*k^4*(35 - 24*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^4 + 64*k^2*(7 - 6*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^6 - 128*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^8)/(384*k^5) - (35*k^8 + 8*k^6*(35 - 16*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^2 + 16*k^4*(35 - 24*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^4 + 64*k^2*(7 - 6*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^6 - 128*(-1 + Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^8)/(640*k^5) + (35*k^8 + 8*k^6*(35 - 16*Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^2 + 16*k^4*(35 - 24*Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^4 + 64*k^2*(7 - 6*Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^6 - 128*(-1 + Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^8)/(1920*k^5) - (35*k^8 + 8*k^6*(35 - 16*Sqrt[1 + k^2/(8*c - I*k0)^2])*(8*c - I*k0)^2 + 16*k^4*(35 - 24*Sqrt[1 + k^2/(8*c - I*k0)^2])*(8*c - I*k0)^4 + 64*k^2*(7 - 6*Sqrt[1 + k^2/(8*c - I*k0)^2])*(8*c - I*k0)^6 - 128*(-1 + Sqrt[1 + k^2/(8*c - I*k0)^2])*(8*c - I*k0)^8)/(13440*k^5))/k0^5 -SeriesData[k, Infinity, {(105*c^7)/k0^5, (-1728*c^8)/k0^5 + ((384*I)*c^7)/k0^4, (315*(125*c^9 - (54*I)*c^8*k0 - 6*c^7*k0^2))/(4*k0^5), 0, (-693*(4819*c^11 - (3960*I)*c^10*k0 - 1250*c^9*k0^2 + (180*I)*c^8*k0^3 + 10*c^7*k0^4))/(16*k0^5), 0, (3003*(73120*c^13 - (86346*I)*c^12*k0 - 43371*c^11*k0^2 + (11880*I)*c^10*k0^3 + 1875*c^9*k0^4 - (162*I)*c^8*k0^5 - 6*c^7*k0^6))/(32*k0^5)}, 4, 11, 1] diff --git a/besseltransforms/7-5-6 b/besseltransforms/7-5-6 deleted file mode 100644 index 676c848..0000000 --- a/besseltransforms/7-5-6 +++ /dev/null @@ -1,2 +0,0 @@ -((k^8*(-315 + 64*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0) + 16*k^6*(-105 + 52*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^3 + 48*k^4*(-63 + 44*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^5 + 64*k^2*(-36 + 31*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^7 + 640*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^9)/(60480*k^6) - (k^8*(-315 + 64*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0) + 16*k^6*(-105 + 52*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^3 + 48*k^4*(-63 + 44*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^5 + 64*k^2*(-36 + 31*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^7 + 640*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^9)/(8640*k^6) + (k^8*(-315 + 64*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0) + 16*k^6*(-105 + 52*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^3 + 48*k^4*(-63 + 44*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^5 + 64*k^2*(-36 + 31*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^7 + 640*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^9)/(2880*k^6) - (k^8*(-315 + 64*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0) + 16*k^6*(-105 + 52*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^3 + 48*k^4*(-63 + 44*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^5 + 64*k^2*(-36 + 31*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^7 + 640*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^9)/(1728*k^6) + (k^8*(-315 + 64*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0) + 16*k^6*(-105 + 52*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^3 + 48*k^4*(-63 + 44*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^5 + 64*k^2*(-36 + 31*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^7 + 640*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^9)/(1728*k^6) - (k^8*(-315 + 64*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0) + 16*k^6*(-105 + 52*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^3 + 48*k^4*(-63 + 44*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^5 + 64*k^2*(-36 + 31*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^7 + 640*(-1 + Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^9)/(2880*k^6) + (k^8*(-315 + 64*Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0) + 16*k^6*(-105 + 52*Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^3 + 48*k^4*(-63 + 44*Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^5 + 64*k^2*(-36 + 31*Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^7 + 640*(-1 + Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^9)/(8640*k^6) - (k^8*(-315 + 64*Sqrt[1 + k^2/(8*c - I*k0)^2])*(8*c - I*k0) + 16*k^6*(-105 + 52*Sqrt[1 + k^2/(8*c - I*k0)^2])*(8*c - I*k0)^3 + 48*k^4*(-63 + 44*Sqrt[1 + k^2/(8*c - I*k0)^2])*(8*c - I*k0)^5 + 64*k^2*(-36 + 31*Sqrt[1 + k^2/(8*c - I*k0)^2])*(8*c - I*k0)^7 + 640*(-1 + Sqrt[1 + k^2/(8*c - I*k0)^2])*(8*c - I*k0)^9)/(60480*k^6))/k0^5 -SeriesData[k, Infinity, {(192*c^7)/k0^5, (-8505*c^8)/(2*k0^5) + ((945*I)*c^7)/k0^4, (40000*c^9)/k0^5 - ((17280*I)*c^8)/k0^4 - (1920*c^7)/k0^3, (-3465*(198*c^10 - (125*I)*c^9*k0 - 27*c^8*k0^2 + (2*I)*c^7*k0^3))/(4*k0^5), 0, (3003*(14391*c^12 - (14457*I)*c^11*k0 - 5940*c^10*k0^2 + (1250*I)*c^9*k0^3 + 135*c^8*k0^4 - (6*I)*c^7*k0^5))/(16*k0^5)}, 4, 11, 1] diff --git a/besseltransforms/7-5-7 b/besseltransforms/7-5-7 deleted file mode 100644 index fd58f5a..0000000 --- a/besseltransforms/7-5-7 +++ /dev/null @@ -1,2 +0,0 @@ -((21*k^10 + 4*k^8*(105 - 32*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^2 + 112*k^6*(15 - 8*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^4 + 384*k^4*(7 - 5*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^6 + 128*k^2*(15 - 13*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^8 - 512*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^10)/(40320*k^7) - (21*k^10 + 4*k^8*(105 - 32*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^2 + 112*k^6*(15 - 8*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^4 + 384*k^4*(7 - 5*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^6 + 128*k^2*(15 - 13*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^8 - 512*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^10)/(5760*k^7) + (21*k^10 + 4*k^8*(105 - 32*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^2 + 112*k^6*(15 - 8*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^4 + 384*k^4*(7 - 5*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^6 + 128*k^2*(15 - 13*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^8 - 512*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^10)/(1920*k^7) - (21*k^10 + 4*k^8*(105 - 32*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^2 + 112*k^6*(15 - 8*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^4 + 384*k^4*(7 - 5*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^6 + 128*k^2*(15 - 13*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^8 - 512*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^10)/(1152*k^7) + (21*k^10 + 4*k^8*(105 - 32*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^2 + 112*k^6*(15 - 8*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^4 + 384*k^4*(7 - 5*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^6 + 128*k^2*(15 - 13*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^8 - 512*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^10)/(1152*k^7) - (21*k^10 + 4*k^8*(105 - 32*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^2 + 112*k^6*(15 - 8*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^4 + 384*k^4*(7 - 5*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^6 + 128*k^2*(15 - 13*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^8 - 512*(-1 + Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^10)/(1920*k^7) + (21*k^10 + 4*k^8*(105 - 32*Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^2 + 112*k^6*(15 - 8*Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^4 + 384*k^4*(7 - 5*Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^6 + 128*k^2*(15 - 13*Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^8 - 512*(-1 + Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^10)/(5760*k^7) - (21*k^10 + 4*k^8*(105 - 32*Sqrt[1 + k^2/(8*c - I*k0)^2])*(8*c - I*k0)^2 + 112*k^6*(15 - 8*Sqrt[1 + k^2/(8*c - I*k0)^2])*(8*c - I*k0)^4 + 384*k^4*(7 - 5*Sqrt[1 + k^2/(8*c - I*k0)^2])*(8*c - I*k0)^6 + 128*k^2*(15 - 13*Sqrt[1 + k^2/(8*c - I*k0)^2])*(8*c - I*k0)^8 - 512*(-1 + Sqrt[1 + k^2/(8*c - I*k0)^2])*(8*c - I*k0)^10)/(40320*k^7))/k0^5 -SeriesData[k, Infinity, {(315*c^7)/k0^5, (-8640*c^8)/k0^5 + ((1920*I)*c^7)/k0^4, (3465*(125*c^9 - (54*I)*c^8*k0 - 6*c^7*k0^2))/(4*k0^5), (-760320*c^10)/k0^5 + ((480000*I)*c^9)/k0^4 + (103680*c^8)/k0^3 - ((7680*I)*c^7)/k0^2, (9009*(4819*c^11 - (3960*I)*c^10*k0 - 1250*c^9*k0^2 + (180*I)*c^8*k0^3 + 10*c^7*k0^4))/(16*k0^5), 0, (-15015*(73120*c^13 - (86346*I)*c^12*k0 - 43371*c^11*k0^2 + (11880*I)*c^10*k0^3 + 1875*c^9*k0^4 - (162*I)*c^8*k0^5 - 6*c^7*k0^6))/(32*k0^5)}, 4, 11, 1] diff --git a/besseltransforms/7-6-0 b/besseltransforms/7-6-0 deleted file mode 100644 index 200acc1..0000000 --- a/besseltransforms/7-6-0 +++ /dev/null @@ -1,9 +0,0 @@ -Integrate[(E^(-(c*x) + I*k0*x)*(1 - E^(-(c*x)))^7*BesselJ[0, k*x])/(k0^6*x^5), {x, 0, Infinity}, Assumptions -> n == 0 && q == 6 && κ == 7 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0] - - -8 c x + I k0 x c x 7 2 2 4 4 6 6 8 8 Pi 2 2 4 4 6 6 8 8 - E (-1 + E ) ((-418854310875 + 29682132480 k x - 3901685760 k x + 1258291200 k x - 2147483648 k x ) Cos[-- + k x] + 4 Sqrt[2] k x (13043905875 - 1229437440 k x + 240844800 k x - 150994944 k x + 2147483648 k x ) (Cos[k x] + Sin[k x])) - 4 -Integrate::idiv: Integral of ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ does not converge on {0, Infinity}. - 19/2 6 29/2 - 8589934592 k k0 Sqrt[2 Pi] x -Series[Integrate[(E^(-(c*x) + I*k0*x)*(1 - E^(-(c*x)))^7*BesselJ[0, k*x])/(k0^6*x^5), {x, 0, Infinity}, Assumptions -> n == 0 && q == 6 && κ == 7 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0], {k, Infinity, 10}] diff --git a/besseltransforms/7-6-1 b/besseltransforms/7-6-1 deleted file mode 100644 index f11cdca..0000000 --- a/besseltransforms/7-6-1 +++ /dev/null @@ -1,9 +0,0 @@ -Integrate[(E^(-(c*x) + I*k0*x)*(1 - E^(-(c*x)))^7*BesselJ[1, k*x])/(k0^6*x^5), {x, 0, Infinity}, Assumptions -> n == 1 && q == 6 && κ == 7 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0] - - -8 c x + I k0 x c x 7 2 2 4 4 6 6 8 8 Pi 2 2 4 4 6 6 8 8 Pi - -(E (-1 + E ) (8 k x (-14783093325 + 1452971520 k x - 309657600 k x + 251658240 k x + 2147483648 k x ) Cos[-- + k x] - 3 (156043762875 - 11416204800 k x + 1589575680 k x - 587202560 k x + 2147483648 k x ) Sin[-- + k x])) - 4 4 -Integrate::idiv: Integral of ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ does not converge on {0, Infinity}. - 19/2 6 29/2 - 8589934592 k k0 Sqrt[2 Pi] x -Series[Integrate[(E^(-(c*x) + I*k0*x)*(1 - E^(-(c*x)))^7*BesselJ[1, k*x])/(k0^6*x^5), {x, 0, Infinity}, Assumptions -> n == 1 && q == 6 && κ == 7 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0], {k, Infinity, 10}] diff --git a/besseltransforms/7-6-2 b/besseltransforms/7-6-2 deleted file mode 100644 index 2dcbcd8..0000000 --- a/besseltransforms/7-6-2 +++ /dev/null @@ -1,9 +0,0 @@ -Integrate[(E^(-(c*x) + I*k0*x)*(1 - E^(-(c*x)))^7*BesselJ[2, k*x])/(k0^6*x^5), {x, 0, Infinity}, Assumptions -> n == 2 && q == 6 && κ == 7 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0] - - -8 c x + I k0 x c x 7 2 2 4 4 6 6 8 8 Pi 2 2 4 4 6 6 8 8 - -(E (-1 + E ) (15 (-43692253605 + 3528645120 k x - 590413824 k x + 352321536 k x + 2147483648 k x ) Cos[-- + k x] + 4 Sqrt[2] k x (21606059475 - 2421619200 k x + 681246720 k x - 1761607680 k x + 2147483648 k x ) (Cos[k x] + Sin[k x]))) - 4 -Integrate::idiv: Integral of --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- does not converge on {0, Infinity}. - 19/2 6 29/2 - 8589934592 k k0 Sqrt[2 Pi] x -Series[Integrate[(E^(-(c*x) + I*k0*x)*(1 - E^(-(c*x)))^7*BesselJ[2, k*x])/(k0^6*x^5), {x, 0, Infinity}, Assumptions -> n == 2 && q == 6 && κ == 7 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0], {k, Infinity, 10}] diff --git a/besseltransforms/7-6-3 b/besseltransforms/7-6-3 deleted file mode 100644 index 72779e9..0000000 --- a/besseltransforms/7-6-3 +++ /dev/null @@ -1,10 +0,0 @@ -Integrate[(E^(-(c*x) + I*k0*x)*(1 - E^(-(c*x)))^7*BesselJ[3, k*x])/(k0^6*x^5), {x, 0, Infinity}, Assumptions -> n == 3 && q == 6 && κ == 7 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0] - - 2 2 4 4 6 6 8 8 - -8 c x + I k0 x c x 7 2 2 4 4 6 6 8 8 Pi 35 (33129291195 - 3192583680 k x + 759103488 k x - 1660944384 k x + 2147483648 k x ) (Cos[k x] + Sin[k x]) - E (-1 + E ) (8 k x (-41247931725 + 5881075200 k x - 2952069120 k x - 15854469120 k x + 2147483648 k x ) Cos[-- + k x] - -----------------------------------------------------------------------------------------------------------------) - 4 Sqrt[2] -Integrate::idiv: Integral of ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- does not converge on {0, Infinity}. - 19/2 6 29/2 - 8589934592 k k0 Sqrt[2 Pi] x -Series[Integrate[(E^(-(c*x) + I*k0*x)*(1 - E^(-(c*x)))^7*BesselJ[3, k*x])/(k0^6*x^5), {x, 0, Infinity}, Assumptions -> n == 3 && q == 6 && κ == 7 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0], {k, Infinity, 10}] diff --git a/besseltransforms/7-6-4 b/besseltransforms/7-6-4 deleted file mode 100644 index 4d79144..0000000 --- a/besseltransforms/7-6-4 +++ /dev/null @@ -1,9 +0,0 @@ -Integrate[(E^(-(c*x) + I*k0*x)*(1 - E^(-(c*x)))^7*BesselJ[4, k*x])/(k0^6*x^5), {x, 0, Infinity}, Assumptions -> n == 4 && q == 6 && κ == 7 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0] - - -8 c x + I k0 x c x 7 2 2 4 4 6 6 8 8 Pi 2 2 4 4 6 6 8 8 - E (-1 + E ) (63 (-41829913125 + 5320972800 k x - 2389770240 k x - 11995709440 k x + 2147483648 k x ) Cos[-- + k x] + 4 Sqrt[2] k x (105411381075 - 22348085760 k x + 44281036800 k x - 58133053440 k x + 2147483648 k x ) (Cos[k x] + Sin[k x])) - 4 -Integrate::idiv: Integral of -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- does not converge on {0, Infinity}. - 19/2 6 29/2 - 8589934592 k k0 Sqrt[2 Pi] x -Series[Integrate[(E^(-(c*x) + I*k0*x)*(1 - E^(-(c*x)))^7*BesselJ[4, k*x])/(k0^6*x^5), {x, 0, Infinity}, Assumptions -> n == 4 && q == 6 && κ == 7 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0], {k, Infinity, 10}] diff --git a/besseltransforms/7-6-5 b/besseltransforms/7-6-5 deleted file mode 100644 index 04e35d5..0000000 --- a/besseltransforms/7-6-5 +++ /dev/null @@ -1,2 +0,0 @@ -((k^8*(-315 + 128*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0) + 8*k^6*(-105 + 64*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^3 + 48*k^4*(-21 + 16*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^5 + 64*k^2*(-9 + 8*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^7 + 128*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^9)/(120960*k^5) - (k^8*(-315 + 128*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0) + 8*k^6*(-105 + 64*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^3 + 48*k^4*(-21 + 16*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^5 + 64*k^2*(-9 + 8*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^7 + 128*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^9)/(17280*k^5) + (k^8*(-315 + 128*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0) + 8*k^6*(-105 + 64*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^3 + 48*k^4*(-21 + 16*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^5 + 64*k^2*(-9 + 8*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^7 + 128*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^9)/(5760*k^5) - (k^8*(-315 + 128*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0) + 8*k^6*(-105 + 64*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^3 + 48*k^4*(-21 + 16*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^5 + 64*k^2*(-9 + 8*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^7 + 128*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^9)/(3456*k^5) + (k^8*(-315 + 128*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0) + 8*k^6*(-105 + 64*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^3 + 48*k^4*(-21 + 16*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^5 + 64*k^2*(-9 + 8*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^7 + 128*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^9)/(3456*k^5) - (k^8*(-315 + 128*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0) + 8*k^6*(-105 + 64*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^3 + 48*k^4*(-21 + 16*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^5 + 64*k^2*(-9 + 8*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^7 + 128*(-1 + Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^9)/(5760*k^5) + (k^8*(-315 + 128*Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0) + 8*k^6*(-105 + 64*Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^3 + 48*k^4*(-21 + 16*Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^5 + 64*k^2*(-9 + 8*Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^7 + 128*(-1 + Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^9)/(17280*k^5) - (k^8*(-315 + 128*Sqrt[1 + k^2/(8*c - I*k0)^2])*(8*c - I*k0) + 8*k^6*(-105 + 64*Sqrt[1 + k^2/(8*c - I*k0)^2])*(8*c - I*k0)^3 + 48*k^4*(-21 + 16*Sqrt[1 + k^2/(8*c - I*k0)^2])*(8*c - I*k0)^5 + 64*k^2*(-9 + 8*Sqrt[1 + k^2/(8*c - I*k0)^2])*(8*c - I*k0)^7 + 128*(-1 + Sqrt[1 + k^2/(8*c - I*k0)^2])*(8*c - I*k0)^9)/(120960*k^5))/k0^6 -SeriesData[k, Infinity, {(24*c^7)/k0^6, (-945*c^8)/(2*k0^6) + ((105*I)*c^7)/k0^5, (4000*c^9)/k0^6 - ((1728*I)*c^8)/k0^5 - (192*c^7)/k0^4, (-315*(198*c^10 - (125*I)*c^9*k0 - 27*c^8*k0^2 + (2*I)*c^7*k0^3))/(4*k0^6), 0, (231*(14391*c^12 - (14457*I)*c^11*k0 - 5940*c^10*k0^2 + (1250*I)*c^9*k0^3 + 135*c^8*k0^4 - (6*I)*c^7*k0^5))/(16*k0^6), 0, (-429*(378720*c^14 - (511840*I)*c^13*k0 - 302211*c^12*k0^2 + (101199*I)*c^11*k0^3 + 20790*c^10*k0^4 - (2625*I)*c^9*k0^5 - 189*c^8*k0^6 + (6*I)*c^7*k0^7))/(32*k0^6)}, 3, 11, 1] diff --git a/besseltransforms/7-6-6 b/besseltransforms/7-6-6 deleted file mode 100644 index 80f7f8d..0000000 --- a/besseltransforms/7-6-6 +++ /dev/null @@ -1,2 +0,0 @@ -((63*k^10 + 2*k^8*(315 - 128*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^2 + 16*k^6*(105 - 64*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^4 + 96*k^4*(21 - 16*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^6 + 128*k^2*(9 - 8*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^8 - 256*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^10)/(241920*k^6) - (63*k^10 + 2*k^8*(315 - 128*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^2 + 16*k^6*(105 - 64*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^4 + 96*k^4*(21 - 16*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^6 + 128*k^2*(9 - 8*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^8 - 256*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^10)/(34560*k^6) + (63*k^10 + 2*k^8*(315 - 128*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^2 + 16*k^6*(105 - 64*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^4 + 96*k^4*(21 - 16*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^6 + 128*k^2*(9 - 8*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^8 - 256*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^10)/(11520*k^6) - (63*k^10 + 2*k^8*(315 - 128*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^2 + 16*k^6*(105 - 64*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^4 + 96*k^4*(21 - 16*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^6 + 128*k^2*(9 - 8*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^8 - 256*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^10)/(6912*k^6) + (63*k^10 + 2*k^8*(315 - 128*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^2 + 16*k^6*(105 - 64*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^4 + 96*k^4*(21 - 16*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^6 + 128*k^2*(9 - 8*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^8 - 256*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^10)/(6912*k^6) - (63*k^10 + 2*k^8*(315 - 128*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^2 + 16*k^6*(105 - 64*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^4 + 96*k^4*(21 - 16*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^6 + 128*k^2*(9 - 8*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^8 - 256*(-1 + Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^10)/(11520*k^6) + (63*k^10 + 2*k^8*(315 - 128*Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^2 + 16*k^6*(105 - 64*Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^4 + 96*k^4*(21 - 16*Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^6 + 128*k^2*(9 - 8*Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^8 - 256*(-1 + Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^10)/(34560*k^6) - (63*k^10 + 2*k^8*(315 - 128*Sqrt[1 + k^2/(8*c - I*k0)^2])*(8*c - I*k0)^2 + 16*k^6*(105 - 64*Sqrt[1 + k^2/(8*c - I*k0)^2])*(8*c - I*k0)^4 + 96*k^4*(21 - 16*Sqrt[1 + k^2/(8*c - I*k0)^2])*(8*c - I*k0)^6 + 128*k^2*(9 - 8*Sqrt[1 + k^2/(8*c - I*k0)^2])*(8*c - I*k0)^8 - 256*(-1 + Sqrt[1 + k^2/(8*c - I*k0)^2])*(8*c - I*k0)^10)/(241920*k^6))/k0^6 -SeriesData[k, Infinity, {(35*c^7)/k0^6, (-864*c^8)/k0^6 + ((192*I)*c^7)/k0^5, (315*(125*c^9 - (54*I)*c^8*k0 - 6*c^7*k0^2))/(4*k0^6), (-63360*c^10)/k0^6 + ((40000*I)*c^9)/k0^5 + (8640*c^8)/k0^4 - ((640*I)*c^7)/k0^3, (693*(4819*c^11 - (3960*I)*c^10*k0 - 1250*c^9*k0^2 + (180*I)*c^8*k0^3 + 10*c^7*k0^4))/(16*k0^6), 0, (-1001*(73120*c^13 - (86346*I)*c^12*k0 - 43371*c^11*k0^2 + (11880*I)*c^10*k0^3 + 1875*c^9*k0^4 - (162*I)*c^8*k0^5 - 6*c^7*k0^6))/(32*k0^6)}, 3, 11, 1] diff --git a/besseltransforms/7-6-7 b/besseltransforms/7-6-7 deleted file mode 100644 index d9750be..0000000 --- a/besseltransforms/7-6-7 +++ /dev/null @@ -1,2 +0,0 @@ -((k^10*(-693 + 128*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0) + 4*k^8*(-1155 + 512*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^3 + 144*k^6*(-77 + 48*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^5 + 128*k^4*(-99 + 76*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^7 + 128*k^2*(-55 + 49*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^9 + 1536*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^11)/(1330560*k^7) - (k^10*(-693 + 128*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0) + 4*k^8*(-1155 + 512*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^3 + 144*k^6*(-77 + 48*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^5 + 128*k^4*(-99 + 76*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^7 + 128*k^2*(-55 + 49*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^9 + 1536*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^11)/(190080*k^7) + (k^10*(-693 + 128*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0) + 4*k^8*(-1155 + 512*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^3 + 144*k^6*(-77 + 48*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^5 + 128*k^4*(-99 + 76*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^7 + 128*k^2*(-55 + 49*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^9 + 1536*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^11)/(63360*k^7) - (k^10*(-693 + 128*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0) + 4*k^8*(-1155 + 512*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^3 + 144*k^6*(-77 + 48*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^5 + 128*k^4*(-99 + 76*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^7 + 128*k^2*(-55 + 49*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^9 + 1536*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^11)/(38016*k^7) + (k^10*(-693 + 128*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0) + 4*k^8*(-1155 + 512*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^3 + 144*k^6*(-77 + 48*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^5 + 128*k^4*(-99 + 76*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^7 + 128*k^2*(-55 + 49*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^9 + 1536*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^11)/(38016*k^7) - (k^10*(-693 + 128*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0) + 4*k^8*(-1155 + 512*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^3 + 144*k^6*(-77 + 48*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^5 + 128*k^4*(-99 + 76*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^7 + 128*k^2*(-55 + 49*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^9 + 1536*(-1 + Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^11)/(63360*k^7) + (k^10*(-693 + 128*Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0) + 4*k^8*(-1155 + 512*Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^3 + 144*k^6*(-77 + 48*Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^5 + 128*k^4*(-99 + 76*Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^7 + 128*k^2*(-55 + 49*Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^9 + 1536*(-1 + Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^11)/(190080*k^7) - (k^10*(-693 + 128*Sqrt[1 + k^2/(8*c - I*k0)^2])*(8*c - I*k0) + 4*k^8*(-1155 + 512*Sqrt[1 + k^2/(8*c - I*k0)^2])*(8*c - I*k0)^3 + 144*k^6*(-77 + 48*Sqrt[1 + k^2/(8*c - I*k0)^2])*(8*c - I*k0)^5 + 128*k^4*(-99 + 76*Sqrt[1 + k^2/(8*c - I*k0)^2])*(8*c - I*k0)^7 + 128*k^2*(-55 + 49*Sqrt[1 + k^2/(8*c - I*k0)^2])*(8*c - I*k0)^9 + 1536*(-1 + Sqrt[1 + k^2/(8*c - I*k0)^2])*(8*c - I*k0)^11)/(1330560*k^7))/k0^6 -SeriesData[k, Infinity, {(48*c^7)/k0^6, (-2835*c^8)/(2*k0^6) + ((315*I)*c^7)/k0^5, (20000*c^9)/k0^6 - ((8640*I)*c^8)/k0^5 - (960*c^7)/k0^4, (-3465*(198*c^10 - (125*I)*c^9*k0 - 27*c^8*k0^2 + (2*I)*c^7*k0^3))/(4*k0^6), (925248*c^11)/k0^6 - ((760320*I)*c^10)/k0^5 - (240000*c^9)/k0^4 + ((34560*I)*c^8)/k0^3 + (1920*c^7)/k0^2, (-3003*(14391*c^12 - (14457*I)*c^11*k0 - 5940*c^10*k0^2 + (1250*I)*c^9*k0^3 + 135*c^8*k0^4 - (6*I)*c^7*k0^5))/(16*k0^6), 0, (2145*(378720*c^14 - (511840*I)*c^13*k0 - 302211*c^12*k0^2 + (101199*I)*c^11*k0^3 + 20790*c^10*k0^4 - (2625*I)*c^9*k0^5 - 189*c^8*k0^6 + (6*I)*c^7*k0^7))/(32*k0^6)}, 3, 11, 1] diff --git a/besseltransforms/7-7-0 b/besseltransforms/7-7-0 deleted file mode 100644 index 78ce17e..0000000 --- a/besseltransforms/7-7-0 +++ /dev/null @@ -1,9 +0,0 @@ -Integrate[(E^(-(c*x) + I*k0*x)*(1 - E^(-(c*x)))^7*BesselJ[0, k*x])/(k0^7*x^6), {x, 0, Infinity}, Assumptions -> n == 0 && q == 7 && κ == 7 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0] - - -8 c x + I k0 x c x 7 2 2 4 4 6 6 8 8 Pi 2 2 4 4 6 6 8 8 - E (-1 + E ) ((-418854310875 + 29682132480 k x - 3901685760 k x + 1258291200 k x - 2147483648 k x ) Cos[-- + k x] + 4 Sqrt[2] k x (13043905875 - 1229437440 k x + 240844800 k x - 150994944 k x + 2147483648 k x ) (Cos[k x] + Sin[k x])) - 4 -Integrate::idiv: Integral of ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ does not converge on {0, Infinity}. - 19/2 7 31/2 - 8589934592 k k0 Sqrt[2 Pi] x -Series[Integrate[(E^(-(c*x) + I*k0*x)*(1 - E^(-(c*x)))^7*BesselJ[0, k*x])/(k0^7*x^6), {x, 0, Infinity}, Assumptions -> n == 0 && q == 7 && κ == 7 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0], {k, Infinity, 10}] diff --git a/besseltransforms/7-7-1 b/besseltransforms/7-7-1 deleted file mode 100644 index 94b1305..0000000 --- a/besseltransforms/7-7-1 +++ /dev/null @@ -1,9 +0,0 @@ -Integrate[(E^(-(c*x) + I*k0*x)*(1 - E^(-(c*x)))^7*BesselJ[1, k*x])/(k0^7*x^6), {x, 0, Infinity}, Assumptions -> n == 1 && q == 7 && κ == 7 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0] - - -8 c x + I k0 x c x 7 2 2 4 4 6 6 8 8 Pi 2 2 4 4 6 6 8 8 Pi - -(E (-1 + E ) (8 k x (-14783093325 + 1452971520 k x - 309657600 k x + 251658240 k x + 2147483648 k x ) Cos[-- + k x] - 3 (156043762875 - 11416204800 k x + 1589575680 k x - 587202560 k x + 2147483648 k x ) Sin[-- + k x])) - 4 4 -Integrate::idiv: Integral of ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ does not converge on {0, Infinity}. - 19/2 7 31/2 - 8589934592 k k0 Sqrt[2 Pi] x -Series[Integrate[(E^(-(c*x) + I*k0*x)*(1 - E^(-(c*x)))^7*BesselJ[1, k*x])/(k0^7*x^6), {x, 0, Infinity}, Assumptions -> n == 1 && q == 7 && κ == 7 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0], {k, Infinity, 10}] diff --git a/besseltransforms/7-7-2 b/besseltransforms/7-7-2 deleted file mode 100644 index 0f84d8c..0000000 --- a/besseltransforms/7-7-2 +++ /dev/null @@ -1,9 +0,0 @@ -Integrate[(E^(-(c*x) + I*k0*x)*(1 - E^(-(c*x)))^7*BesselJ[2, k*x])/(k0^7*x^6), {x, 0, Infinity}, Assumptions -> n == 2 && q == 7 && κ == 7 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0] - - -8 c x + I k0 x c x 7 2 2 4 4 6 6 8 8 Pi 2 2 4 4 6 6 8 8 - -(E (-1 + E ) (15 (-43692253605 + 3528645120 k x - 590413824 k x + 352321536 k x + 2147483648 k x ) Cos[-- + k x] + 4 Sqrt[2] k x (21606059475 - 2421619200 k x + 681246720 k x - 1761607680 k x + 2147483648 k x ) (Cos[k x] + Sin[k x]))) - 4 -Integrate::idiv: Integral of --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- does not converge on {0, Infinity}. - 19/2 7 31/2 - 8589934592 k k0 Sqrt[2 Pi] x -Series[Integrate[(E^(-(c*x) + I*k0*x)*(1 - E^(-(c*x)))^7*BesselJ[2, k*x])/(k0^7*x^6), {x, 0, Infinity}, Assumptions -> n == 2 && q == 7 && κ == 7 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0], {k, Infinity, 10}] diff --git a/besseltransforms/7-7-3 b/besseltransforms/7-7-3 deleted file mode 100644 index f1a860c..0000000 --- a/besseltransforms/7-7-3 +++ /dev/null @@ -1,9 +0,0 @@ -Integrate[(E^(-(c*x) + I*k0*x)*(1 - E^(-(c*x)))^7*BesselJ[3, k*x])/(k0^7*x^6), {x, 0, Infinity}, Assumptions -> n == 3 && q == 7 && κ == 7 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0] - - -8 c x + I k0 x Pi -7 c x + I k0 x Pi -6 c x + I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi -8 c x + I k0 x Pi -7 c x + I k0 x Pi -6 c x + I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi -8 c x + I k0 x Pi -7 c x + I k0 x Pi -6 c x + I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi -8 c x + I k0 x Pi -7 c x + I k0 x Pi -6 c x + I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi -8 c x + I k0 x 2 Pi -7 c x + I k0 x 2 Pi -6 c x + I k0 x 2 Pi -5 c x + I k0 x 2 Pi -4 c x + I k0 x 2 Pi -3 c x + I k0 x 2 Pi -2 c x + I k0 x 2 Pi -(c x) + I k0 x 2 Pi -8 c x + I k0 x Pi -7 c x + I k0 x Pi -6 c x + I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi -8 c x + I k0 x Pi -7 c x + I k0 x Pi -6 c x + I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi -8 c x + I k0 x Pi -7 c x + I k0 x Pi -6 c x + I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi -8 c x + I k0 x Pi -7 c x + I k0 x Pi -6 c x + I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi -8 c x + I k0 x Pi -7 c x + I k0 x Pi -6 c x + I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi - 41247931725 E Cos[-- + k x] 288735522075 E Cos[-- + k x] 866206566225 E Cos[-- + k x] 1443677610375 E Cos[-- + k x] 1443677610375 E Cos[-- + k x] 866206566225 E Cos[-- + k x] 288735522075 E Cos[-- + k x] 41247931725 E Cos[-- + k x] 11486475 E Cos[-- + k x] 80405325 E Cos[-- + k x] 241215975 E Cos[-- + k x] 402026625 E Cos[-- + k x] 402026625 E Cos[-- + k x] 241215975 E Cos[-- + k x] 80405325 E Cos[-- + k x] 11486475 E Cos[-- + k x] 45045 E Cos[-- + k x] 315315 E Cos[-- + k x] 945945 E Cos[-- + k x] 1576575 E Cos[-- + k x] 1576575 E Cos[-- + k x] 945945 E Cos[-- + k x] 315315 E Cos[-- + k x] 45045 E Cos[-- + k x] 945 E Cos[-- + k x] 6615 E Cos[-- + k x] 19845 E Cos[-- + k x] 33075 E Cos[-- + k x] 33075 E Cos[-- + k x] 19845 E Cos[-- + k x] 6615 E Cos[-- + k x] 945 E Cos[-- + k x] E Sqrt[--] Cos[-- + k x] 7 E Sqrt[--] Cos[-- + k x] 21 E Sqrt[--] Cos[-- + k x] 35 E Sqrt[--] Cos[-- + k x] 35 E Sqrt[--] Cos[-- + k x] 21 E Sqrt[--] Cos[-- + k x] 7 E Sqrt[--] Cos[-- + k x] E Sqrt[--] Cos[-- + k x] 1159525191825 E Sin[-- + k x] 8116676342775 E Sin[-- + k x] 24350029028325 E Sin[-- + k x] 40583381713875 E Sin[-- + k x] 40583381713875 E Sin[-- + k x] 24350029028325 E Sin[-- + k x] 8116676342775 E Sin[-- + k x] 1159525191825 E Sin[-- + k x] 218243025 E Sin[-- + k x] 1527701175 E Sin[-- + k x] 4583103525 E Sin[-- + k x] 7638505875 E Sin[-- + k x] 7638505875 E Sin[-- + k x] 4583103525 E Sin[-- + k x] 1527701175 E Sin[-- + k x] 218243025 E Sin[-- + k x] 405405 E Sin[-- + k x] 2837835 E Sin[-- + k x] 8513505 E Sin[-- + k x] 14189175 E Sin[-- + k x] 14189175 E Sin[-- + k x] 8513505 E Sin[-- + k x] 2837835 E Sin[-- + k x] 405405 E Sin[-- + k x] 3465 E Sin[-- + k x] 24255 E Sin[-- + k x] 72765 E Sin[-- + k x] 121275 E Sin[-- + k x] 121275 E Sin[-- + k x] 72765 E Sin[-- + k x] 24255 E Sin[-- + k x] 3465 E Sin[-- + k x] 35 E Sin[-- + k x] 245 E Sin[-- + k x] 735 E Sin[-- + k x] 1225 E Sin[-- + k x] 1225 E Sin[-- + k x] 735 E Sin[-- + k x] 245 E Sin[-- + k x] 35 E Sin[-- + k x] - 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 Pi 4 Pi 4 Pi 4 Pi 4 Pi 4 Pi 4 Pi 4 Pi 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 -Integrate::idiv: Integral of ------------------------------------------ - ------------------------------------------- + ------------------------------------------- - -------------------------------------------- + -------------------------------------------- - ------------------------------------------- + ------------------------------------------- - ------------------------------------------ - --------------------------------------- + --------------------------------------- - ---------------------------------------- + ---------------------------------------- - ---------------------------------------- + ---------------------------------------- - --------------------------------------- + --------------------------------------- + ------------------------------------ - ------------------------------------- + ------------------------------------- - 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--------------------------------------------- + --------------------------------------------- - --------------------------------------------- + -------------------------------------------- - -------------------------------------------- - ---------------------------------------- + ----------------------------------------- - ----------------------------------------- + ----------------------------------------- - ----------------------------------------- + ----------------------------------------- - ----------------------------------------- + ---------------------------------------- + ------------------------------------- - -------------------------------------- + -------------------------------------- - --------------------------------------- + --------------------------------------- - -------------------------------------- + -------------------------------------- - ------------------------------------- - ----------------------------------- + ------------------------------------ - ------------------------------------ + ------------------------------------- - ------------------------------------- + ------------------------------------ - ------------------------------------ + ----------------------------------- + --------------------------------- - ---------------------------------- + ---------------------------------- - ----------------------------------- + ----------------------------------- - ---------------------------------- + ---------------------------------- - --------------------------------- does not converge on {0, Infinity}. - 17/2 7 29/2 17/2 7 29/2 17/2 7 29/2 17/2 7 29/2 17/2 7 29/2 17/2 7 29/2 17/2 7 29/2 17/2 7 29/2 13/2 7 25/2 13/2 7 25/2 13/2 7 25/2 13/2 7 25/2 13/2 7 25/2 13/2 7 25/2 13/2 7 25/2 13/2 7 25/2 9/2 7 21/2 9/2 7 21/2 9/2 7 21/2 9/2 7 21/2 9/2 7 21/2 9/2 7 21/2 9/2 7 21/2 9/2 7 21/2 5/2 7 17/2 5/2 7 17/2 5/2 7 17/2 5/2 7 17/2 5/2 7 17/2 5/2 7 17/2 5/2 7 17/2 5/2 7 17/2 7 13/2 7 13/2 7 13/2 7 13/2 7 13/2 7 13/2 7 13/2 7 13/2 19/2 7 31/2 19/2 7 31/2 19/2 7 31/2 19/2 7 31/2 19/2 7 31/2 19/2 7 31/2 19/2 7 31/2 19/2 7 31/2 15/2 7 27/2 15/2 7 27/2 15/2 7 27/2 15/2 7 27/2 15/2 7 27/2 15/2 7 27/2 15/2 7 27/2 15/2 7 27/2 11/2 7 23/2 11/2 7 23/2 11/2 7 23/2 11/2 7 23/2 11/2 7 23/2 11/2 7 23/2 11/2 7 23/2 11/2 7 23/2 7/2 7 19/2 7/2 7 19/2 7/2 7 19/2 7/2 7 19/2 7/2 7 19/2 7/2 7 19/2 7/2 7 19/2 7/2 7 19/2 3/2 7 15/2 3/2 7 15/2 3/2 7 15/2 3/2 7 15/2 3/2 7 15/2 3/2 7 15/2 3/2 7 15/2 3/2 7 15/2 - 1073741824 k k0 Sqrt[2 Pi] x 1073741824 k k0 Sqrt[2 Pi] x 1073741824 k k0 Sqrt[2 Pi] x 1073741824 k k0 Sqrt[2 Pi] x 1073741824 k k0 Sqrt[2 Pi] x 1073741824 k k0 Sqrt[2 Pi] x 1073741824 k k0 Sqrt[2 Pi] x 1073741824 k k0 Sqrt[2 Pi] x 2097152 k k0 Sqrt[2 Pi] x 2097152 k k0 Sqrt[2 Pi] x 2097152 k k0 Sqrt[2 Pi] x 2097152 k k0 Sqrt[2 Pi] x 2097152 k k0 Sqrt[2 Pi] x 2097152 k k0 Sqrt[2 Pi] x 2097152 k k0 Sqrt[2 Pi] x 2097152 k k0 Sqrt[2 Pi] x 16384 k k0 Sqrt[2 Pi] x 16384 k k0 Sqrt[2 Pi] x 16384 k k0 Sqrt[2 Pi] x 16384 k k0 Sqrt[2 Pi] x 16384 k k0 Sqrt[2 Pi] x 16384 k k0 Sqrt[2 Pi] x 16384 k k0 Sqrt[2 Pi] x 16384 k k0 Sqrt[2 Pi] x 64 k k0 Sqrt[2 Pi] x 64 k k0 Sqrt[2 Pi] x 64 k k0 Sqrt[2 Pi] x 64 k k0 Sqrt[2 Pi] x 64 k k0 Sqrt[2 Pi] x 64 k k0 Sqrt[2 Pi] x 64 k k0 Sqrt[2 Pi] x 64 k k0 Sqrt[2 Pi] x Sqrt[k] k0 x Sqrt[k] k0 x Sqrt[k] k0 x Sqrt[k] k0 x Sqrt[k] k0 x Sqrt[k] k0 x Sqrt[k] k0 x Sqrt[k] k0 x 8589934592 k k0 Sqrt[2 Pi] x 8589934592 k k0 Sqrt[2 Pi] x 8589934592 k k0 Sqrt[2 Pi] x 8589934592 k k0 Sqrt[2 Pi] x 8589934592 k k0 Sqrt[2 Pi] x 8589934592 k k0 Sqrt[2 Pi] x 8589934592 k k0 Sqrt[2 Pi] x 8589934592 k k0 Sqrt[2 Pi] x 16777216 k k0 Sqrt[2 Pi] x 16777216 k k0 Sqrt[2 Pi] x 16777216 k k0 Sqrt[2 Pi] x 16777216 k k0 Sqrt[2 Pi] x 16777216 k k0 Sqrt[2 Pi] x 16777216 k k0 Sqrt[2 Pi] x 16777216 k k0 Sqrt[2 Pi] x 16777216 k k0 Sqrt[2 Pi] x 131072 k k0 Sqrt[2 Pi] x 131072 k k0 Sqrt[2 Pi] x 131072 k k0 Sqrt[2 Pi] x 131072 k k0 Sqrt[2 Pi] x 131072 k k0 Sqrt[2 Pi] x 131072 k k0 Sqrt[2 Pi] x 131072 k k0 Sqrt[2 Pi] x 131072 k k0 Sqrt[2 Pi] x 512 k k0 Sqrt[2 Pi] x 512 k k0 Sqrt[2 Pi] x 512 k k0 Sqrt[2 Pi] x 512 k k0 Sqrt[2 Pi] x 512 k k0 Sqrt[2 Pi] x 512 k k0 Sqrt[2 Pi] x 512 k k0 Sqrt[2 Pi] x 512 k k0 Sqrt[2 Pi] x 4 k k0 Sqrt[2 Pi] x 4 k k0 Sqrt[2 Pi] x 4 k k0 Sqrt[2 Pi] x 4 k k0 Sqrt[2 Pi] x 4 k k0 Sqrt[2 Pi] x 4 k k0 Sqrt[2 Pi] x 4 k k0 Sqrt[2 Pi] x 4 k k0 Sqrt[2 Pi] x -Series[Integrate[(E^(-(c*x) + I*k0*x)*(1 - E^(-(c*x)))^7*BesselJ[3, k*x])/(k0^7*x^6), {x, 0, Infinity}, Assumptions -> n == 3 && q == 7 && κ == 7 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0], {k, Infinity, 10}] diff --git a/besseltransforms/7-7-4 b/besseltransforms/7-7-4 deleted file mode 100644 index d3a9a10..0000000 --- a/besseltransforms/7-7-4 +++ /dev/null @@ -1,9 +0,0 @@ -Integrate[(E^(-(c*x) + I*k0*x)*(1 - E^(-(c*x)))^7*BesselJ[4, k*x])/(k0^7*x^6), {x, 0, Infinity}, Assumptions -> n == 4 && q == 7 && κ == 7 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0] - - -8 c x + I k0 x c x 7 2 2 4 4 6 6 8 8 Pi 2 2 4 4 6 6 8 8 - E (-1 + E ) (63 (-41829913125 + 5320972800 k x - 2389770240 k x - 11995709440 k x + 2147483648 k x ) Cos[-- + k x] + 4 Sqrt[2] k x (105411381075 - 22348085760 k x + 44281036800 k x - 58133053440 k x + 2147483648 k x ) (Cos[k x] + Sin[k x])) - 4 -Integrate::idiv: Integral of -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- does not converge on {0, Infinity}. - 19/2 7 31/2 - 8589934592 k k0 Sqrt[2 Pi] x -Series[Integrate[(E^(-(c*x) + I*k0*x)*(1 - E^(-(c*x)))^7*BesselJ[4, k*x])/(k0^7*x^6), {x, 0, Infinity}, Assumptions -> n == 4 && q == 7 && κ == 7 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0], {k, Infinity, 10}] diff --git a/besseltransforms/7-7-5 b/besseltransforms/7-7-5 deleted file mode 100644 index c51b688..0000000 --- a/besseltransforms/7-7-5 +++ /dev/null @@ -1,10 +0,0 @@ -Integrate[(E^(-(c*x) + I*k0*x)*(1 - E^(-(c*x)))^7*BesselJ[5, k*x])/(k0^7*x^6), {x, 0, Infinity}, Assumptions -> n == 5 && q == 7 && κ == 7 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0] - - 2 2 4 4 6 6 8 8 - -8 c x + I k0 x c x 7 2 2 4 4 6 6 8 8 Pi 99 (79857106875 - 15575938560 k x + 28894494720 k x - 38168166400 k x + 2147483648 k x ) (Cos[k x] + Sin[k x]) - -(E (-1 + E ) (8 k x (-376469218125 + 156436600320 k x + 752777625600 k x - 151145938944 k x + 2147483648 k x ) Cos[-- + k x] - ---------------------------------------------------------------------------------------------------------------------)) - 4 Sqrt[2] -Integrate::idiv: Integral of -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- does not converge on {0, Infinity}. - 19/2 7 31/2 - 8589934592 k k0 Sqrt[2 Pi] x -Series[Integrate[(E^(-(c*x) + I*k0*x)*(1 - E^(-(c*x)))^7*BesselJ[5, k*x])/(k0^7*x^6), {x, 0, Infinity}, Assumptions -> n == 5 && q == 7 && κ == 7 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0], {k, Infinity, 10}] diff --git a/besseltransforms/7-7-6 b/besseltransforms/7-7-6 deleted file mode 100644 index 3ddda62..0000000 --- a/besseltransforms/7-7-6 +++ /dev/null @@ -1,2 +0,0 @@ -((k^10*(-693 + 256*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0) + 10*k^8*(-231 + 128*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^3 + 16*k^6*(-231 + 160*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^5 + 32*k^4*(-99 + 80*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^7 + 128*k^2*(-11 + 10*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^9 + 256*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^11)/(2661120*k^6) - (k^10*(-693 + 256*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0) + 10*k^8*(-231 + 128*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^3 + 16*k^6*(-231 + 160*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^5 + 32*k^4*(-99 + 80*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^7 + 128*k^2*(-11 + 10*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^9 + 256*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^11)/(380160*k^6) + (k^10*(-693 + 256*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0) + 10*k^8*(-231 + 128*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^3 + 16*k^6*(-231 + 160*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^5 + 32*k^4*(-99 + 80*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^7 + 128*k^2*(-11 + 10*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^9 + 256*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^11)/(126720*k^6) - (k^10*(-693 + 256*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0) + 10*k^8*(-231 + 128*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^3 + 16*k^6*(-231 + 160*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^5 + 32*k^4*(-99 + 80*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^7 + 128*k^2*(-11 + 10*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^9 + 256*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^11)/(76032*k^6) + (k^10*(-693 + 256*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0) + 10*k^8*(-231 + 128*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^3 + 16*k^6*(-231 + 160*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^5 + 32*k^4*(-99 + 80*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^7 + 128*k^2*(-11 + 10*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^9 + 256*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^11)/(76032*k^6) - (k^10*(-693 + 256*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0) + 10*k^8*(-231 + 128*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^3 + 16*k^6*(-231 + 160*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^5 + 32*k^4*(-99 + 80*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^7 + 128*k^2*(-11 + 10*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^9 + 256*(-1 + Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^11)/(126720*k^6) + (k^10*(-693 + 256*Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0) + 10*k^8*(-231 + 128*Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^3 + 16*k^6*(-231 + 160*Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^5 + 32*k^4*(-99 + 80*Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^7 + 128*k^2*(-11 + 10*Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^9 + 256*(-1 + Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^11)/(380160*k^6) - (k^10*(-693 + 256*Sqrt[1 + k^2/(8*c - I*k0)^2])*(8*c - I*k0) + 10*k^8*(-231 + 128*Sqrt[1 + k^2/(8*c - I*k0)^2])*(8*c - I*k0)^3 + 16*k^6*(-231 + 160*Sqrt[1 + k^2/(8*c - I*k0)^2])*(8*c - I*k0)^5 + 32*k^4*(-99 + 80*Sqrt[1 + k^2/(8*c - I*k0)^2])*(8*c - I*k0)^7 + 128*k^2*(-11 + 10*Sqrt[1 + k^2/(8*c - I*k0)^2])*(8*c - I*k0)^9 + 256*(-1 + Sqrt[1 + k^2/(8*c - I*k0)^2])*(8*c - I*k0)^11)/(2661120*k^6))/k0^7 -SeriesData[k, Infinity, {(6*c^7)/k0^7, (-315*c^8)/(2*k0^7) + ((35*I)*c^7)/k0^6, (2000*c^9)/k0^7 - ((864*I)*c^8)/k0^6 - (96*c^7)/k0^5, (-315*(198*c^10 - (125*I)*c^9*k0 - 27*c^8*k0^2 + (2*I)*c^7*k0^3))/(4*k0^7), (77104*c^11)/k0^7 - ((63360*I)*c^10)/k0^6 - (20000*c^9)/k0^5 + ((2880*I)*c^8)/k0^4 + (160*c^7)/k0^3, (-231*(14391*c^12 - (14457*I)*c^11*k0 - 5940*c^10*k0^2 + (1250*I)*c^9*k0^3 + 135*c^8*k0^4 - (6*I)*c^7*k0^5))/(16*k0^7), 0, (143*(378720*c^14 - (511840*I)*c^13*k0 - 302211*c^12*k0^2 + (101199*I)*c^11*k0^3 + 20790*c^10*k0^4 - (2625*I)*c^9*k0^5 - 189*c^8*k0^6 + (6*I)*c^7*k0^7))/(32*k0^7)}, 2, 11, 1] diff --git a/besseltransforms/7-7-7 b/besseltransforms/7-7-7 deleted file mode 100644 index 96b3cc1..0000000 --- a/besseltransforms/7-7-7 +++ /dev/null @@ -1,2 +0,0 @@ -((231*k^12 + 4*k^10*(693 - 256*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^2 + 40*k^8*(231 - 128*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^4 + 64*k^6*(231 - 160*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^6 + 128*k^4*(99 - 80*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^8 + 512*k^2*(11 - 10*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^10 - 1024*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^12)/(10644480*k^7) - (231*k^12 + 4*k^10*(693 - 256*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^2 + 40*k^8*(231 - 128*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^4 + 64*k^6*(231 - 160*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^6 + 128*k^4*(99 - 80*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^8 + 512*k^2*(11 - 10*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^10 - 1024*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^12)/(1520640*k^7) + (231*k^12 + 4*k^10*(693 - 256*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^2 + 40*k^8*(231 - 128*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^4 + 64*k^6*(231 - 160*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^6 + 128*k^4*(99 - 80*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^8 + 512*k^2*(11 - 10*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^10 - 1024*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^12)/(506880*k^7) - (231*k^12 + 4*k^10*(693 - 256*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^2 + 40*k^8*(231 - 128*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^4 + 64*k^6*(231 - 160*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^6 + 128*k^4*(99 - 80*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^8 + 512*k^2*(11 - 10*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^10 - 1024*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^12)/(304128*k^7) + (231*k^12 + 4*k^10*(693 - 256*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^2 + 40*k^8*(231 - 128*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^4 + 64*k^6*(231 - 160*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^6 + 128*k^4*(99 - 80*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^8 + 512*k^2*(11 - 10*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^10 - 1024*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^12)/(304128*k^7) - (231*k^12 + 4*k^10*(693 - 256*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^2 + 40*k^8*(231 - 128*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^4 + 64*k^6*(231 - 160*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^6 + 128*k^4*(99 - 80*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^8 + 512*k^2*(11 - 10*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^10 - 1024*(-1 + Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^12)/(506880*k^7) + (231*k^12 + 4*k^10*(693 - 256*Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^2 + 40*k^8*(231 - 128*Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^4 + 64*k^6*(231 - 160*Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^6 + 128*k^4*(99 - 80*Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^8 + 512*k^2*(11 - 10*Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^10 - 1024*(-1 + Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^12)/(1520640*k^7) - (231*k^12 + 4*k^10*(693 - 256*Sqrt[1 + k^2/(8*c - I*k0)^2])*(8*c - I*k0)^2 + 40*k^8*(231 - 128*Sqrt[1 + k^2/(8*c - I*k0)^2])*(8*c - I*k0)^4 + 64*k^6*(231 - 160*Sqrt[1 + k^2/(8*c - I*k0)^2])*(8*c - I*k0)^6 + 128*k^4*(99 - 80*Sqrt[1 + k^2/(8*c - I*k0)^2])*(8*c - I*k0)^8 + 512*k^2*(11 - 10*Sqrt[1 + k^2/(8*c - I*k0)^2])*(8*c - I*k0)^10 - 1024*(-1 + Sqrt[1 + k^2/(8*c - I*k0)^2])*(8*c - I*k0)^12)/(10644480*k^7))/k0^7 -SeriesData[k, Infinity, {(7*c^7)/k0^7, (-24*(9*c^8 - (2*I)*c^7*k0))/k0^7, (105*(125*c^9 - (54*I)*c^8*k0 - 6*c^7*k0^2))/(4*k0^7), (-160*(198*c^10 - (125*I)*c^9*k0 - 27*c^8*k0^2 + (2*I)*c^7*k0^3))/k0^7, (693*(4819*c^11 - (3960*I)*c^10*k0 - 1250*c^9*k0^2 + (180*I)*c^8*k0^3 + 10*c^7*k0^4))/(16*k0^7), (-64*(14391*c^12 - (14457*I)*c^11*k0 - 5940*c^10*k0^2 + (1250*I)*c^9*k0^3 + 135*c^8*k0^4 - (6*I)*c^7*k0^5))/k0^7, (1001*(73120*c^13 - (86346*I)*c^12*k0 - 43371*c^11*k0^2 + (11880*I)*c^10*k0^3 + 1875*c^9*k0^4 - (162*I)*c^8*k0^5 - 6*c^7*k0^6))/(32*k0^7), 0, (-429*(4992457*c^15 - (7574400*I)*c^14*k0 - 5118400*c^13*k0^2 + (2014740*I)*c^12*k0^3 + 505995*c^11*k0^4 - (83160*I)*c^10*k0^5 - 8750*c^9*k0^6 + (540*I)*c^8*k0^7 + 15*c^7*k0^8))/(128*k0^7)}, 2, 11, 1] diff --git a/besseltransforms/klarge/5-1-0 b/besseltransforms/klarge/5-1-0 deleted file mode 100644 index 76201ee..0000000 --- a/besseltransforms/klarge/5-1-0 +++ /dev/null @@ -1,4 +0,0 @@ -(-5/(Sqrt[1 + k^2/(c - I*k0)^2]*(c - I*k0)) + 10/(Sqrt[1 + k^2/(2*c - I*k0)^2]*(2*c - I*k0)) - 10/(Sqrt[1 + k^2/(3*c - I*k0)^2]*(3*c - I*k0)) + 5/(Sqrt[1 + k^2/(4*c - I*k0)^2]*(4*c - I*k0)) - 1/(Sqrt[1 + k^2/(5*c - I*k0)^2]*(5*c - I*k0)) + 1/Sqrt[k^2 - k0^2])/k0 -(-5/(Sqrt(1 + Power(k,2)/Power(c - Complex(0,1)*k0,2))*(c - Complex(0,1)*k0)) + 10/(Sqrt(1 + Power(k,2)/Power(2*c - Complex(0,1)*k0,2))*(2*c - Complex(0,1)*k0)) - 10/(Sqrt(1 + Power(k,2)/Power(3*c - Complex(0,1)*k0,2))*(3*c - Complex(0,1)*k0)) + 5/(Sqrt(1 + Power(k,2)/Power(4*c - Complex(0,1)*k0,2))*(4*c - Complex(0,1)*k0)) - 1/(Sqrt(1 + Power(k,2)/Power(5*c - Complex(0,1)*k0,2))*(5*c - Complex(0,1)*k0)) + 1/Sqrt(Power(k,2) - Power(k0,2)))/k0 -SeriesData[k, Infinity, {-(1/(k*k0)), k0^(-1), -k0/(2*k), k0/2, ((-15*(c - I*k0)^3*(c/k - (I*k0)/k))/8 + (15*(2*c - I*k0)^3*((2*c)/k - (I*k0)/k))/4 - (15*(3*c - I*k0)^3*((3*c)/k - (I*k0)/k))/4 + (15*(4*c - I*k0)^3*((4*c)/k - (I*k0)/k))/8 - (3*(5*c - I*k0)^3*((5*c)/k - (I*k0)/k))/8)/k0, (3*k0^3)/8, ((25*(c - I*k0)^5*(c/k - (I*k0)/k))/16 - (25*(2*c - I*k0)^5*((2*c)/k - (I*k0)/k))/8 + (25*(3*c - I*k0)^5*((3*c)/k - (I*k0)/k))/8 - (25*(4*c - I*k0)^5*((4*c)/k - (I*k0)/k))/16 + (5*(5*c - I*k0)^5*((5*c)/k - (I*k0)/k))/16)/k0, (5*k0^5)/16, ((-175*(c - I*k0)^7*(c/k - (I*k0)/k))/128 + (175*(2*c - I*k0)^7*((2*c)/k - (I*k0)/k))/64 - (175*(3*c - I*k0)^7*((3*c)/k - (I*k0)/k))/64 + (175*(4*c - I*k0)^7*((4*c)/k - (I*k0)/k))/128 - (35*(5*c - I*k0)^7*((5*c)/k - (I*k0)/k))/128)/k0, (35*k0^7)/128, ((315*(c - I*k0)^9*(c/k - (I*k0)/k))/256 - (315*(2*c - I*k0)^9*((2*c)/k - (I*k0)/k))/128 + (315*(3*c - I*k0)^9*((3*c)/k - (I*k0)/k))/128 - (315*(4*c - I*k0)^9*((4*c)/k - (I*k0)/k))/256 + (63*(5*c - I*k0)^9*((5*c)/k - (I*k0)/k))/256)/k0}, 0, 11, 1] -(-5/(Sqrt[1 + k^2/(c - I*k0)^2]*(c - I*k0)) + 10/(Sqrt[1 + k^2/(2*c - I*k0)^2]*(2*c - I*k0)) - 10/(Sqrt[1 + k^2/(3*c - I*k0)^2]*(3*c - I*k0)) + 5/(Sqrt[1 + k^2/(4*c - I*k0)^2]*(4*c - I*k0)) - 1/(Sqrt[1 + k^2/(5*c - I*k0)^2]*(5*c - I*k0)) + 1/Sqrt[k^2 - k0^2])/k0 diff --git a/besseltransforms/klarge/5-1-1 b/besseltransforms/klarge/5-1-1 deleted file mode 100644 index fcae90b..0000000 --- a/besseltransforms/klarge/5-1-1 +++ /dev/null @@ -1,4 +0,0 @@ -(-k^(-1) - 5*(k^(-1) - 1/(k*Sqrt[1 + k^2/(c - I*k0)^2])) + 10*(k^(-1) - 1/(k*Sqrt[1 + k^2/(2*c - I*k0)^2])) - 10*(k^(-1) - 1/(k*Sqrt[1 + k^2/(3*c - I*k0)^2])) + 5*(k^(-1) - 1/(k*Sqrt[1 + k^2/(4*c - I*k0)^2])) + 1/(k*Sqrt[1 + k^2/(5*c - I*k0)^2]) + (1 + (I*k0)/Sqrt[k^2 - k0^2])/k)/k0 -(-(1/k) - 5*(1/k - 1/(k*Sqrt(1 + Power(k,2)/Power(c - Complex(0,1)*k0,2)))) + 10*(1/k - 1/(k*Sqrt(1 + Power(k,2)/Power(2*c - Complex(0,1)*k0,2)))) - 10*(1/k - 1/(k*Sqrt(1 + Power(k,2)/Power(3*c - Complex(0,1)*k0,2)))) + 5*(1/k - 1/(k*Sqrt(1 + Power(k,2)/Power(4*c - Complex(0,1)*k0,2)))) + 1/(k*Sqrt(1 + Power(k,2)/Power(5*c - Complex(0,1)*k0,2))) + (1 + (Complex(0,1)*k0)/Sqrt(Power(k,2) - Power(k0,2)))/k)/k0 -SeriesData[k, Infinity, {-I/k, I, (-I/2*k0^2)/k, I/2*k0^2, (3*(120*c^5 - I*k0^5))/(8*k*k0), (3*I)/8*k0^4, (-5*(16800*c^7 - (12600*I)*c^6*k0 - 2520*c^5*k0^2 + I*k0^7))/(16*k*k0), (5*I)/16*k0^6, (35*(834120*c^9 - (1134000*I)*c^8*k0 - 604800*c^7*k0^2 + (151200*I)*c^6*k0^3 + 15120*c^5*k0^4 - I*k0^9))/(128*k*k0), (35*I)/128*k0^8}, 1, 11, 1] -(-5*(1 - 1/Sqrt[1 + k^2/(c - I*k0)^2]) + 10*(1 - 1/Sqrt[1 + k^2/(2*c - I*k0)^2]) - 10*(1 - 1/Sqrt[1 + k^2/(3*c - I*k0)^2]) + 5*(1 - 1/Sqrt[1 + k^2/(4*c - I*k0)^2]) + 1/Sqrt[1 + k^2/(5*c - I*k0)^2] + (I*k0)/Sqrt[k^2 - k0^2])/(k*k0) diff --git a/besseltransforms/klarge/5-1-2 b/besseltransforms/klarge/5-1-2 deleted file mode 100644 index e772728..0000000 --- a/besseltransforms/klarge/5-1-2 +++ /dev/null @@ -1,4 +0,0 @@ -(-5*(1/(Sqrt[1 + k^2/(c - I*k0)^2]*(c - I*k0)) - (2*(c - I*k0))/k^2 + (2*(c - I*k0))/(k^2*Sqrt[1 + k^2/(c - I*k0)^2])) + 10*(1/(Sqrt[1 + k^2/(2*c - I*k0)^2]*(2*c - I*k0)) - (2*(2*c - I*k0))/k^2 + (2*(2*c - I*k0))/(k^2*Sqrt[1 + k^2/(2*c - I*k0)^2])) - 10*(1/(Sqrt[1 + k^2/(3*c - I*k0)^2]*(3*c - I*k0)) - (2*(3*c - I*k0))/k^2 + (2*(3*c - I*k0))/(k^2*Sqrt[1 + k^2/(3*c - I*k0)^2])) + 5*(1/(Sqrt[1 + k^2/(4*c - I*k0)^2]*(4*c - I*k0)) - (2*(4*c - I*k0))/k^2 + (2*(4*c - I*k0))/(k^2*Sqrt[1 + k^2/(4*c - I*k0)^2])) - 1/(Sqrt[1 + k^2/(5*c - I*k0)^2]*(5*c - I*k0)) + (2*(5*c - I*k0))/k^2 - (2*(5*c - I*k0))/(k^2*Sqrt[1 + k^2/(5*c - I*k0)^2]) + ((2*I)*k*k0 + (k*(k^2 - 2*k0^2))/Sqrt[k^2 - k0^2])/k^3)/k0 -(-5*(1/(Sqrt(1 + Power(k,2)/Power(c - Complex(0,1)*k0,2))*(c - Complex(0,1)*k0)) - (2*(c - Complex(0,1)*k0))/Power(k,2) + (2*(c - Complex(0,1)*k0))/(Power(k,2)*Sqrt(1 + Power(k,2)/Power(c - Complex(0,1)*k0,2)))) + 10*(1/(Sqrt(1 + Power(k,2)/Power(2*c - Complex(0,1)*k0,2))*(2*c - Complex(0,1)*k0)) - (2*(2*c - Complex(0,1)*k0))/Power(k,2) + (2*(2*c - Complex(0,1)*k0))/(Power(k,2)*Sqrt(1 + Power(k,2)/Power(2*c - Complex(0,1)*k0,2)))) - 10*(1/(Sqrt(1 + Power(k,2)/Power(3*c - Complex(0,1)*k0,2))*(3*c - Complex(0,1)*k0)) - (2*(3*c - Complex(0,1)*k0))/Power(k,2) + (2*(3*c - Complex(0,1)*k0))/(Power(k,2)*Sqrt(1 + Power(k,2)/Power(3*c - Complex(0,1)*k0,2)))) + 5*(1/(Sqrt(1 + Power(k,2)/Power(4*c - Complex(0,1)*k0,2))*(4*c - Complex(0,1)*k0)) - (2*(4*c - Complex(0,1)*k0))/Power(k,2) + (2*(4*c - Complex(0,1)*k0))/(Power(k,2)*Sqrt(1 + Power(k,2)/Power(4*c - Complex(0,1)*k0,2)))) - 1/(Sqrt(1 + Power(k,2)/Power(5*c - Complex(0,1)*k0,2))*(5*c - Complex(0,1)*k0)) + (2*(5*c - Complex(0,1)*k0))/Power(k,2) - (2*(5*c - Complex(0,1)*k0))/(Power(k,2)*Sqrt(1 + Power(k,2)/Power(5*c - Complex(0,1)*k0,2))) + (Complex(0,2)*k*k0 + (k*(Power(k,2) - 2*Power(k0,2)))/Sqrt(Power(k,2) - Power(k0,2)))/Power(k,3))/k0 -SeriesData[k, Infinity, {-(1/(k*k0)), k0^(-1), (3*k0)/(2*k), (-3*k0)/2, ((5*c - I*k0)^4/k - (3*(5*c - I*k0)^3*((5*c)/k - (I*k0)/k))/8 - 5*(-((c - I*k0)^4/k) + (3*(c - I*k0)^3*(c/k - (I*k0)/k))/8) + 10*(-((2*c - I*k0)^4/k) + (3*(2*c - I*k0)^3*((2*c)/k - (I*k0)/k))/8) - 10*(-((3*c - I*k0)^4/k) + (3*(3*c - I*k0)^3*((3*c)/k - (I*k0)/k))/8) + 5*(-((4*c - I*k0)^4/k) + (3*(4*c - I*k0)^3*((4*c)/k - (I*k0)/k))/8))/k0, (-5*k0^3)/8, ((-3*(5*c - I*k0)^6)/(4*k) + (5*(5*c - I*k0)^5*((5*c)/k - (I*k0)/k))/16 - 5*((3*(c - I*k0)^6)/(4*k) - (5*(c - I*k0)^5*(c/k - (I*k0)/k))/16) + 10*((3*(2*c - I*k0)^6)/(4*k) - (5*(2*c - I*k0)^5*((2*c)/k - (I*k0)/k))/16) - 10*((3*(3*c - I*k0)^6)/(4*k) - (5*(3*c - I*k0)^5*((3*c)/k - (I*k0)/k))/16) + 5*((3*(4*c - I*k0)^6)/(4*k) - (5*(4*c - I*k0)^5*((4*c)/k - (I*k0)/k))/16))/k0, (-7*k0^5)/16, ((5*(5*c - I*k0)^8)/(8*k) - (35*(5*c - I*k0)^7*((5*c)/k - (I*k0)/k))/128 - 5*((-5*(c - I*k0)^8)/(8*k) + (35*(c - I*k0)^7*(c/k - (I*k0)/k))/128) + 10*((-5*(2*c - I*k0)^8)/(8*k) + (35*(2*c - I*k0)^7*((2*c)/k - (I*k0)/k))/128) - 10*((-5*(3*c - I*k0)^8)/(8*k) + (35*(3*c - I*k0)^7*((3*c)/k - (I*k0)/k))/128) + 5*((-5*(4*c - I*k0)^8)/(8*k) + (35*(4*c - I*k0)^7*((4*c)/k - (I*k0)/k))/128))/k0, (-45*k0^7)/128, ((-35*(5*c - I*k0)^10)/(64*k) + (63*(5*c - I*k0)^9*((5*c)/k - (I*k0)/k))/256 - 5*((35*(c - I*k0)^10)/(64*k) - (63*(c - I*k0)^9*(c/k - (I*k0)/k))/256) + 10*((35*(2*c - I*k0)^10)/(64*k) - (63*(2*c - I*k0)^9*((2*c)/k - (I*k0)/k))/256) - 10*((35*(3*c - I*k0)^10)/(64*k) - (63*(3*c - I*k0)^9*((3*c)/k - (I*k0)/k))/256) + 5*((35*(4*c - I*k0)^10)/(64*k) - (63*(4*c - I*k0)^9*((4*c)/k - (I*k0)/k))/256))/k0}, 0, 11, 1] -(-5*(1/(Sqrt[1 + k^2/(c - I*k0)^2]*(c - I*k0)) - (2*(c - I*k0))/k^2 + (2*(c - I*k0))/(k^2*Sqrt[1 + k^2/(c - I*k0)^2])) + 5*(1/(Sqrt[1 + k^2/(4*c - I*k0)^2]*(4*c - I*k0)) + (8*c - (2*I)*k0)/(k^2*Sqrt[1 + k^2/(4*c - I*k0)^2]) + (-8*c + (2*I)*k0)/k^2) - 10*(1/(Sqrt[1 + k^2/(3*c - I*k0)^2]*(3*c - I*k0)) + (6*c - (2*I)*k0)/(k^2*Sqrt[1 + k^2/(3*c - I*k0)^2]) + (-6*c + (2*I)*k0)/k^2) + 10*(1/(Sqrt[1 + k^2/(2*c - I*k0)^2]*(2*c - I*k0)) + (4*c - (2*I)*k0)/(k^2*Sqrt[1 + k^2/(2*c - I*k0)^2]) + (-4*c + (2*I)*k0)/k^2) - 1/(Sqrt[1 + k^2/(5*c - I*k0)^2]*(5*c - I*k0)) + (10*c - (2*I)*k0)/k^2 + (-10*c + (2*I)*k0)/(k^2*Sqrt[1 + k^2/(5*c - I*k0)^2]) + ((2*I)*k*k0 + (k*(k^2 - 2*k0^2))/Sqrt[k^2 - k0^2])/k^3)/k0 diff --git a/besseltransforms/klarge/5-1-3 b/besseltransforms/klarge/5-1-3 deleted file mode 100644 index c2eaff4..0000000 --- a/besseltransforms/klarge/5-1-3 +++ /dev/null @@ -1,4 +0,0 @@ -((-5*(k^2*(-3 + Sqrt[1 + k^2/(c - I*k0)^2]) + 4*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^2))/(k^3*Sqrt[1 + k^2/(c - I*k0)^2]) + (10*(k^2*(-3 + Sqrt[1 + k^2/(2*c - I*k0)^2]) + 4*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^2))/(k^3*Sqrt[1 + k^2/(2*c - I*k0)^2]) - (10*(k^2*(-3 + Sqrt[1 + k^2/(3*c - I*k0)^2]) + 4*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^2))/(k^3*Sqrt[1 + k^2/(3*c - I*k0)^2]) + (5*(k^2*(-3 + Sqrt[1 + k^2/(4*c - I*k0)^2]) + 4*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^2))/(k^3*Sqrt[1 + k^2/(4*c - I*k0)^2]) - (k^2*(-3 + Sqrt[1 + k^2/(5*c - I*k0)^2]) + 4*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^2)/(k^3*Sqrt[1 + k^2/(5*c - I*k0)^2]) + (k^3 - 4*k*k0^2 + (I*k*k0*(3*k^2 - 4*k0^2))/Sqrt[k^2 - k0^2])/k^4)/k0 -((-5*(Power(k,2)*(-3 + Sqrt(1 + Power(k,2)/Power(c - Complex(0,1)*k0,2))) + 4*(-1 + Sqrt(1 + Power(k,2)/Power(c - Complex(0,1)*k0,2)))*Power(c - Complex(0,1)*k0,2)))/(Power(k,3)*Sqrt(1 + Power(k,2)/Power(c - Complex(0,1)*k0,2))) + (10*(Power(k,2)*(-3 + Sqrt(1 + Power(k,2)/Power(2*c - Complex(0,1)*k0,2))) + 4*(-1 + Sqrt(1 + Power(k,2)/Power(2*c - Complex(0,1)*k0,2)))*Power(2*c - Complex(0,1)*k0,2)))/(Power(k,3)*Sqrt(1 + Power(k,2)/Power(2*c - Complex(0,1)*k0,2))) - (10*(Power(k,2)*(-3 + Sqrt(1 + Power(k,2)/Power(3*c - Complex(0,1)*k0,2))) + 4*(-1 + Sqrt(1 + Power(k,2)/Power(3*c - Complex(0,1)*k0,2)))*Power(3*c - Complex(0,1)*k0,2)))/(Power(k,3)*Sqrt(1 + Power(k,2)/Power(3*c - Complex(0,1)*k0,2))) + (5*(Power(k,2)*(-3 + Sqrt(1 + Power(k,2)/Power(4*c - Complex(0,1)*k0,2))) + 4*(-1 + Sqrt(1 + Power(k,2)/Power(4*c - Complex(0,1)*k0,2)))*Power(4*c - Complex(0,1)*k0,2)))/(Power(k,3)*Sqrt(1 + Power(k,2)/Power(4*c - Complex(0,1)*k0,2))) - (Power(k,2)*(-3 + Sqrt(1 + Power(k,2)/Power(5*c - Complex(0,1)*k0,2))) + 4*(-1 + Sqrt(1 + Power(k,2)/Power(5*c - Complex(0,1)*k0,2)))*Power(5*c - Complex(0,1)*k0,2))/(Power(k,3)*Sqrt(1 + Power(k,2)/Power(5*c - Complex(0,1)*k0,2))) + (Power(k,3) - 4*k*Power(k0,2) + (Complex(0,1)*k*k0*(3*Power(k,2) - 4*Power(k0,2)))/Sqrt(Power(k,2) - Power(k0,2)))/Power(k,4))/k0 -SeriesData[k, Infinity, {-(1/(k*k0)), (k - (3*I)*k0)/(k*k0), (I*(3*k - (4*I)*k0))/k, (-8*k*k0 + (5*I)*k0^2)/(2*k), ((3*(5*c - I*k0)^4)/(8*k) - (5*I)/2*k0^3 - (3*(5*c - I*k0)^3*((5*c)/k - (I*k0)/k))/8 - 5*((-3*(c - I*k0)^4)/(8*k) + (3*(c - I*k0)^3*(c/k - (I*k0)/k))/8) + 10*((-3*(2*c - I*k0)^4)/(8*k) + (3*(2*c - I*k0)^3*((2*c)/k - (I*k0)/k))/8) - 10*((-3*(3*c - I*k0)^4)/(8*k) + (3*(3*c - I*k0)^3*((3*c)/k - (I*k0)/k))/8) + 5*((-3*(4*c - I*k0)^4)/(8*k) + (3*(4*c - I*k0)^3*((4*c)/k - (I*k0)/k))/8))/k0, ((-2*(5*c - I*k0)^5)/k + (9*(5*c - I*k0)^4*((5*c)/k - (I*k0)/k))/8 - 5*((2*(c - I*k0)^5)/k - (9*(c - I*k0)^4*(c/k - (I*k0)/k))/8) + 10*((2*(2*c - I*k0)^5)/k - (9*(2*c - I*k0)^4*((2*c)/k - (I*k0)/k))/8) - 10*((2*(3*c - I*k0)^5)/k - (9*(3*c - I*k0)^4*((3*c)/k - (I*k0)/k))/8) + 5*((2*(4*c - I*k0)^5)/k - (9*(4*c - I*k0)^4*((4*c)/k - (I*k0)/k))/8))/k0, ((11*(5*c - I*k0)^6)/(8*k) - (7*I)/8*k0^5 - (11*(5*c - I*k0)^5*((5*c)/k - (I*k0)/k))/8 - 5*((-11*(c - I*k0)^6)/(8*k) + (11*(c - I*k0)^5*(c/k - (I*k0)/k))/8) + 10*((-11*(2*c - I*k0)^6)/(8*k) + (11*(2*c - I*k0)^5*((2*c)/k - (I*k0)/k))/8) - 10*((-11*(3*c - I*k0)^6)/(8*k) + (11*(3*c - I*k0)^5*((3*c)/k - (I*k0)/k))/8) + 5*((-11*(4*c - I*k0)^6)/(8*k) + (11*(4*c - I*k0)^5*((4*c)/k - (I*k0)/k))/8))/k0, ((45*(c - I*k0)^6*(c/k - (I*k0)/k))/16 - (45*(2*c - I*k0)^6*((2*c)/k - (I*k0)/k))/8 + (45*(3*c - I*k0)^6*((3*c)/k - (I*k0)/k))/8 - (45*(4*c - I*k0)^6*((4*c)/k - (I*k0)/k))/16 + (9*(5*c - I*k0)^6*((5*c)/k - (I*k0)/k))/16)/k0, ((-55*(5*c - I*k0)^8)/(128*k) - (9*I)/16*k0^7 + (55*(5*c - I*k0)^7*((5*c)/k - (I*k0)/k))/128 - 5*((55*(c - I*k0)^8)/(128*k) - (55*(c - I*k0)^7*(c/k - (I*k0)/k))/128) + 10*((55*(2*c - I*k0)^8)/(128*k) - (55*(2*c - I*k0)^7*((2*c)/k - (I*k0)/k))/128) - 10*((55*(3*c - I*k0)^8)/(128*k) - (55*(3*c - I*k0)^7*((3*c)/k - (I*k0)/k))/128) + 5*((55*(4*c - I*k0)^8)/(128*k) - (55*(4*c - I*k0)^7*((4*c)/k - (I*k0)/k))/128))/k0, ((-275*(c - I*k0)^8*(c/k - (I*k0)/k))/128 + (275*(2*c - I*k0)^8*((2*c)/k - (I*k0)/k))/64 - (275*(3*c - I*k0)^8*((3*c)/k - (I*k0)/k))/64 + (275*(4*c - I*k0)^8*((4*c)/k - (I*k0)/k))/128 - (55*(5*c - I*k0)^8*((5*c)/k - (I*k0)/k))/128)/k0, ((15*(5*c - I*k0)^10)/(64*k) - (55*I)/128*k0^9 - (15*(5*c - I*k0)^9*((5*c)/k - (I*k0)/k))/64 - 5*((-15*(c - I*k0)^10)/(64*k) + (15*(c - I*k0)^9*(c/k - (I*k0)/k))/64) + 10*((-15*(2*c - I*k0)^10)/(64*k) + (15*(2*c - I*k0)^9*((2*c)/k - (I*k0)/k))/64) - 10*((-15*(3*c - I*k0)^10)/(64*k) + (15*(3*c - I*k0)^9*((3*c)/k - (I*k0)/k))/64) + 5*((-15*(4*c - I*k0)^10)/(64*k) + (15*(4*c - I*k0)^9*((4*c)/k - (I*k0)/k))/64))/k0}, 0, 11, 1] -(k^2 - (5*(k^2*(-3 + Sqrt[1 + k^2/(c - I*k0)^2]) + 4*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^2))/Sqrt[1 + k^2/(c - I*k0)^2] + (10*(k^2*(-3 + Sqrt[1 + k^2/(2*c - I*k0)^2]) + 4*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^2))/Sqrt[1 + k^2/(2*c - I*k0)^2] - (10*(k^2*(-3 + Sqrt[1 + k^2/(3*c - I*k0)^2]) + 4*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^2))/Sqrt[1 + k^2/(3*c - I*k0)^2] + (5*(k^2*(-3 + Sqrt[1 + k^2/(4*c - I*k0)^2]) + 4*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^2))/Sqrt[1 + k^2/(4*c - I*k0)^2] - (k^2*(-3 + Sqrt[1 + k^2/(5*c - I*k0)^2]) + 4*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^2)/Sqrt[1 + k^2/(5*c - I*k0)^2] - 4*k0^2 + (I*k0*(3*k^2 - 4*k0^2))/Sqrt[k^2 - k0^2])/(k^3*k0) diff --git a/besseltransforms/klarge/5-1-4 b/besseltransforms/klarge/5-1-4 deleted file mode 100644 index b00a8b7..0000000 --- a/besseltransforms/klarge/5-1-4 +++ /dev/null @@ -1,4 +0,0 @@ -((-5*(k^4 - 4*k^2*(-2 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^2 - 8*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^4))/(k^4*Sqrt[1 + k^2/(c - I*k0)^2]*(c - I*k0)) + (10*(k^4 - 4*k^2*(-2 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^2 - 8*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^4))/(k^4*Sqrt[1 + k^2/(2*c - I*k0)^2]*(2*c - I*k0)) - (10*(k^4 - 4*k^2*(-2 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^2 - 8*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^4))/(k^4*Sqrt[1 + k^2/(3*c - I*k0)^2]*(3*c - I*k0)) + (5*(k^4 - 4*k^2*(-2 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^2 - 8*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^4))/(k^4*Sqrt[1 + k^2/(4*c - I*k0)^2]*(4*c - I*k0)) - (k^4 - 4*k^2*(-2 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^2 - 8*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^4)/(k^4*Sqrt[1 + k^2/(5*c - I*k0)^2]*(5*c - I*k0)) + ((4*I)*k*k0*(k^2 - 2*k0^2) + (k*(k^4 - 8*k^2*k0^2 + 8*k0^4))/Sqrt[k^2 - k0^2])/k^5)/k0 -((-5*(Power(k,4) - 4*Power(k,2)*(-2 + Sqrt(1 + Power(k,2)/Power(c - Complex(0,1)*k0,2)))*Power(c - Complex(0,1)*k0,2) - 8*(-1 + Sqrt(1 + Power(k,2)/Power(c - Complex(0,1)*k0,2)))*Power(c - Complex(0,1)*k0,4)))/(Power(k,4)*Sqrt(1 + Power(k,2)/Power(c - Complex(0,1)*k0,2))*(c - Complex(0,1)*k0)) + (10*(Power(k,4) - 4*Power(k,2)*(-2 + Sqrt(1 + Power(k,2)/Power(2*c - Complex(0,1)*k0,2)))*Power(2*c - Complex(0,1)*k0,2) - 8*(-1 + Sqrt(1 + Power(k,2)/Power(2*c - Complex(0,1)*k0,2)))*Power(2*c - Complex(0,1)*k0,4)))/(Power(k,4)*Sqrt(1 + Power(k,2)/Power(2*c - Complex(0,1)*k0,2))*(2*c - Complex(0,1)*k0)) - (10*(Power(k,4) - 4*Power(k,2)*(-2 + Sqrt(1 + Power(k,2)/Power(3*c - Complex(0,1)*k0,2)))*Power(3*c - Complex(0,1)*k0,2) - 8*(-1 + Sqrt(1 + Power(k,2)/Power(3*c - Complex(0,1)*k0,2)))*Power(3*c - Complex(0,1)*k0,4)))/(Power(k,4)*Sqrt(1 + Power(k,2)/Power(3*c - Complex(0,1)*k0,2))*(3*c - Complex(0,1)*k0)) + (5*(Power(k,4) - 4*Power(k,2)*(-2 + Sqrt(1 + Power(k,2)/Power(4*c - Complex(0,1)*k0,2)))*Power(4*c - Complex(0,1)*k0,2) - 8*(-1 + Sqrt(1 + Power(k,2)/Power(4*c - Complex(0,1)*k0,2)))*Power(4*c - Complex(0,1)*k0,4)))/(Power(k,4)*Sqrt(1 + Power(k,2)/Power(4*c - Complex(0,1)*k0,2))*(4*c - Complex(0,1)*k0)) - (Power(k,4) - 4*Power(k,2)*(-2 + Sqrt(1 + Power(k,2)/Power(5*c - Complex(0,1)*k0,2)))*Power(5*c - Complex(0,1)*k0,2) - 8*(-1 + Sqrt(1 + Power(k,2)/Power(5*c - Complex(0,1)*k0,2)))*Power(5*c - Complex(0,1)*k0,4))/(Power(k,4)*Sqrt(1 + Power(k,2)/Power(5*c - Complex(0,1)*k0,2))*(5*c - Complex(0,1)*k0)) + (Complex(0,4)*k*k0*(Power(k,2) - 2*Power(k0,2)) + (k*(Power(k,4) - 8*Power(k,2)*Power(k0,2) + 8*Power(k0,4)))/Sqrt(Power(k,2) - Power(k0,2)))/Power(k,5))/k0 -SeriesData[k, Infinity, {-(1/(k*k0)), (k - (4*I)*k0)/(k*k0), (I/2*(8*k - (15*I)*k0))/k, (-15*k*k0 + (16*I)*k0^2)/(2*k), ((-8*I)*k0^3 - (5*((4*(c - I*k0)^5)/k + (3*(c - I*k0)^4*(c/k - (I*k0)/k))/8))/(c - I*k0) + (10*((4*(2*c - I*k0)^5)/k + (3*(2*c - I*k0)^4*((2*c)/k - (I*k0)/k))/8))/(2*c - I*k0) - (10*((4*(3*c - I*k0)^5)/k + (3*(3*c - I*k0)^4*((3*c)/k - (I*k0)/k))/8))/(3*c - I*k0) + (5*((4*(4*c - I*k0)^5)/k + (3*(4*c - I*k0)^4*((4*c)/k - (I*k0)/k))/8))/(4*c - I*k0) + ((-4*(5*c - I*k0)^5)/k - (3*(5*c - I*k0)^4*((5*c)/k - (I*k0)/k))/8)/(5*c - I*k0))/k0, ((35*k0^4)/8 - (5*((3*(c - I*k0)^6)/(2*k) - (3*(c - I*k0)^5*(c/k - (I*k0)/k))/2))/(c - I*k0) + (10*((3*(2*c - I*k0)^6)/(2*k) - (3*(2*c - I*k0)^5*((2*c)/k - (I*k0)/k))/2))/(2*c - I*k0) - (10*((3*(3*c - I*k0)^6)/(2*k) - (3*(3*c - I*k0)^5*((3*c)/k - (I*k0)/k))/2))/(3*c - I*k0) + (5*((3*(4*c - I*k0)^6)/(2*k) - (3*(4*c - I*k0)^5*((4*c)/k - (I*k0)/k))/2))/(4*c - I*k0) + ((-3*(5*c - I*k0)^6)/(2*k) + (3*(5*c - I*k0)^5*((5*c)/k - (I*k0)/k))/2)/(5*c - I*k0))/k0, ((-5*((-4*(c - I*k0)^7)/k + (43*(c - I*k0)^6*(c/k - (I*k0)/k))/16))/(c - I*k0) + (10*((-4*(2*c - I*k0)^7)/k + (43*(2*c - I*k0)^6*((2*c)/k - (I*k0)/k))/16))/(2*c - I*k0) - (10*((-4*(3*c - I*k0)^7)/k + (43*(3*c - I*k0)^6*((3*c)/k - (I*k0)/k))/16))/(3*c - I*k0) + (5*((-4*(4*c - I*k0)^7)/k + (43*(4*c - I*k0)^6*((4*c)/k - (I*k0)/k))/16))/(4*c - I*k0) + ((4*(5*c - I*k0)^7)/k - (43*(5*c - I*k0)^6*((5*c)/k - (I*k0)/k))/16)/(5*c - I*k0))/k0, ((21*k0^6)/16 - (5*((5*(c - I*k0)^8)/(2*k) - (5*(c - I*k0)^7*(c/k - (I*k0)/k))/2))/(c - I*k0) + (10*((5*(2*c - I*k0)^8)/(2*k) - (5*(2*c - I*k0)^7*((2*c)/k - (I*k0)/k))/2))/(2*c - I*k0) - (10*((5*(3*c - I*k0)^8)/(2*k) - (5*(3*c - I*k0)^7*((3*c)/k - (I*k0)/k))/2))/(3*c - I*k0) + (5*((5*(4*c - I*k0)^8)/(2*k) - (5*(4*c - I*k0)^7*((4*c)/k - (I*k0)/k))/2))/(4*c - I*k0) + ((-5*(5*c - I*k0)^8)/(2*k) + (5*(5*c - I*k0)^7*((5*c)/k - (I*k0)/k))/2)/(5*c - I*k0))/k0, ((-495*(c - I*k0)^7*(c/k - (I*k0)/k))/128 + (495*(2*c - I*k0)^7*((2*c)/k - (I*k0)/k))/64 - (495*(3*c - I*k0)^7*((3*c)/k - (I*k0)/k))/64 + (495*(4*c - I*k0)^7*((4*c)/k - (I*k0)/k))/128 - (99*(5*c - I*k0)^7*((5*c)/k - (I*k0)/k))/128)/k0, ((99*k0^8)/128 - (5*((-23*(c - I*k0)^10)/(32*k) + (23*(c - I*k0)^9*(c/k - (I*k0)/k))/32))/(c - I*k0) + (10*((-23*(2*c - I*k0)^10)/(32*k) + (23*(2*c - I*k0)^9*((2*c)/k - (I*k0)/k))/32))/(2*c - I*k0) - (10*((-23*(3*c - I*k0)^10)/(32*k) + (23*(3*c - I*k0)^9*((3*c)/k - (I*k0)/k))/32))/(3*c - I*k0) + (5*((-23*(4*c - I*k0)^10)/(32*k) + (23*(4*c - I*k0)^9*((4*c)/k - (I*k0)/k))/32))/(4*c - I*k0) + ((23*(5*c - I*k0)^10)/(32*k) - (23*(5*c - I*k0)^9*((5*c)/k - (I*k0)/k))/32)/(5*c - I*k0))/k0, ((715*(c - I*k0)^9*(c/k - (I*k0)/k))/256 - (715*(2*c - I*k0)^9*((2*c)/k - (I*k0)/k))/128 + (715*(3*c - I*k0)^9*((3*c)/k - (I*k0)/k))/128 - (715*(4*c - I*k0)^9*((4*c)/k - (I*k0)/k))/256 + (143*(5*c - I*k0)^9*((5*c)/k - (I*k0)/k))/256)/k0}, 0, 11, 1] -((-5*(k^4 - 4*k^2*(-2 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^2 - 8*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^4))/(Sqrt[1 + k^2/(c - I*k0)^2]*(c - I*k0)) + (10*(k^4 - 4*k^2*(-2 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^2 - 8*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^4))/(Sqrt[1 + k^2/(2*c - I*k0)^2]*(2*c - I*k0)) - (10*(k^4 - 4*k^2*(-2 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^2 - 8*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^4))/(Sqrt[1 + k^2/(3*c - I*k0)^2]*(3*c - I*k0)) + (5*(k^4 - 4*k^2*(-2 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^2 - 8*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^4))/(Sqrt[1 + k^2/(4*c - I*k0)^2]*(4*c - I*k0)) - (k^4 - 4*k^2*(-2 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^2 - 8*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^4)/(Sqrt[1 + k^2/(5*c - I*k0)^2]*(5*c - I*k0)) + (4*I)*k0*(k^2 - 2*k0^2) + (k^4 - 8*k^2*k0^2 + 8*k0^4)/Sqrt[k^2 - k0^2])/(k^4*k0) diff --git a/besseltransforms/klarge/5-1-5 b/besseltransforms/klarge/5-1-5 deleted file mode 100644 index edfe47a..0000000 --- a/besseltransforms/klarge/5-1-5 +++ /dev/null @@ -1,4 +0,0 @@ -((-5*(k^4*(-5 + Sqrt[1 + k^2/(c - I*k0)^2]) + 4*k^2*(-5 + 3*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^2 + 16*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^4))/(k^5*Sqrt[1 + k^2/(c - I*k0)^2]) + (10*(k^4*(-5 + Sqrt[1 + k^2/(2*c - I*k0)^2]) + 4*k^2*(-5 + 3*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^2 + 16*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^4))/(k^5*Sqrt[1 + k^2/(2*c - I*k0)^2]) - (10*(k^4*(-5 + Sqrt[1 + k^2/(3*c - I*k0)^2]) + 4*k^2*(-5 + 3*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^2 + 16*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^4))/(k^5*Sqrt[1 + k^2/(3*c - I*k0)^2]) + (5*(k^4*(-5 + Sqrt[1 + k^2/(4*c - I*k0)^2]) + 4*k^2*(-5 + 3*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^2 + 16*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^4))/(k^5*Sqrt[1 + k^2/(4*c - I*k0)^2]) - (k^4*(-5 + Sqrt[1 + k^2/(5*c - I*k0)^2]) + 4*k^2*(-5 + 3*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^2 + 16*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^4)/(k^5*Sqrt[1 + k^2/(5*c - I*k0)^2]) + (k^5 - 12*k^3*k0^2 + 16*k*k0^4 + (I*k*k0*(5*k^4 - 20*k^2*k0^2 + 16*k0^4))/Sqrt[k^2 - k0^2])/k^6)/k0 -((-5*(Power(k,4)*(-5 + Sqrt(1 + Power(k,2)/Power(c - Complex(0,1)*k0,2))) + 4*Power(k,2)*(-5 + 3*Sqrt(1 + Power(k,2)/Power(c - Complex(0,1)*k0,2)))*Power(c - Complex(0,1)*k0,2) + 16*(-1 + Sqrt(1 + Power(k,2)/Power(c - Complex(0,1)*k0,2)))*Power(c - Complex(0,1)*k0,4)))/(Power(k,5)*Sqrt(1 + Power(k,2)/Power(c - Complex(0,1)*k0,2))) + (10*(Power(k,4)*(-5 + Sqrt(1 + Power(k,2)/Power(2*c - Complex(0,1)*k0,2))) + 4*Power(k,2)*(-5 + 3*Sqrt(1 + Power(k,2)/Power(2*c - Complex(0,1)*k0,2)))*Power(2*c - Complex(0,1)*k0,2) + 16*(-1 + Sqrt(1 + Power(k,2)/Power(2*c - Complex(0,1)*k0,2)))*Power(2*c - Complex(0,1)*k0,4)))/(Power(k,5)*Sqrt(1 + Power(k,2)/Power(2*c - Complex(0,1)*k0,2))) - (10*(Power(k,4)*(-5 + Sqrt(1 + Power(k,2)/Power(3*c - Complex(0,1)*k0,2))) + 4*Power(k,2)*(-5 + 3*Sqrt(1 + Power(k,2)/Power(3*c - Complex(0,1)*k0,2)))*Power(3*c - Complex(0,1)*k0,2) + 16*(-1 + Sqrt(1 + Power(k,2)/Power(3*c - Complex(0,1)*k0,2)))*Power(3*c - Complex(0,1)*k0,4)))/(Power(k,5)*Sqrt(1 + Power(k,2)/Power(3*c - Complex(0,1)*k0,2))) + (5*(Power(k,4)*(-5 + Sqrt(1 + Power(k,2)/Power(4*c - Complex(0,1)*k0,2))) + 4*Power(k,2)*(-5 + 3*Sqrt(1 + Power(k,2)/Power(4*c - Complex(0,1)*k0,2)))*Power(4*c - Complex(0,1)*k0,2) + 16*(-1 + Sqrt(1 + Power(k,2)/Power(4*c - Complex(0,1)*k0,2)))*Power(4*c - Complex(0,1)*k0,4)))/(Power(k,5)*Sqrt(1 + Power(k,2)/Power(4*c - Complex(0,1)*k0,2))) - (Power(k,4)*(-5 + Sqrt(1 + Power(k,2)/Power(5*c - Complex(0,1)*k0,2))) + 4*Power(k,2)*(-5 + 3*Sqrt(1 + Power(k,2)/Power(5*c - Complex(0,1)*k0,2)))*Power(5*c - Complex(0,1)*k0,2) + 16*(-1 + Sqrt(1 + Power(k,2)/Power(5*c - Complex(0,1)*k0,2)))*Power(5*c - Complex(0,1)*k0,4))/(Power(k,5)*Sqrt(1 + Power(k,2)/Power(5*c - Complex(0,1)*k0,2))) + (Power(k,5) - 12*Power(k,3)*Power(k0,2) + 16*k*Power(k0,4) + (Complex(0,1)*k*k0*(5*Power(k,4) - 20*Power(k,2)*Power(k0,2) + 16*Power(k0,4)))/Sqrt(Power(k,2) - Power(k0,2)))/Power(k,6))/k0 -SeriesData[k, Infinity, {-(1/(k*k0)), (k - (5*I)*k0)/(k*k0), (I*(5*k - (12*I)*k0))/k, (-24*k*k0 + (35*I)*k0^2)/(2*k), ((-125*(5*c - I*k0)^4)/(8*k) - (35*I)/2*k0^3 - (3*(5*c - I*k0)^3*((5*c)/k - (I*k0)/k))/8 - 5*((125*(c - I*k0)^4)/(8*k) + (3*(c - I*k0)^3*(c/k - (I*k0)/k))/8) + 10*((125*(2*c - I*k0)^4)/(8*k) + (3*(2*c - I*k0)^3*((2*c)/k - (I*k0)/k))/8) - 10*((125*(3*c - I*k0)^4)/(8*k) + (3*(3*c - I*k0)^3*((3*c)/k - (I*k0)/k))/8) + 5*((125*(4*c - I*k0)^4)/(8*k) + (3*(4*c - I*k0)^3*((4*c)/k - (I*k0)/k))/8))/k0, ((6*(5*c - I*k0)^5)/k + 16*k0^4 + (15*(5*c - I*k0)^4*((5*c)/k - (I*k0)/k))/8 - 5*((-6*(c - I*k0)^5)/k - (15*(c - I*k0)^4*(c/k - (I*k0)/k))/8) + 10*((-6*(2*c - I*k0)^5)/k - (15*(2*c - I*k0)^4*((2*c)/k - (I*k0)/k))/8) - 10*((-6*(3*c - I*k0)^5)/k - (15*(3*c - I*k0)^4*((3*c)/k - (I*k0)/k))/8) + 5*((-6*(4*c - I*k0)^5)/k - (15*(4*c - I*k0)^4*((4*c)/k - (I*k0)/k))/8))/k0, ((35*(5*c - I*k0)^6)/(8*k) + (63*I)/8*k0^5 - (35*(5*c - I*k0)^5*((5*c)/k - (I*k0)/k))/8 - 5*((-35*(c - I*k0)^6)/(8*k) + (35*(c - I*k0)^5*(c/k - (I*k0)/k))/8) + 10*((-35*(2*c - I*k0)^6)/(8*k) + (35*(2*c - I*k0)^5*((2*c)/k - (I*k0)/k))/8) - 10*((-35*(3*c - I*k0)^6)/(8*k) + (35*(3*c - I*k0)^5*((3*c)/k - (I*k0)/k))/8) + 5*((-35*(4*c - I*k0)^6)/(8*k) + (35*(4*c - I*k0)^5*((4*c)/k - (I*k0)/k))/8))/k0, ((-8*(5*c - I*k0)^7)/k + (95*(5*c - I*k0)^6*((5*c)/k - (I*k0)/k))/16 - 5*((8*(c - I*k0)^7)/k - (95*(c - I*k0)^6*(c/k - (I*k0)/k))/16) + 10*((8*(2*c - I*k0)^7)/k - (95*(2*c - I*k0)^6*((2*c)/k - (I*k0)/k))/16) - 10*((8*(3*c - I*k0)^7)/k - (95*(3*c - I*k0)^6*((3*c)/k - (I*k0)/k))/16) + 5*((8*(4*c - I*k0)^7)/k - (95*(4*c - I*k0)^6*((4*c)/k - (I*k0)/k))/16))/k0, ((585*(5*c - I*k0)^8)/(128*k) + (33*I)/16*k0^7 - (585*(5*c - I*k0)^7*((5*c)/k - (I*k0)/k))/128 - 5*((-585*(c - I*k0)^8)/(128*k) + (585*(c - I*k0)^7*(c/k - (I*k0)/k))/128) + 10*((-585*(2*c - I*k0)^8)/(128*k) + (585*(2*c - I*k0)^7*((2*c)/k - (I*k0)/k))/128) - 10*((-585*(3*c - I*k0)^8)/(128*k) + (585*(3*c - I*k0)^7*((3*c)/k - (I*k0)/k))/128) + 5*((-585*(4*c - I*k0)^8)/(128*k) + (585*(4*c - I*k0)^7*((4*c)/k - (I*k0)/k))/128))/k0, ((715*(c - I*k0)^8*(c/k - (I*k0)/k))/128 - (715*(2*c - I*k0)^8*((2*c)/k - (I*k0)/k))/64 + (715*(3*c - I*k0)^8*((3*c)/k - (I*k0)/k))/64 - (715*(4*c - I*k0)^8*((4*c)/k - (I*k0)/k))/128 + (143*(5*c - I*k0)^8*((5*c)/k - (I*k0)/k))/128)/k0, ((-77*(5*c - I*k0)^10)/(64*k) + (143*I)/128*k0^9 + (77*(5*c - I*k0)^9*((5*c)/k - (I*k0)/k))/64 - 5*((77*(c - I*k0)^10)/(64*k) - (77*(c - I*k0)^9*(c/k - (I*k0)/k))/64) + 10*((77*(2*c - I*k0)^10)/(64*k) - (77*(2*c - I*k0)^9*((2*c)/k - (I*k0)/k))/64) - 10*((77*(3*c - I*k0)^10)/(64*k) - (77*(3*c - I*k0)^9*((3*c)/k - (I*k0)/k))/64) + 5*((77*(4*c - I*k0)^10)/(64*k) - (77*(4*c - I*k0)^9*((4*c)/k - (I*k0)/k))/64))/k0}, 0, 11, 1] -(k^4 - (5*(k^4*(-5 + Sqrt[1 + k^2/(c - I*k0)^2]) + 4*k^2*(-5 + 3*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^2 + 16*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^4))/Sqrt[1 + k^2/(c - I*k0)^2] + (10*(k^4*(-5 + Sqrt[1 + k^2/(2*c - I*k0)^2]) + 4*k^2*(-5 + 3*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^2 + 16*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^4))/Sqrt[1 + k^2/(2*c - I*k0)^2] - (10*(k^4*(-5 + Sqrt[1 + k^2/(3*c - I*k0)^2]) + 4*k^2*(-5 + 3*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^2 + 16*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^4))/Sqrt[1 + k^2/(3*c - I*k0)^2] + (5*(k^4*(-5 + Sqrt[1 + k^2/(4*c - I*k0)^2]) + 4*k^2*(-5 + 3*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^2 + 16*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^4))/Sqrt[1 + k^2/(4*c - I*k0)^2] - (k^4*(-5 + Sqrt[1 + k^2/(5*c - I*k0)^2]) + 4*k^2*(-5 + 3*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^2 + 16*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^4)/Sqrt[1 + k^2/(5*c - I*k0)^2] - 12*k^2*k0^2 + 16*k0^4 + (I*k0*(5*k^4 - 20*k^2*k0^2 + 16*k0^4))/Sqrt[k^2 - k0^2])/(k^5*k0) diff --git a/besseltransforms/klarge/5-2-0 b/besseltransforms/klarge/5-2-0 deleted file mode 100644 index bc5d03b..0000000 --- a/besseltransforms/klarge/5-2-0 +++ /dev/null @@ -1,14 +0,0 @@ -Integrate[(E^(I*k0*x)*(1 - E^(-(c*x)))^5*BesselJ[0, k*x])/(k0^2*x), {x, 0, Infinity}, Assumptions -> n == 0 && q == 2 && κ == 5 && k > k0 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0] -Integrate((Power(E,I*k0*x)*Power(1 - Power(E,-(c*x)),5)*BesselJ(0,k*x))/(Power(k0,2)*x),List(x,0,DirectedInfinity(1)),Rule(Assumptions,n == 0 && q == 2 && κ == 5 && k > k0 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0)) - - -5 c x + I k0 x c x 5 2 2 4 4 6 6 8 8 Pi 2 2 4 4 6 6 8 8 - E (-1 + E ) ((-418854310875 + 29682132480 k x - 3901685760 k x + 1258291200 k x - 2147483648 k x ) Cos[-- + k x] + 4 Sqrt[2] k x (13043905875 - 1229437440 k x + 240844800 k x - 150994944 k x + 2147483648 k x ) (Cos[k x] + Sin[k x])) - 4 -Integrate::idiv: Integral of ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ does not converge on {0, Infinity}. - 19/2 2 21/2 - 8589934592 k k0 Sqrt[2 Pi] x -Series[Integrate[(E^(I*k0*x)*(1 - E^(-(c*x)))^5*BesselJ[0, k*x])/(k0^2*x), {x, 0, Infinity}, Assumptions -> n == 0 && q == 2 && κ == 5 && k > k0 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0], {k, Infinity, 10}] - - 12 -Simplify::time: Time spent on a transformation exceeded -3.93292 10 seconds, and the transformation was aborted. Increasing the value of TimeConstraint option may improve the result of simplification. -Integrate[(E^(I*k0*x)*(1 - E^(-(c*x)))^5*BesselJ[0, k*x])/(k0^2*x), {x, 0, Infinity}, Assumptions -> n == 0 && q == 2 && κ == 5] diff --git a/besseltransforms/klarge/5-2-1 b/besseltransforms/klarge/5-2-1 deleted file mode 100644 index 2f6c076..0000000 --- a/besseltransforms/klarge/5-2-1 +++ /dev/null @@ -1,4 +0,0 @@ -(-5*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0) + 10*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0) - 10*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0) + 5*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0) - (-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0) + I*k0 + Sqrt[k^2 - k0^2])/(k*k0^2) -(-5*(-1 + Sqrt(1 + Power(k,2)/Power(c - Complex(0,1)*k0,2)))*(c - Complex(0,1)*k0) + 10*(-1 + Sqrt(1 + Power(k,2)/Power(2*c - Complex(0,1)*k0,2)))*(2*c - Complex(0,1)*k0) - 10*(-1 + Sqrt(1 + Power(k,2)/Power(3*c - Complex(0,1)*k0,2)))*(3*c - Complex(0,1)*k0) + 5*(-1 + Sqrt(1 + Power(k,2)/Power(4*c - Complex(0,1)*k0,2)))*(4*c - Complex(0,1)*k0) - (-1 + Sqrt(1 + Power(k,2)/Power(5*c - Complex(0,1)*k0,2)))*(5*c - Complex(0,1)*k0) + Complex(0,1)*k0 + Sqrt(Power(k,2) - Power(k0,2)))/(k*Power(k0,2)) -SeriesData[k, Infinity, {(-225*c^6)/(2*k0^2) + ((45*I)*c^5)/k0, 0, (-7875*c^6)/4 + (39375*c^8)/(8*k0^2) - ((5250*I)*c^7)/k0 + (525*I)/2*c^5*k0, 0, (-2205*(2025*c^10 - (3310*I)*c^9*k0 - 2250*c^8*k0^2 + (800*I)*c^7*k0^3 + 150*c^6*k0^4 - (12*I)*c^5*k0^5))/(32*k0^2)}, 6, 11, 1] -(-5*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0) + 10*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0) - 10*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0) + 5*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0) - (-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0) + I*k0 + Sqrt[k^2 - k0^2])/(k*k0^2) diff --git a/besseltransforms/klarge/5-2-2 b/besseltransforms/klarge/5-2-2 deleted file mode 100644 index b9240a6..0000000 --- a/besseltransforms/klarge/5-2-2 +++ /dev/null @@ -1,4 +0,0 @@ -(5*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^2 - 10*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^2 + 10*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^2 - 5*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^2 + (-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^2 - k0^2 + I*k0*Sqrt[k^2 - k0^2])/(k^2*k0^2) -(5*(-1 + Sqrt(1 + Power(k,2)/Power(c - Complex(0,1)*k0,2)))*Power(c - Complex(0,1)*k0,2) - 10*(-1 + Sqrt(1 + Power(k,2)/Power(2*c - Complex(0,1)*k0,2)))*Power(2*c - Complex(0,1)*k0,2) + 10*(-1 + Sqrt(1 + Power(k,2)/Power(3*c - Complex(0,1)*k0,2)))*Power(3*c - Complex(0,1)*k0,2) - 5*(-1 + Sqrt(1 + Power(k,2)/Power(4*c - Complex(0,1)*k0,2)))*Power(4*c - Complex(0,1)*k0,2) + (-1 + Sqrt(1 + Power(k,2)/Power(5*c - Complex(0,1)*k0,2)))*Power(5*c - Complex(0,1)*k0,2) - Power(k0,2) + Complex(0,1)*k0*Sqrt(Power(k,2) - Power(k0,2)))/(Power(k,2)*Power(k0,2)) -SeriesData[k, Infinity, {(-15*c^5)/k0^2, 0, (-315*c^5)/2 + (1050*c^7)/k0^2 - ((1575*I)/2*c^6)/k0, 0, (-1575*(331*c^9 - (450*I)*c^8*k0 - 240*c^7*k0^2 + (60*I)*c^6*k0^3 + 6*c^5*k0^4))/(16*k0^2)}, 5, 11, 1] -(5*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^2 - 10*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^2 + 10*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^2 - 5*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^2 + (-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^2 - k0^2 + I*k0*Sqrt[k^2 - k0^2])/(k^2*k0^2) diff --git a/besseltransforms/klarge/5-2-3 b/besseltransforms/klarge/5-2-3 deleted file mode 100644 index 8e9b09c..0000000 --- a/besseltransforms/klarge/5-2-3 +++ /dev/null @@ -1,4 +0,0 @@ -((-5*(k^2*(-3 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0) + 4*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^3))/(3*k^3) + (10*(k^2*(-3 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0) + 4*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^3))/(3*k^3) - (10*(k^2*(-3 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0) + 4*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^3))/(3*k^3) + (5*(k^2*(-3 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0) + 4*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^3))/(3*k^3) - (k^2*(-3 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0) + 4*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^3)/(3*k^3) + (-4*k0^2*(I*k0 + Sqrt[k^2 - k0^2]) + k^2*((3*I)*k0 + Sqrt[k^2 - k0^2]))/(3*k^3))/k0^2 -((-5*(Power(k,2)*(-3 + Sqrt(1 + Power(k,2)/Power(c - Complex(0,1)*k0,2)))*(c - Complex(0,1)*k0) + 4*(-1 + Sqrt(1 + Power(k,2)/Power(c - Complex(0,1)*k0,2)))*Power(c - Complex(0,1)*k0,3)))/(3.*Power(k,3)) + (10*(Power(k,2)*(-3 + Sqrt(1 + Power(k,2)/Power(2*c - Complex(0,1)*k0,2)))*(2*c - Complex(0,1)*k0) + 4*(-1 + Sqrt(1 + Power(k,2)/Power(2*c - Complex(0,1)*k0,2)))*Power(2*c - Complex(0,1)*k0,3)))/(3.*Power(k,3)) - (10*(Power(k,2)*(-3 + Sqrt(1 + Power(k,2)/Power(3*c - Complex(0,1)*k0,2)))*(3*c - Complex(0,1)*k0) + 4*(-1 + Sqrt(1 + Power(k,2)/Power(3*c - Complex(0,1)*k0,2)))*Power(3*c - Complex(0,1)*k0,3)))/(3.*Power(k,3)) + (5*(Power(k,2)*(-3 + Sqrt(1 + Power(k,2)/Power(4*c - Complex(0,1)*k0,2)))*(4*c - Complex(0,1)*k0) + 4*(-1 + Sqrt(1 + Power(k,2)/Power(4*c - Complex(0,1)*k0,2)))*Power(4*c - Complex(0,1)*k0,3)))/(3.*Power(k,3)) - (Power(k,2)*(-3 + Sqrt(1 + Power(k,2)/Power(5*c - Complex(0,1)*k0,2)))*(5*c - Complex(0,1)*k0) + 4*(-1 + Sqrt(1 + Power(k,2)/Power(5*c - Complex(0,1)*k0,2)))*Power(5*c - Complex(0,1)*k0,3))/(3.*Power(k,3)) + (-4*Power(k0,2)*(Complex(0,1)*k0 + Sqrt(Power(k,2) - Power(k0,2))) + Power(k,2)*(Complex(0,3)*k0 + Sqrt(Power(k,2) - Power(k0,2))))/(3.*Power(k,3)))/Power(k0,2) -SeriesData[k, Infinity, {(525*c^6)/(2*k0^2) - ((105*I)*c^5)/k0, 0, (14175*c^6)/4 - (70875*c^8)/(8*k0^2) + ((9450*I)*c^7)/k0 - (945*I)/2*c^5*k0, 0, (3465*(2025*c^10 - (3310*I)*c^9*k0 - 2250*c^8*k0^2 + (800*I)*c^7*k0^3 + 150*c^6*k0^4 - (12*I)*c^5*k0^5))/(32*k0^2)}, 6, 11, 1] --(5*k^2*(-3 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0) + 20*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^3 - 10*k^2*(-3 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0) - 40*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^3 + 10*k^2*(-3 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0) + 40*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^3 - 5*k^2*(-3 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0) - 20*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^3 + k^2*(-3 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0) + 4*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^3 + 4*k0^2*(I*k0 + Sqrt[k^2 - k0^2]) - k^2*((3*I)*k0 + Sqrt[k^2 - k0^2]))/(3*k^3*k0^2) diff --git a/besseltransforms/klarge/5-2-4 b/besseltransforms/klarge/5-2-4 deleted file mode 100644 index 5945190..0000000 --- a/besseltransforms/klarge/5-2-4 +++ /dev/null @@ -1,4 +0,0 @@ -(-5*(1/4 - ((-2 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^2)/k^2 - (2*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^4)/k^4) + 10*(1/4 - ((-2 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^2)/k^2 - (2*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^4)/k^4) - 10*(1/4 - ((-2 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^2)/k^2 - (2*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^4)/k^4) + 5*(1/4 - ((-2 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^2)/k^2 - (2*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^4)/k^4) + ((-2 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^2)/k^2 + (2*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^4)/k^4 + (2*k0^3*(k0 - I*Sqrt[k^2 - k0^2]))/k^4 + (I*k0*((2*I)*k0 + Sqrt[k^2 - k0^2]))/k^2)/k0^2 -(-5*(0.25 - ((-2 + Sqrt(1 + Power(k,2)/Power(c - Complex(0,1)*k0,2)))*Power(c - Complex(0,1)*k0,2))/Power(k,2) - (2*(-1 + Sqrt(1 + Power(k,2)/Power(c - Complex(0,1)*k0,2)))*Power(c - Complex(0,1)*k0,4))/Power(k,4)) + 10*(0.25 - ((-2 + Sqrt(1 + Power(k,2)/Power(2*c - Complex(0,1)*k0,2)))*Power(2*c - Complex(0,1)*k0,2))/Power(k,2) - (2*(-1 + Sqrt(1 + Power(k,2)/Power(2*c - Complex(0,1)*k0,2)))*Power(2*c - Complex(0,1)*k0,4))/Power(k,4)) - 10*(0.25 - ((-2 + Sqrt(1 + Power(k,2)/Power(3*c - Complex(0,1)*k0,2)))*Power(3*c - Complex(0,1)*k0,2))/Power(k,2) - (2*(-1 + Sqrt(1 + Power(k,2)/Power(3*c - Complex(0,1)*k0,2)))*Power(3*c - Complex(0,1)*k0,4))/Power(k,4)) + 5*(0.25 - ((-2 + Sqrt(1 + Power(k,2)/Power(4*c - Complex(0,1)*k0,2)))*Power(4*c - Complex(0,1)*k0,2))/Power(k,2) - (2*(-1 + Sqrt(1 + Power(k,2)/Power(4*c - Complex(0,1)*k0,2)))*Power(4*c - Complex(0,1)*k0,4))/Power(k,4)) + ((-2 + Sqrt(1 + Power(k,2)/Power(5*c - Complex(0,1)*k0,2)))*Power(5*c - Complex(0,1)*k0,2))/Power(k,2) + (2*(-1 + Sqrt(1 + Power(k,2)/Power(5*c - Complex(0,1)*k0,2)))*Power(5*c - Complex(0,1)*k0,4))/Power(k,4) + (2*Power(k0,3)*(k0 - Complex(0,1)*Sqrt(Power(k,2) - Power(k0,2))))/Power(k,4) + (Complex(0,1)*k0*(Complex(0,2)*k0 + Sqrt(Power(k,2) - Power(k0,2))))/Power(k,2))/Power(k0,2) -SeriesData[k, Infinity, {(105*c^5)/k0^2, 0, (945*c^5)/2 - (3150*c^7)/k0^2 + ((4725*I)/2*c^6)/k0, 0, (3465*(331*c^9 - (450*I)*c^8*k0 - 240*c^7*k0^2 + (60*I)*c^6*k0^3 + 6*c^5*k0^4))/(16*k0^2)}, 5, 11, 1] -(5*k^2*(-2 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^2 + 10*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^4 - 10*k^2*(-2 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^2 - 20*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^4 + 10*k^2*(-2 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^2 + 20*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^4 - 5*k^2*(-2 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^2 - 10*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^4 + k^2*(-2 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^2 + 2*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^4 + 2*k0^3*(k0 - I*Sqrt[k^2 - k0^2]) + I*k^2*k0*((2*I)*k0 + Sqrt[k^2 - k0^2]))/(k^4*k0^2) diff --git a/besseltransforms/klarge/5-2-5 b/besseltransforms/klarge/5-2-5 deleted file mode 100644 index f382318..0000000 --- a/besseltransforms/klarge/5-2-5 +++ /dev/null @@ -1,4 +0,0 @@ -(-((k^4*(-5 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0) + 4*k^2*(-5 + 3*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^3 + 16*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^5)/k^5) + (2*(k^4*(-5 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0) + 4*k^2*(-5 + 3*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^3 + 16*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^5))/k^5 - (2*(k^4*(-5 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0) + 4*k^2*(-5 + 3*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^3 + 16*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^5))/k^5 + (k^4*(-5 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0) + 4*k^2*(-5 + 3*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^3 + 16*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^5)/k^5 - (k^4*(-5 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0) + 4*k^2*(-5 + 3*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^3 + 16*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^5)/(5*k^5) + (16*k0^4*(I*k0 + Sqrt[k^2 - k0^2]) + k^4*((5*I)*k0 + Sqrt[k^2 - k0^2]) - 4*k^2*k0^2*((5*I)*k0 + 3*Sqrt[k^2 - k0^2]))/(5*k^5))/k0^2 -(-((Power(k,4)*(-5 + Sqrt(1 + Power(k,2)/Power(c - Complex(0,1)*k0,2)))*(c - Complex(0,1)*k0) + 4*Power(k,2)*(-5 + 3*Sqrt(1 + Power(k,2)/Power(c - Complex(0,1)*k0,2)))*Power(c - Complex(0,1)*k0,3) + 16*(-1 + Sqrt(1 + Power(k,2)/Power(c - Complex(0,1)*k0,2)))*Power(c - Complex(0,1)*k0,5))/Power(k,5)) + (2*(Power(k,4)*(-5 + Sqrt(1 + Power(k,2)/Power(2*c - Complex(0,1)*k0,2)))*(2*c - Complex(0,1)*k0) + 4*Power(k,2)*(-5 + 3*Sqrt(1 + Power(k,2)/Power(2*c - Complex(0,1)*k0,2)))*Power(2*c - Complex(0,1)*k0,3) + 16*(-1 + Sqrt(1 + Power(k,2)/Power(2*c - Complex(0,1)*k0,2)))*Power(2*c - Complex(0,1)*k0,5)))/Power(k,5) - (2*(Power(k,4)*(-5 + Sqrt(1 + Power(k,2)/Power(3*c - Complex(0,1)*k0,2)))*(3*c - Complex(0,1)*k0) + 4*Power(k,2)*(-5 + 3*Sqrt(1 + Power(k,2)/Power(3*c - Complex(0,1)*k0,2)))*Power(3*c - Complex(0,1)*k0,3) + 16*(-1 + Sqrt(1 + Power(k,2)/Power(3*c - Complex(0,1)*k0,2)))*Power(3*c - Complex(0,1)*k0,5)))/Power(k,5) + (Power(k,4)*(-5 + Sqrt(1 + Power(k,2)/Power(4*c - Complex(0,1)*k0,2)))*(4*c - Complex(0,1)*k0) + 4*Power(k,2)*(-5 + 3*Sqrt(1 + Power(k,2)/Power(4*c - Complex(0,1)*k0,2)))*Power(4*c - Complex(0,1)*k0,3) + 16*(-1 + Sqrt(1 + Power(k,2)/Power(4*c - Complex(0,1)*k0,2)))*Power(4*c - Complex(0,1)*k0,5))/Power(k,5) - (Power(k,4)*(-5 + Sqrt(1 + Power(k,2)/Power(5*c - Complex(0,1)*k0,2)))*(5*c - Complex(0,1)*k0) + 4*Power(k,2)*(-5 + 3*Sqrt(1 + Power(k,2)/Power(5*c - Complex(0,1)*k0,2)))*Power(5*c - Complex(0,1)*k0,3) + 16*(-1 + Sqrt(1 + Power(k,2)/Power(5*c - Complex(0,1)*k0,2)))*Power(5*c - Complex(0,1)*k0,5))/(5.*Power(k,5)) + (16*Power(k0,4)*(Complex(0,1)*k0 + Sqrt(Power(k,2) - Power(k0,2))) + Power(k,4)*(Complex(0,5)*k0 + Sqrt(Power(k,2) - Power(k0,2))) - 4*Power(k,2)*Power(k0,2)*(Complex(0,5)*k0 + 3*Sqrt(Power(k,2) - Power(k0,2))))/(5.*Power(k,5)))/Power(k0,2) -SeriesData[k, Infinity, {(384*c^5)/k0^2, (-4725*c^6)/(2*k0^2) + ((945*I)*c^5)/k0, 0, (-51975*c^6)/4 + (259875*c^8)/(8*k0^2) - ((34650*I)*c^7)/k0 + (3465*I)/2*c^5*k0, 0, (-9009*(2025*c^10 - (3310*I)*c^9*k0 - 2250*c^8*k0^2 + (800*I)*c^7*k0^3 + 150*c^6*k0^4 - (12*I)*c^5*k0^5))/(32*k0^2)}, 5, 11, 1] --(5*(k^4*(-5 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0) + 4*k^2*(-5 + 3*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^3 + 16*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^5) - 10*(k^4*(-5 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0) + 4*k^2*(-5 + 3*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^3 + 16*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^5) + 10*(k^4*(-5 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0) + 4*k^2*(-5 + 3*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^3 + 16*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^5) - 5*(k^4*(-5 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0) + 4*k^2*(-5 + 3*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^3 + 16*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^5) + k^4*(-5 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0) + 4*k^2*(-5 + 3*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^3 + 16*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^5 - 16*k0^4*(I*k0 + Sqrt[k^2 - k0^2]) - k^4*((5*I)*k0 + Sqrt[k^2 - k0^2]) + 4*k^2*k0^2*((5*I)*k0 + 3*Sqrt[k^2 - k0^2]))/(5*k^5*k0^2) diff --git a/besseltransforms/klarge/5-3-0 b/besseltransforms/klarge/5-3-0 deleted file mode 100644 index 24dbc15..0000000 --- a/besseltransforms/klarge/5-3-0 +++ /dev/null @@ -1,11 +0,0 @@ -Integrate[(E^(I*k0*x)*(1 - E^(-(c*x)))^5*BesselJ[0, k*x])/(k0^3*x^2), {x, 0, Infinity}, Assumptions -> n == 0 && q == 3 && κ == 5 && k > k0 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0] -Integrate((Power(E,I*k0*x)*Power(1 - Power(E,-(c*x)),5)*BesselJ(0,k*x))/(Power(k0,3)*Power(x,2)),List(x,0,DirectedInfinity(1)),Rule(Assumptions,n == 0 && q == 3 && κ == 5 && k > k0 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0)) - - -5 c x + I k0 x c x 5 2 2 4 4 6 6 8 8 Pi 2 2 4 4 6 6 8 8 - E (-1 + E ) ((-418854310875 + 29682132480 k x - 3901685760 k x + 1258291200 k x - 2147483648 k x ) Cos[-- + k x] + 4 Sqrt[2] k x (13043905875 - 1229437440 k x + 240844800 k x - 150994944 k x + 2147483648 k x ) (Cos[k x] + Sin[k x])) - 4 -Integrate::idiv: Integral of ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ does not converge on {0, Infinity}. - 19/2 3 23/2 - 8589934592 k k0 Sqrt[2 Pi] x -Series[Integrate[(E^(I*k0*x)*(1 - E^(-(c*x)))^5*BesselJ[0, k*x])/(k0^3*x^2), {x, 0, Infinity}, Assumptions -> n == 0 && q == 3 && κ == 5 && k > k0 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0], {k, Infinity, 10}] -Integrate[(E^(I*k0*x)*(1 - E^(-(c*x)))^5*BesselJ[0, k*x])/(k0^3*x^2), {x, 0, Infinity}, Assumptions -> n == 0 && q == 3 && κ == 5] diff --git a/besseltransforms/klarge/5-3-1 b/besseltransforms/klarge/5-3-1 deleted file mode 100644 index f14813c..0000000 --- a/besseltransforms/klarge/5-3-1 +++ /dev/null @@ -1,11 +0,0 @@ -Integrate[(E^(I*k0*x)*(1 - E^(-(c*x)))^5*BesselJ[1, k*x])/(k0^3*x^2), {x, 0, Infinity}, Assumptions -> n == 1 && q == 3 && κ == 5 && k > k0 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0] -Integrate((Power(E,I*k0*x)*Power(1 - Power(E,-(c*x)),5)*BesselJ(1,k*x))/(Power(k0,3)*Power(x,2)),List(x,0,DirectedInfinity(1)),Rule(Assumptions,n == 1 && q == 3 && κ == 5 && k > k0 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0)) - - I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi I k0 x 2 Pi -5 c x + I k0 x 2 Pi -4 c x + I k0 x 2 Pi -3 c x + I k0 x 2 Pi -2 c x + I k0 x 2 Pi -(c x) + I k0 x 2 Pi I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi - 14783093325 E Cos[-- + k x] 14783093325 E Cos[-- + k x] 73915466625 E Cos[-- + k x] 73915466625 E Cos[-- + k x] 73915466625 E Cos[-- + k x] 73915466625 E Cos[-- + k x] 2837835 E Cos[-- + k x] 2837835 E Cos[-- + k x] 14189175 E Cos[-- + k x] 14189175 E Cos[-- + k x] 14189175 E Cos[-- + k x] 14189175 E Cos[-- + k x] 4725 E Cos[-- + k x] 4725 E Cos[-- + k x] 23625 E Cos[-- + k x] 23625 E Cos[-- + k x] 23625 E Cos[-- + k x] 23625 E Cos[-- + k x] 15 E Cos[-- + k x] 15 E Cos[-- + k x] 75 E Cos[-- + k x] 75 E Cos[-- + k x] 75 E Cos[-- + k x] 75 E Cos[-- + k x] E Sqrt[--] Cos[-- + k x] E Sqrt[--] Cos[-- + k x] 5 E Sqrt[--] Cos[-- + k x] 10 E Sqrt[--] Cos[-- + k x] 10 E Sqrt[--] Cos[-- + k x] 5 E Sqrt[--] Cos[-- + k x] 468131288625 E Sin[-- + k x] 468131288625 E Sin[-- + k x] 2340656443125 E Sin[-- + k x] 2340656443125 E Sin[-- + k x] 2340656443125 E Sin[-- + k x] 2340656443125 E Sin[-- + k x] 66891825 E Sin[-- + k x] 66891825 E Sin[-- + k x] 334459125 E Sin[-- + k x] 334459125 E Sin[-- + k x] 334459125 E Sin[-- + k x] 334459125 E Sin[-- + k x] 72765 E Sin[-- + k x] 72765 E Sin[-- + k x] 363825 E Sin[-- + k x] 363825 E Sin[-- + k x] 363825 E Sin[-- + k x] 363825 E Sin[-- + k x] 105 E Sin[-- + k x] 105 E Sin[-- + k x] 525 E Sin[-- + k x] 525 E Sin[-- + k x] 525 E Sin[-- + k x] 525 E Sin[-- + k x] 3 E Sin[-- + k x] 3 E Sin[-- + k x] 15 E Sin[-- + k x] 15 E Sin[-- + k x] 15 E Sin[-- + k x] 15 E Sin[-- + k x] - 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 Pi 4 Pi 4 Pi 4 Pi 4 Pi 4 Pi 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 -Integrate::idiv: Integral of ------------------------------------- - ------------------------------------------ + ------------------------------------------ - ------------------------------------------ + ------------------------------------------ - ------------------------------------------ - ---------------------------------- + -------------------------------------- - --------------------------------------- + --------------------------------------- - --------------------------------------- + --------------------------------------- + ------------------------------- - ----------------------------------- + ------------------------------------ - ------------------------------------ + ------------------------------------ - ------------------------------------ - --------------------------- + --------------------------------- - --------------------------------- + --------------------------------- - --------------------------------- + --------------------------------- - ------------------------------ + --------------------------------------- - ----------------------------------------- + ------------------------------------------ - ------------------------------------------ + ----------------------------------------- + ------------------------------------- - ------------------------------------------- + -------------------------------------------- - -------------------------------------------- + -------------------------------------------- - -------------------------------------------- - ----------------------------------- + --------------------------------------- - ---------------------------------------- + ---------------------------------------- - ---------------------------------------- + ---------------------------------------- + --------------------------------- - ------------------------------------ + ------------------------------------- - ------------------------------------- + ------------------------------------- - ------------------------------------- - ----------------------------- + ---------------------------------- - ---------------------------------- + ---------------------------------- - ---------------------------------- + ---------------------------------- + -------------------------- - -------------------------------- + --------------------------------- - --------------------------------- + --------------------------------- - --------------------------------- does not converge on {0, Infinity}. - 17/2 3 21/2 17/2 3 21/2 17/2 3 21/2 17/2 3 21/2 17/2 3 21/2 17/2 3 21/2 13/2 3 17/2 13/2 3 17/2 13/2 3 17/2 13/2 3 17/2 13/2 3 17/2 13/2 3 17/2 9/2 3 13/2 9/2 3 13/2 9/2 3 13/2 9/2 3 13/2 9/2 3 13/2 9/2 3 13/2 5/2 3 9/2 5/2 3 9/2 5/2 3 9/2 5/2 3 9/2 5/2 3 9/2 5/2 3 9/2 3 5/2 3 5/2 3 5/2 3 5/2 3 5/2 3 5/2 19/2 3 23/2 19/2 3 23/2 19/2 3 23/2 19/2 3 23/2 19/2 3 23/2 19/2 3 23/2 15/2 3 19/2 15/2 3 19/2 15/2 3 19/2 15/2 3 19/2 15/2 3 19/2 15/2 3 19/2 11/2 3 15/2 11/2 3 15/2 11/2 3 15/2 11/2 3 15/2 11/2 3 15/2 11/2 3 15/2 7/2 3 11/2 7/2 3 11/2 7/2 3 11/2 7/2 3 11/2 7/2 3 11/2 7/2 3 11/2 3/2 3 7/2 3/2 3 7/2 3/2 3 7/2 3/2 3 7/2 3/2 3 7/2 3/2 3 7/2 - 1073741824 k k0 Sqrt[2 Pi] x 1073741824 k k0 Sqrt[2 Pi] x 1073741824 k k0 Sqrt[2 Pi] x 536870912 k k0 Sqrt[2 Pi] x 536870912 k k0 Sqrt[2 Pi] x 1073741824 k k0 Sqrt[2 Pi] x 2097152 k k0 Sqrt[2 Pi] x 2097152 k k0 Sqrt[2 Pi] x 2097152 k k0 Sqrt[2 Pi] x 1048576 k k0 Sqrt[2 Pi] x 1048576 k k0 Sqrt[2 Pi] x 2097152 k k0 Sqrt[2 Pi] x 16384 k k0 Sqrt[2 Pi] x 16384 k k0 Sqrt[2 Pi] x 16384 k k0 Sqrt[2 Pi] x 8192 k k0 Sqrt[2 Pi] x 8192 k k0 Sqrt[2 Pi] x 16384 k k0 Sqrt[2 Pi] x 64 k k0 Sqrt[2 Pi] x 64 k k0 Sqrt[2 Pi] x 64 k k0 Sqrt[2 Pi] x 32 k k0 Sqrt[2 Pi] x 32 k k0 Sqrt[2 Pi] x 64 k k0 Sqrt[2 Pi] x Sqrt[k] k0 x Sqrt[k] k0 x Sqrt[k] k0 x Sqrt[k] k0 x Sqrt[k] k0 x Sqrt[k] k0 x 8589934592 k k0 Sqrt[2 Pi] x 8589934592 k k0 Sqrt[2 Pi] x 8589934592 k k0 Sqrt[2 Pi] x 4294967296 k k0 Sqrt[2 Pi] x 4294967296 k k0 Sqrt[2 Pi] x 8589934592 k k0 Sqrt[2 Pi] x 16777216 k k0 Sqrt[2 Pi] x 16777216 k k0 Sqrt[2 Pi] x 16777216 k k0 Sqrt[2 Pi] x 8388608 k k0 Sqrt[2 Pi] x 8388608 k k0 Sqrt[2 Pi] x 16777216 k k0 Sqrt[2 Pi] x 131072 k k0 Sqrt[2 Pi] x 131072 k k0 Sqrt[2 Pi] x 131072 k k0 Sqrt[2 Pi] x 65536 k k0 Sqrt[2 Pi] x 65536 k k0 Sqrt[2 Pi] x 131072 k k0 Sqrt[2 Pi] x 512 k k0 Sqrt[2 Pi] x 512 k k0 Sqrt[2 Pi] x 512 k k0 Sqrt[2 Pi] x 256 k k0 Sqrt[2 Pi] x 256 k k0 Sqrt[2 Pi] x 512 k k0 Sqrt[2 Pi] x 4 k k0 Sqrt[2 Pi] x 4 k k0 Sqrt[2 Pi] x 4 k k0 Sqrt[2 Pi] x 2 k k0 Sqrt[2 Pi] x 2 k k0 Sqrt[2 Pi] x 4 k k0 Sqrt[2 Pi] x -Series[Integrate[(E^(I*k0*x)*(1 - E^(-(c*x)))^5*BesselJ[1, k*x])/(k0^3*x^2), {x, 0, Infinity}, Assumptions -> n == 1 && q == 3 && κ == 5 && k > k0 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0], {k, Infinity, 10}] -Integrate[(E^(I*k0*x)*(1 - E^(-(c*x)))^5*BesselJ[1, k*x])/(k0^3*x^2), {x, 0, Infinity}, Assumptions -> n == 1 && q == 3 && κ == 5] diff --git a/besseltransforms/klarge/5-3-2 b/besseltransforms/klarge/5-3-2 deleted file mode 100644 index a8ee4a3..0000000 --- a/besseltransforms/klarge/5-3-2 +++ /dev/null @@ -1,4 +0,0 @@ -(-5*(((-3 + 2*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0))/6 + ((-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^3)/(3*k^2)) + 10*(((-3 + 2*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0))/6 + ((-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^3)/(3*k^2)) - 10*(((-3 + 2*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0))/6 + ((-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^3)/(3*k^2)) + 5*(((-3 + 2*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0))/6 + ((-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^3)/(3*k^2)) - ((-3 + 2*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0))/6 - ((-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^3)/(3*k^2) + ((3*I)*k0 + 2*Sqrt[k^2 - k0^2] - (2*k0^2*(I*k0 + Sqrt[k^2 - k0^2]))/k^2)/6)/k0^3 -(-5*(((-3 + 2*Sqrt(1 + Power(k,2)/Power(c - Complex(0,1)*k0,2)))*(c - Complex(0,1)*k0))/6. + ((-1 + Sqrt(1 + Power(k,2)/Power(c - Complex(0,1)*k0,2)))*Power(c - Complex(0,1)*k0,3))/(3.*Power(k,2))) + 10*(((-3 + 2*Sqrt(1 + Power(k,2)/Power(2*c - Complex(0,1)*k0,2)))*(2*c - Complex(0,1)*k0))/6. + ((-1 + Sqrt(1 + Power(k,2)/Power(2*c - Complex(0,1)*k0,2)))*Power(2*c - Complex(0,1)*k0,3))/(3.*Power(k,2))) - 10*(((-3 + 2*Sqrt(1 + Power(k,2)/Power(3*c - Complex(0,1)*k0,2)))*(3*c - Complex(0,1)*k0))/6. + ((-1 + Sqrt(1 + Power(k,2)/Power(3*c - Complex(0,1)*k0,2)))*Power(3*c - Complex(0,1)*k0,3))/(3.*Power(k,2))) + 5*(((-3 + 2*Sqrt(1 + Power(k,2)/Power(4*c - Complex(0,1)*k0,2)))*(4*c - Complex(0,1)*k0))/6. + ((-1 + Sqrt(1 + Power(k,2)/Power(4*c - Complex(0,1)*k0,2)))*Power(4*c - Complex(0,1)*k0,3))/(3.*Power(k,2))) - ((-3 + 2*Sqrt(1 + Power(k,2)/Power(5*c - Complex(0,1)*k0,2)))*(5*c - Complex(0,1)*k0))/6. - ((-1 + Sqrt(1 + Power(k,2)/Power(5*c - Complex(0,1)*k0,2)))*Power(5*c - Complex(0,1)*k0,3))/(3.*Power(k,2)) + (Complex(0,3)*k0 + 2*Sqrt(Power(k,2) - Power(k0,2)) - (2*Power(k0,2)*(Complex(0,1)*k0 + Sqrt(Power(k,2) - Power(k0,2))))/Power(k,2))/6.)/Power(k0,3) -SeriesData[k, Infinity, {(75*c^6)/(2*k0^3) - ((15*I)*c^5)/k0^2, 0, (-105*(75*c^8 - (80*I)*c^7*k0 - 30*c^6*k0^2 + (4*I)*c^5*k0^3))/(8*k0^3), 0, (315*(2025*c^10 - (3310*I)*c^9*k0 - 2250*c^8*k0^2 + (800*I)*c^7*k0^3 + 150*c^6*k0^4 - (12*I)*c^5*k0^5))/(32*k0^3)}, 5, 11, 1] -(5*(3 - 2*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0) - (10*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^3)/k^2 + 10*(-3 + 2*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0) + (20*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^3)/k^2 + 10*(3 - 2*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0) - (20*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^3)/k^2 + 5*(-3 + 2*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0) + (10*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^3)/k^2 + (3 - 2*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0) - (2*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^3)/k^2 + (3*I)*k0 + 2*Sqrt[k^2 - k0^2] - (2*k0^2*(I*k0 + Sqrt[k^2 - k0^2]))/k^2)/(6*k0^3) diff --git a/besseltransforms/klarge/5-3-3 b/besseltransforms/klarge/5-3-3 deleted file mode 100644 index 3009210..0000000 --- a/besseltransforms/klarge/5-3-3 +++ /dev/null @@ -1,4 +0,0 @@ -((-5*(3*k^4 + 4*k^2*(3 - 2*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^2 - 8*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^4))/(24*k^3) + (5*(3*k^4 + 4*k^2*(3 - 2*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^2 - 8*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^4))/(12*k^3) - (5*(3*k^4 + 4*k^2*(3 - 2*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^2 - 8*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^4))/(12*k^3) + (5*(3*k^4 + 4*k^2*(3 - 2*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^2 - 8*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^4))/(24*k^3) - (3*k^4 + 4*k^2*(3 - 2*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^2 - 8*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^4)/(24*k^3) + (3*k^4 + 8*k0^3*(k0 - I*Sqrt[k^2 - k0^2]) + 4*k^2*k0*(-3*k0 + (2*I)*Sqrt[k^2 - k0^2]))/(24*k^3))/k0^3 -((-5*(3*Power(k,4) + 4*Power(k,2)*(3 - 2*Sqrt(1 + Power(k,2)/Power(c - Complex(0,1)*k0,2)))*Power(c - Complex(0,1)*k0,2) - 8*(-1 + Sqrt(1 + Power(k,2)/Power(c - Complex(0,1)*k0,2)))*Power(c - Complex(0,1)*k0,4)))/(24.*Power(k,3)) + (5*(3*Power(k,4) + 4*Power(k,2)*(3 - 2*Sqrt(1 + Power(k,2)/Power(2*c - Complex(0,1)*k0,2)))*Power(2*c - Complex(0,1)*k0,2) - 8*(-1 + Sqrt(1 + Power(k,2)/Power(2*c - Complex(0,1)*k0,2)))*Power(2*c - Complex(0,1)*k0,4)))/(12.*Power(k,3)) - (5*(3*Power(k,4) + 4*Power(k,2)*(3 - 2*Sqrt(1 + Power(k,2)/Power(3*c - Complex(0,1)*k0,2)))*Power(3*c - Complex(0,1)*k0,2) - 8*(-1 + Sqrt(1 + Power(k,2)/Power(3*c - Complex(0,1)*k0,2)))*Power(3*c - Complex(0,1)*k0,4)))/(12.*Power(k,3)) + (5*(3*Power(k,4) + 4*Power(k,2)*(3 - 2*Sqrt(1 + Power(k,2)/Power(4*c - Complex(0,1)*k0,2)))*Power(4*c - Complex(0,1)*k0,2) - 8*(-1 + Sqrt(1 + Power(k,2)/Power(4*c - Complex(0,1)*k0,2)))*Power(4*c - Complex(0,1)*k0,4)))/(24.*Power(k,3)) - (3*Power(k,4) + 4*Power(k,2)*(3 - 2*Sqrt(1 + Power(k,2)/Power(5*c - Complex(0,1)*k0,2)))*Power(5*c - Complex(0,1)*k0,2) - 8*(-1 + Sqrt(1 + Power(k,2)/Power(5*c - Complex(0,1)*k0,2)))*Power(5*c - Complex(0,1)*k0,4))/(24.*Power(k,3)) + (3*Power(k,4) + 8*Power(k0,3)*(k0 - Complex(0,1)*Sqrt(Power(k,2) - Power(k0,2))) + 4*Power(k,2)*k0*(-3*k0 + Complex(0,2)*Sqrt(Power(k,2) - Power(k0,2))))/(24.*Power(k,3)))/Power(k0,3) -SeriesData[k, Infinity, {(15*c^5)/k0^3, 0, (-35*(20*c^7 - (15*I)*c^6*k0 - 3*c^5*k0^2))/(2*k0^3), 0, (315*(331*c^9 - (450*I)*c^8*k0 - 240*c^7*k0^2 + (60*I)*c^6*k0^3 + 6*c^5*k0^4))/(16*k0^3), 0, (-165*(22430*c^11 - (42525*I)*c^10*k0 - 34755*c^9*k0^2 + (15750*I)*c^8*k0^3 + 4200*c^7*k0^4 - (630*I)*c^6*k0^5 - 42*c^5*k0^6))/(32*k0^3)}, 4, 11, 1] -(5*k^2*(-3 + 2*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^2 + 10*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^4 + 10*k^2*(3 - 2*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^2 - 20*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^4 + 10*k^2*(-3 + 2*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^2 + 20*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^4 + 5*k^2*(3 - 2*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^2 - 10*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^4 + k^2*(-3 + 2*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^2 + 2*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^4 + 2*k0^3*(k0 - I*Sqrt[k^2 - k0^2]) + k^2*k0*(-3*k0 + (2*I)*Sqrt[k^2 - k0^2]))/(6*k^3*k0^3) diff --git a/besseltransforms/klarge/5-3-4 b/besseltransforms/klarge/5-3-4 deleted file mode 100644 index 770fd7f..0000000 --- a/besseltransforms/klarge/5-3-4 +++ /dev/null @@ -1,4 +0,0 @@ -(-(k^4*(-15 + 4*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0) + 4*k^2*(-10 + 7*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^3 + 24*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^5)/(12*k^4) + (k^4*(-15 + 4*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0) + 4*k^2*(-10 + 7*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^3 + 24*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^5)/(6*k^4) - (k^4*(-15 + 4*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0) + 4*k^2*(-10 + 7*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^3 + 24*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^5)/(6*k^4) + (k^4*(-15 + 4*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0) + 4*k^2*(-10 + 7*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^3 + 24*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^5)/(12*k^4) - (k^4*(-15 + 4*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0) + 4*k^2*(-10 + 7*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^3 + 24*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^5)/(60*k^4) + (4*Sqrt[k^2 - k0^2]*(k^4 - 7*k^2*k0^2 + 6*k0^4) + I*(15*k^4*k0 - 40*k^2*k0^3 + 24*k0^5))/(60*k^4))/k0^3 -(-(Power(k,4)*(-15 + 4*Sqrt(1 + Power(k,2)/Power(c - Complex(0,1)*k0,2)))*(c - Complex(0,1)*k0) + 4*Power(k,2)*(-10 + 7*Sqrt(1 + Power(k,2)/Power(c - Complex(0,1)*k0,2)))*Power(c - Complex(0,1)*k0,3) + 24*(-1 + Sqrt(1 + Power(k,2)/Power(c - Complex(0,1)*k0,2)))*Power(c - Complex(0,1)*k0,5))/(12.*Power(k,4)) + (Power(k,4)*(-15 + 4*Sqrt(1 + Power(k,2)/Power(2*c - Complex(0,1)*k0,2)))*(2*c - Complex(0,1)*k0) + 4*Power(k,2)*(-10 + 7*Sqrt(1 + Power(k,2)/Power(2*c - Complex(0,1)*k0,2)))*Power(2*c - Complex(0,1)*k0,3) + 24*(-1 + Sqrt(1 + Power(k,2)/Power(2*c - Complex(0,1)*k0,2)))*Power(2*c - Complex(0,1)*k0,5))/(6.*Power(k,4)) - (Power(k,4)*(-15 + 4*Sqrt(1 + Power(k,2)/Power(3*c - Complex(0,1)*k0,2)))*(3*c - Complex(0,1)*k0) + 4*Power(k,2)*(-10 + 7*Sqrt(1 + Power(k,2)/Power(3*c - Complex(0,1)*k0,2)))*Power(3*c - Complex(0,1)*k0,3) + 24*(-1 + Sqrt(1 + Power(k,2)/Power(3*c - Complex(0,1)*k0,2)))*Power(3*c - Complex(0,1)*k0,5))/(6.*Power(k,4)) + (Power(k,4)*(-15 + 4*Sqrt(1 + Power(k,2)/Power(4*c - Complex(0,1)*k0,2)))*(4*c - Complex(0,1)*k0) + 4*Power(k,2)*(-10 + 7*Sqrt(1 + Power(k,2)/Power(4*c - Complex(0,1)*k0,2)))*Power(4*c - Complex(0,1)*k0,3) + 24*(-1 + Sqrt(1 + Power(k,2)/Power(4*c - Complex(0,1)*k0,2)))*Power(4*c - Complex(0,1)*k0,5))/(12.*Power(k,4)) - (Power(k,4)*(-15 + 4*Sqrt(1 + Power(k,2)/Power(5*c - Complex(0,1)*k0,2)))*(5*c - Complex(0,1)*k0) + 4*Power(k,2)*(-10 + 7*Sqrt(1 + Power(k,2)/Power(5*c - Complex(0,1)*k0,2)))*Power(5*c - Complex(0,1)*k0,3) + 24*(-1 + Sqrt(1 + Power(k,2)/Power(5*c - Complex(0,1)*k0,2)))*Power(5*c - Complex(0,1)*k0,5))/(60.*Power(k,4)) + (4*Sqrt(Power(k,2) - Power(k0,2))*(Power(k,4) - 7*Power(k,2)*Power(k0,2) + 6*Power(k0,4)) + Complex(0,1)*(15*Power(k,4)*k0 - 40*Power(k,2)*Power(k0,3) + 24*Power(k0,5)))/(60.*Power(k,4)))/Power(k0,3) -SeriesData[k, Infinity, {(48*c^5)/k0^3, (-525*c^6)/(2*k0^3) + ((105*I)*c^5)/k0^2, 0, (315*(75*c^8 - (80*I)*c^7*k0 - 30*c^6*k0^2 + (4*I)*c^5*k0^3))/(8*k0^3), 0, (-693*(2025*c^10 - (3310*I)*c^9*k0 - 2250*c^8*k0^2 + (800*I)*c^7*k0^3 + 150*c^6*k0^4 - (12*I)*c^5*k0^5))/(32*k0^3)}, 4, 11, 1] --(5*(k^4*(-15 + 4*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0) + 4*k^2*(-10 + 7*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^3 + 24*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^5) - 10*(k^4*(-15 + 4*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0) + 4*k^2*(-10 + 7*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^3 + 24*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^5) + 10*(k^4*(-15 + 4*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0) + 4*k^2*(-10 + 7*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^3 + 24*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^5) - 5*(k^4*(-15 + 4*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0) + 4*k^2*(-10 + 7*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^3 + 24*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^5) + k^4*(-15 + 4*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0) + 4*k^2*(-10 + 7*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^3 + 24*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^5 - 4*Sqrt[k^2 - k0^2]*(k^4 - 7*k^2*k0^2 + 6*k0^4) - I*(15*k^4*k0 - 40*k^2*k0^3 + 24*k0^5))/(60*k^4*k0^3) diff --git a/besseltransforms/klarge/5-3-5 b/besseltransforms/klarge/5-3-5 deleted file mode 100644 index 299257d..0000000 --- a/besseltransforms/klarge/5-3-5 +++ /dev/null @@ -1,4 +0,0 @@ -(-(5*k^6 + 12*k^4*(5 - 2*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^2 + 8*k^2*(15 - 11*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^4 - 64*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^6)/(24*k^5) + (5*k^6 + 12*k^4*(5 - 2*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^2 + 8*k^2*(15 - 11*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^4 - 64*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^6)/(12*k^5) - (5*k^6 + 12*k^4*(5 - 2*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^2 + 8*k^2*(15 - 11*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^4 - 64*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^6)/(12*k^5) + (5*k^6 + 12*k^4*(5 - 2*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^2 + 8*k^2*(15 - 11*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^4 - 64*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^6)/(24*k^5) - (5*k^6 + 12*k^4*(5 - 2*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^2 + 8*k^2*(15 - 11*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^4 - 64*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^6)/(120*k^5) + (5*k^6 + 12*k^4*k0*(-5*k0 + (2*I)*Sqrt[k^2 - k0^2]) + 8*k^2*k0^3*(15*k0 - (11*I)*Sqrt[k^2 - k0^2]) + (64*I)*k0^5*(I*k0 + Sqrt[k^2 - k0^2]))/(120*k^5))/k0^3 -(-(5*Power(k,6) + 12*Power(k,4)*(5 - 2*Sqrt(1 + Power(k,2)/Power(c - Complex(0,1)*k0,2)))*Power(c - Complex(0,1)*k0,2) + 8*Power(k,2)*(15 - 11*Sqrt(1 + Power(k,2)/Power(c - Complex(0,1)*k0,2)))*Power(c - Complex(0,1)*k0,4) - 64*(-1 + Sqrt(1 + Power(k,2)/Power(c - Complex(0,1)*k0,2)))*Power(c - Complex(0,1)*k0,6))/(24.*Power(k,5)) + (5*Power(k,6) + 12*Power(k,4)*(5 - 2*Sqrt(1 + Power(k,2)/Power(2*c - Complex(0,1)*k0,2)))*Power(2*c - Complex(0,1)*k0,2) + 8*Power(k,2)*(15 - 11*Sqrt(1 + Power(k,2)/Power(2*c - Complex(0,1)*k0,2)))*Power(2*c - Complex(0,1)*k0,4) - 64*(-1 + Sqrt(1 + Power(k,2)/Power(2*c - Complex(0,1)*k0,2)))*Power(2*c - Complex(0,1)*k0,6))/(12.*Power(k,5)) - (5*Power(k,6) + 12*Power(k,4)*(5 - 2*Sqrt(1 + Power(k,2)/Power(3*c - Complex(0,1)*k0,2)))*Power(3*c - Complex(0,1)*k0,2) + 8*Power(k,2)*(15 - 11*Sqrt(1 + Power(k,2)/Power(3*c - Complex(0,1)*k0,2)))*Power(3*c - Complex(0,1)*k0,4) - 64*(-1 + Sqrt(1 + Power(k,2)/Power(3*c - Complex(0,1)*k0,2)))*Power(3*c - Complex(0,1)*k0,6))/(12.*Power(k,5)) + (5*Power(k,6) + 12*Power(k,4)*(5 - 2*Sqrt(1 + Power(k,2)/Power(4*c - Complex(0,1)*k0,2)))*Power(4*c - Complex(0,1)*k0,2) + 8*Power(k,2)*(15 - 11*Sqrt(1 + Power(k,2)/Power(4*c - Complex(0,1)*k0,2)))*Power(4*c - Complex(0,1)*k0,4) - 64*(-1 + Sqrt(1 + Power(k,2)/Power(4*c - Complex(0,1)*k0,2)))*Power(4*c - Complex(0,1)*k0,6))/(24.*Power(k,5)) - (5*Power(k,6) + 12*Power(k,4)*(5 - 2*Sqrt(1 + Power(k,2)/Power(5*c - Complex(0,1)*k0,2)))*Power(5*c - Complex(0,1)*k0,2) + 8*Power(k,2)*(15 - 11*Sqrt(1 + Power(k,2)/Power(5*c - Complex(0,1)*k0,2)))*Power(5*c - Complex(0,1)*k0,4) - 64*(-1 + Sqrt(1 + Power(k,2)/Power(5*c - Complex(0,1)*k0,2)))*Power(5*c - Complex(0,1)*k0,6))/(120.*Power(k,5)) + (5*Power(k,6) + 12*Power(k,4)*k0*(-5*k0 + Complex(0,2)*Sqrt(Power(k,2) - Power(k0,2))) + 8*Power(k,2)*Power(k0,3)*(15*k0 - Complex(0,11)*Sqrt(Power(k,2) - Power(k0,2))) + Complex(0,64)*Power(k0,5)*(Complex(0,1)*k0 + Sqrt(Power(k,2) - Power(k0,2))))/(120.*Power(k,5)))/Power(k0,3) -SeriesData[k, Infinity, {(105*c^5)/k0^3, (-960*c^6)/k0^3 + ((384*I)*c^5)/k0^2, (315*(20*c^7 - (15*I)*c^6*k0 - 3*c^5*k0^2))/(2*k0^3), 0, (-1155*(331*c^9 - (450*I)*c^8*k0 - 240*c^7*k0^2 + (60*I)*c^6*k0^3 + 6*c^5*k0^4))/(16*k0^3), 0, (429*(22430*c^11 - (42525*I)*c^10*k0 - 34755*c^9*k0^2 + (15750*I)*c^8*k0^3 + 4200*c^7*k0^4 - (630*I)*c^6*k0^5 - 42*c^5*k0^6))/(32*k0^3)}, 4, 11, 1] -(15*k^4*(-5 + 2*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^2 + 10*k^2*(-15 + 11*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^4 + 80*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^6 + 30*k^4*(5 - 2*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^2 + 20*k^2*(15 - 11*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^4 - 160*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^6 + 30*k^4*(-5 + 2*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^2 + 20*k^2*(-15 + 11*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^4 + 160*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^6 + 15*k^4*(5 - 2*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^2 + 10*k^2*(15 - 11*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^4 - 80*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^6 + 3*k^4*(-5 + 2*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^2 + 2*k^2*(-15 + 11*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^4 + 16*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^6 + 3*k^4*k0*(-5*k0 + (2*I)*Sqrt[k^2 - k0^2]) + 2*k^2*k0^3*(15*k0 - (11*I)*Sqrt[k^2 - k0^2]) + (16*I)*k0^5*(I*k0 + Sqrt[k^2 - k0^2]))/(30*k^5*k0^3) diff --git a/besseltransforms/klarge/5-4-0 b/besseltransforms/klarge/5-4-0 deleted file mode 100644 index d82c8a2..0000000 --- a/besseltransforms/klarge/5-4-0 +++ /dev/null @@ -1,11 +0,0 @@ -Integrate[(E^(I*k0*x)*(1 - E^(-(c*x)))^5*BesselJ[0, k*x])/(k0^4*x^3), {x, 0, Infinity}, Assumptions -> n == 0 && q == 4 && κ == 5 && k > k0 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0] -Integrate((Power(E,I*k0*x)*Power(1 - Power(E,-(c*x)),5)*BesselJ(0,k*x))/(Power(k0,4)*Power(x,3)),List(x,0,DirectedInfinity(1)),Rule(Assumptions,n == 0 && q == 4 && κ == 5 && k > k0 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0)) - - -5 c x + I k0 x c x 5 2 2 4 4 6 6 8 8 Pi 2 2 4 4 6 6 8 8 - E (-1 + E ) ((-418854310875 + 29682132480 k x - 3901685760 k x + 1258291200 k x - 2147483648 k x ) Cos[-- + k x] + 4 Sqrt[2] k x (13043905875 - 1229437440 k x + 240844800 k x - 150994944 k x + 2147483648 k x ) (Cos[k x] + Sin[k x])) - 4 -Integrate::idiv: Integral of ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ does not converge on {0, Infinity}. - 19/2 4 25/2 - 8589934592 k k0 Sqrt[2 Pi] x -Series[Integrate[(E^(I*k0*x)*(1 - E^(-(c*x)))^5*BesselJ[0, k*x])/(k0^4*x^3), {x, 0, Infinity}, Assumptions -> n == 0 && q == 4 && κ == 5 && k > k0 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0], {k, Infinity, 10}] -Integrate[(E^(I*k0*x)*(1 - E^(-(c*x)))^5*BesselJ[0, k*x])/(k0^4*x^3), {x, 0, Infinity}, Assumptions -> n == 0 && q == 4 && κ == 5] diff --git a/besseltransforms/klarge/5-4-1 b/besseltransforms/klarge/5-4-1 deleted file mode 100644 index bcb3949..0000000 --- a/besseltransforms/klarge/5-4-1 +++ /dev/null @@ -1,11 +0,0 @@ -Integrate[(E^(I*k0*x)*(1 - E^(-(c*x)))^5*BesselJ[1, k*x])/(k0^4*x^3), {x, 0, Infinity}, Assumptions -> n == 1 && q == 4 && κ == 5 && k > k0 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0] -Integrate((Power(E,I*k0*x)*Power(1 - Power(E,-(c*x)),5)*BesselJ(1,k*x))/(Power(k0,4)*Power(x,3)),List(x,0,DirectedInfinity(1)),Rule(Assumptions,n == 1 && q == 4 && κ == 5 && k > k0 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0)) - - -5 c x + I k0 x c x 5 2 2 4 4 6 6 8 8 Pi 2 2 4 4 6 6 8 8 Pi - -(E (-1 + E ) (8 k x (-14783093325 + 1452971520 k x - 309657600 k x + 251658240 k x + 2147483648 k x ) Cos[-- + k x] - 3 (156043762875 - 11416204800 k x + 1589575680 k x - 587202560 k x + 2147483648 k x ) Sin[-- + k x])) - 4 4 -Integrate::idiv: Integral of ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ does not converge on {0, Infinity}. - 19/2 4 25/2 - 8589934592 k k0 Sqrt[2 Pi] x -Series[Integrate[(E^(I*k0*x)*(1 - E^(-(c*x)))^5*BesselJ[1, k*x])/(k0^4*x^3), {x, 0, Infinity}, Assumptions -> n == 1 && q == 4 && κ == 5 && k > k0 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0], {k, Infinity, 10}] -Integrate[(E^(I*k0*x)*(1 - E^(-(c*x)))^5*BesselJ[1, k*x])/(k0^4*x^3), {x, 0, Infinity}, Assumptions -> n == 1 && q == 4 && κ == 5] diff --git a/besseltransforms/klarge/5-4-2 b/besseltransforms/klarge/5-4-2 deleted file mode 100644 index b3fdd58..0000000 --- a/besseltransforms/klarge/5-4-2 +++ /dev/null @@ -1,13 +0,0 @@ -Integrate[(E^(I*k0*x)*(1 - E^(-(c*x)))^5*BesselJ[2, k*x])/(k0^4*x^3), {x, 0, Infinity}, Assumptions -> n == 2 && q == 4 && κ == 5 && k > k0 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0] -Integrate((Power(E,I*k0*x)*Power(1 - Power(E,-(c*x)),5)*BesselJ(2,k*x))/(Power(k0,4)*Power(x,3)),List(x,0,DirectedInfinity(1)),Rule(Assumptions,n == 2 && q == 4 && κ == 5 && k > k0 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0)) - - I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi I k0 x 2 Pi -5 c x + I k0 x 2 Pi -4 c x + I k0 x 2 Pi -3 c x + I k0 x 2 Pi -2 c x + I k0 x 2 Pi -(c x) + I k0 x 2 Pi I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi - -21606059475 E Cos[-- - k x] 21606059475 E Cos[-- - k x] 108030297375 E Cos[-- - k x] 108030297375 E Cos[-- - k x] 108030297375 E Cos[-- - k x] 108030297375 E Cos[-- - k x] 4729725 E Cos[-- - k x] 4729725 E Cos[-- - k x] 23648625 E Cos[-- - k x] 23648625 E Cos[-- - k x] 23648625 E Cos[-- - k x] 23648625 E Cos[-- - k x] 10395 E Cos[-- - k x] 10395 E Cos[-- - k x] 51975 E Cos[-- - k x] 51975 E Cos[-- - k x] 51975 E Cos[-- - k x] 51975 E Cos[-- - k x] 105 E Cos[-- - k x] 105 E Cos[-- - k x] 525 E Cos[-- - k x] 525 E Cos[-- - k x] 525 E Cos[-- - k x] 525 E Cos[-- - k x] E Sqrt[--] Cos[-- - k x] E Sqrt[--] Cos[-- - k x] 5 E Sqrt[--] Cos[-- - k x] 10 E Sqrt[--] Cos[-- - k x] 10 E Sqrt[--] Cos[-- - k x] 5 E Sqrt[--] Cos[-- - k x] 655383804075 E Sin[-- - k x] 655383804075 E Sin[-- - k x] 3276919020375 E Sin[-- - k x] 3276919020375 E Sin[-- - k x] 3276919020375 E Sin[-- - k x] 3276919020375 E Sin[-- - k x] 103378275 E Sin[-- - k x] 103378275 E Sin[-- - k x] 516891375 E Sin[-- - k x] 516891375 E Sin[-- - k x] 516891375 E Sin[-- - k x] 516891375 E Sin[-- - k x] 135135 E Sin[-- - k x] 135135 E Sin[-- - k x] 675675 E Sin[-- - k x] 675675 E Sin[-- - k x] 675675 E Sin[-- - k x] 675675 E Sin[-- - k x] 315 E Sin[-- - k x] 315 E Sin[-- - k x] 1575 E Sin[-- - k x] 1575 E Sin[-- - k x] 1575 E Sin[-- - k x] 1575 E Sin[-- - k x] 15 E Sin[-- - k x] 15 E Sin[-- - k x] 75 E Sin[-- - k x] 75 E Sin[-- - k x] 75 E Sin[-- - k x] 75 E Sin[-- - k x] - 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 Pi 4 Pi 4 Pi 4 Pi 4 Pi 4 Pi 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 -Integrate::idiv: Integral of ------------------------------------- + ------------------------------------------ - ------------------------------------------- + ------------------------------------------- - ------------------------------------------- + ------------------------------------------- + ---------------------------------- - -------------------------------------- + --------------------------------------- - --------------------------------------- + --------------------------------------- - --------------------------------------- - ------------------------------- + ------------------------------------ - ------------------------------------ + ------------------------------------ - ------------------------------------ + ------------------------------------ + ---------------------------- - ---------------------------------- + ---------------------------------- - ---------------------------------- + ---------------------------------- - ---------------------------------- - ------------------------------ + --------------------------------------- - ----------------------------------------- + ------------------------------------------ - ------------------------------------------ + ----------------------------------------- + ------------------------------------- - ------------------------------------------- + -------------------------------------------- - -------------------------------------------- + -------------------------------------------- - -------------------------------------------- - ----------------------------------- + ---------------------------------------- - ---------------------------------------- + ---------------------------------------- - ---------------------------------------- + ---------------------------------------- + --------------------------------- - ------------------------------------- + ------------------------------------- - ------------------------------------- + ------------------------------------- - ------------------------------------- - ----------------------------- + ---------------------------------- - ----------------------------------- + ----------------------------------- - ----------------------------------- + ----------------------------------- - -------------------------- + --------------------------------- - --------------------------------- + --------------------------------- - --------------------------------- + --------------------------------- does not converge on {0, Infinity}. - 17/2 4 23/2 17/2 4 23/2 17/2 4 23/2 17/2 4 23/2 17/2 4 23/2 17/2 4 23/2 13/2 4 19/2 13/2 4 19/2 13/2 4 19/2 13/2 4 19/2 13/2 4 19/2 13/2 4 19/2 9/2 4 15/2 9/2 4 15/2 9/2 4 15/2 9/2 4 15/2 9/2 4 15/2 9/2 4 15/2 5/2 4 11/2 5/2 4 11/2 5/2 4 11/2 5/2 4 11/2 5/2 4 11/2 5/2 4 11/2 4 7/2 4 7/2 4 7/2 4 7/2 4 7/2 4 7/2 19/2 4 25/2 19/2 4 25/2 19/2 4 25/2 19/2 4 25/2 19/2 4 25/2 19/2 4 25/2 15/2 4 21/2 15/2 4 21/2 15/2 4 21/2 15/2 4 21/2 15/2 4 21/2 15/2 4 21/2 11/2 4 17/2 11/2 4 17/2 11/2 4 17/2 11/2 4 17/2 11/2 4 17/2 11/2 4 17/2 7/2 4 13/2 7/2 4 13/2 7/2 4 13/2 7/2 4 13/2 7/2 4 13/2 7/2 4 13/2 3/2 4 9/2 3/2 4 9/2 3/2 4 9/2 3/2 4 9/2 3/2 4 9/2 3/2 4 9/2 - 1073741824 k k0 Sqrt[2 Pi] x 1073741824 k k0 Sqrt[2 Pi] x 1073741824 k k0 Sqrt[2 Pi] x 536870912 k k0 Sqrt[2 Pi] x 536870912 k k0 Sqrt[2 Pi] x 1073741824 k k0 Sqrt[2 Pi] x 2097152 k k0 Sqrt[2 Pi] x 2097152 k k0 Sqrt[2 Pi] x 2097152 k k0 Sqrt[2 Pi] x 1048576 k k0 Sqrt[2 Pi] x 1048576 k k0 Sqrt[2 Pi] x 2097152 k k0 Sqrt[2 Pi] x 16384 k k0 Sqrt[2 Pi] x 16384 k k0 Sqrt[2 Pi] x 16384 k k0 Sqrt[2 Pi] x 8192 k k0 Sqrt[2 Pi] x 8192 k k0 Sqrt[2 Pi] x 16384 k k0 Sqrt[2 Pi] x 64 k k0 Sqrt[2 Pi] x 64 k k0 Sqrt[2 Pi] x 64 k k0 Sqrt[2 Pi] x 32 k k0 Sqrt[2 Pi] x 32 k k0 Sqrt[2 Pi] x 64 k k0 Sqrt[2 Pi] x Sqrt[k] k0 x Sqrt[k] k0 x Sqrt[k] k0 x Sqrt[k] k0 x Sqrt[k] k0 x Sqrt[k] k0 x 8589934592 k k0 Sqrt[2 Pi] x 8589934592 k k0 Sqrt[2 Pi] x 8589934592 k k0 Sqrt[2 Pi] x 4294967296 k k0 Sqrt[2 Pi] x 4294967296 k k0 Sqrt[2 Pi] x 8589934592 k k0 Sqrt[2 Pi] x 16777216 k k0 Sqrt[2 Pi] x 16777216 k k0 Sqrt[2 Pi] x 16777216 k k0 Sqrt[2 Pi] x 8388608 k k0 Sqrt[2 Pi] x 8388608 k k0 Sqrt[2 Pi] x 16777216 k k0 Sqrt[2 Pi] x 131072 k k0 Sqrt[2 Pi] x 131072 k k0 Sqrt[2 Pi] x 131072 k k0 Sqrt[2 Pi] x 65536 k k0 Sqrt[2 Pi] x 65536 k k0 Sqrt[2 Pi] x 131072 k k0 Sqrt[2 Pi] x 512 k k0 Sqrt[2 Pi] x 512 k k0 Sqrt[2 Pi] x 512 k k0 Sqrt[2 Pi] x 256 k k0 Sqrt[2 Pi] x 256 k k0 Sqrt[2 Pi] x 512 k k0 Sqrt[2 Pi] x 4 k k0 Sqrt[2 Pi] x 4 k k0 Sqrt[2 Pi] x 4 k k0 Sqrt[2 Pi] x 2 k k0 Sqrt[2 Pi] x 2 k k0 Sqrt[2 Pi] x 4 k k0 Sqrt[2 Pi] x -Series[Integrate[(E^(I*k0*x)*(1 - E^(-(c*x)))^5*BesselJ[2, k*x])/(k0^4*x^3), {x, 0, Infinity}, Assumptions -> n == 2 && q == 4 && κ == 5 && k > k0 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0], {k, Infinity, 10}] - -Simplify::time: Time spent on a transformation exceeded 300. seconds, and the transformation was aborted. Increasing the value of TimeConstraint option may improve the result of simplification. -Integrate[(E^(I*k0*x)*(1 - E^(-(c*x)))^5*BesselJ[2, k*x])/(k0^4*x^3), {x, 0, Infinity}, Assumptions -> n == 2 && q == 4 && κ == 5] diff --git a/besseltransforms/klarge/5-4-3 b/besseltransforms/klarge/5-4-3 deleted file mode 100644 index fdc32b9..0000000 --- a/besseltransforms/klarge/5-4-3 +++ /dev/null @@ -1,4 +0,0 @@ -(-(k^4*(-15 + 8*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0) + 4*k^2*(-5 + 4*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^3 + 8*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^5)/(24*k^3) + (k^4*(-15 + 8*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0) + 4*k^2*(-5 + 4*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^3 + 8*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^5)/(12*k^3) - (k^4*(-15 + 8*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0) + 4*k^2*(-5 + 4*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^3 + 8*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^5)/(12*k^3) + (k^4*(-15 + 8*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0) + 4*k^2*(-5 + 4*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^3 + 8*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^5)/(24*k^3) - (k^4*(-15 + 8*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0) + 4*k^2*(-5 + 4*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^3 + 8*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^5)/(120*k^3) + (8*(k^2 - k0^2)^(5/2) + I*(15*k^4*k0 - 20*k^2*k0^3 + 8*k0^5))/(120*k^3))/k0^4 -(-(Power(k,4)*(-15 + 8*Sqrt(1 + Power(k,2)/Power(c - Complex(0,1)*k0,2)))*(c - Complex(0,1)*k0) + 4*Power(k,2)*(-5 + 4*Sqrt(1 + Power(k,2)/Power(c - Complex(0,1)*k0,2)))*Power(c - Complex(0,1)*k0,3) + 8*(-1 + Sqrt(1 + Power(k,2)/Power(c - Complex(0,1)*k0,2)))*Power(c - Complex(0,1)*k0,5))/(24.*Power(k,3)) + (Power(k,4)*(-15 + 8*Sqrt(1 + Power(k,2)/Power(2*c - Complex(0,1)*k0,2)))*(2*c - Complex(0,1)*k0) + 4*Power(k,2)*(-5 + 4*Sqrt(1 + Power(k,2)/Power(2*c - Complex(0,1)*k0,2)))*Power(2*c - Complex(0,1)*k0,3) + 8*(-1 + Sqrt(1 + Power(k,2)/Power(2*c - Complex(0,1)*k0,2)))*Power(2*c - Complex(0,1)*k0,5))/(12.*Power(k,3)) - (Power(k,4)*(-15 + 8*Sqrt(1 + Power(k,2)/Power(3*c - Complex(0,1)*k0,2)))*(3*c - Complex(0,1)*k0) + 4*Power(k,2)*(-5 + 4*Sqrt(1 + Power(k,2)/Power(3*c - Complex(0,1)*k0,2)))*Power(3*c - Complex(0,1)*k0,3) + 8*(-1 + Sqrt(1 + Power(k,2)/Power(3*c - Complex(0,1)*k0,2)))*Power(3*c - Complex(0,1)*k0,5))/(12.*Power(k,3)) + (Power(k,4)*(-15 + 8*Sqrt(1 + Power(k,2)/Power(4*c - Complex(0,1)*k0,2)))*(4*c - Complex(0,1)*k0) + 4*Power(k,2)*(-5 + 4*Sqrt(1 + Power(k,2)/Power(4*c - Complex(0,1)*k0,2)))*Power(4*c - Complex(0,1)*k0,3) + 8*(-1 + Sqrt(1 + Power(k,2)/Power(4*c - Complex(0,1)*k0,2)))*Power(4*c - Complex(0,1)*k0,5))/(24.*Power(k,3)) - (Power(k,4)*(-15 + 8*Sqrt(1 + Power(k,2)/Power(5*c - Complex(0,1)*k0,2)))*(5*c - Complex(0,1)*k0) + 4*Power(k,2)*(-5 + 4*Sqrt(1 + Power(k,2)/Power(5*c - Complex(0,1)*k0,2)))*Power(5*c - Complex(0,1)*k0,3) + 8*(-1 + Sqrt(1 + Power(k,2)/Power(5*c - Complex(0,1)*k0,2)))*Power(5*c - Complex(0,1)*k0,5))/(120.*Power(k,3)) + (8*Power(Power(k,2) - Power(k0,2),2.5) + Complex(0,1)*(15*Power(k,4)*k0 - 20*Power(k,2)*Power(k0,3) + 8*Power(k0,5)))/(120.*Power(k,3)))/Power(k0,4) -SeriesData[k, Infinity, {(8*c^5)/k0^4, (-75*c^6)/(2*k0^4) + ((15*I)*c^5)/k0^3, 0, (35*(75*c^8 - (80*I)*c^7*k0 - 30*c^6*k0^2 + (4*I)*c^5*k0^3))/(8*k0^4), 0, (-63*(2025*c^10 - (3310*I)*c^9*k0 - 2250*c^8*k0^2 + (800*I)*c^7*k0^3 + 150*c^6*k0^4 - (12*I)*c^5*k0^5))/(32*k0^4), 0, (165*(20900*c^12 - (44860*I)*c^11*k0 - 42525*c^10*k0^2 + (23170*I)*c^9*k0^3 + 7875*c^8*k0^4 - (1680*I)*c^7*k0^5 - 210*c^6*k0^6 + (12*I)*c^5*k0^7))/(64*k0^4)}, 3, 11, 1] --(5*(k^4*(-15 + 8*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0) + 4*k^2*(-5 + 4*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^3 + 8*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^5) - 10*(k^4*(-15 + 8*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0) + 4*k^2*(-5 + 4*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^3 + 8*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^5) + 10*(k^4*(-15 + 8*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0) + 4*k^2*(-5 + 4*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^3 + 8*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^5) - 5*(k^4*(-15 + 8*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0) + 4*k^2*(-5 + 4*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^3 + 8*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^5) + k^4*(-15 + 8*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0) + 4*k^2*(-5 + 4*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^3 + 8*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^5 - 8*(k^2 - k0^2)^(5/2) - I*(15*k^4*k0 - 20*k^2*k0^3 + 8*k0^5))/(120*k^3*k0^4) diff --git a/besseltransforms/klarge/5-4-4 b/besseltransforms/klarge/5-4-4 deleted file mode 100644 index fce5312..0000000 --- a/besseltransforms/klarge/5-4-4 +++ /dev/null @@ -1,4 +0,0 @@ -(-(5*k^6 + 2*k^4*(15 - 8*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^2 + 8*k^2*(5 - 4*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^4 - 16*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^6)/(48*k^4) + (5*k^6 + 2*k^4*(15 - 8*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^2 + 8*k^2*(5 - 4*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^4 - 16*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^6)/(24*k^4) - (5*k^6 + 2*k^4*(15 - 8*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^2 + 8*k^2*(5 - 4*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^4 - 16*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^6)/(24*k^4) + (5*k^6 + 2*k^4*(15 - 8*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^2 + 8*k^2*(5 - 4*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^4 - 16*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^6)/(48*k^4) - (5*k^6 + 2*k^4*(15 - 8*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^2 + 8*k^2*(5 - 4*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^4 - 16*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^6)/(240*k^4) + (5*k^6 - 30*k^4*k0^2 + 40*k^2*k0^4 - 16*k0^6 + (16*I)*k0*(k^2 - k0^2)^(5/2))/(240*k^4))/k0^4 -(-(5*Power(k,6) + 2*Power(k,4)*(15 - 8*Sqrt(1 + Power(k,2)/Power(c - Complex(0,1)*k0,2)))*Power(c - Complex(0,1)*k0,2) + 8*Power(k,2)*(5 - 4*Sqrt(1 + Power(k,2)/Power(c - Complex(0,1)*k0,2)))*Power(c - Complex(0,1)*k0,4) - 16*(-1 + Sqrt(1 + Power(k,2)/Power(c - Complex(0,1)*k0,2)))*Power(c - Complex(0,1)*k0,6))/(48.*Power(k,4)) + (5*Power(k,6) + 2*Power(k,4)*(15 - 8*Sqrt(1 + Power(k,2)/Power(2*c - Complex(0,1)*k0,2)))*Power(2*c - Complex(0,1)*k0,2) + 8*Power(k,2)*(5 - 4*Sqrt(1 + Power(k,2)/Power(2*c - Complex(0,1)*k0,2)))*Power(2*c - Complex(0,1)*k0,4) - 16*(-1 + Sqrt(1 + Power(k,2)/Power(2*c - Complex(0,1)*k0,2)))*Power(2*c - Complex(0,1)*k0,6))/(24.*Power(k,4)) - (5*Power(k,6) + 2*Power(k,4)*(15 - 8*Sqrt(1 + Power(k,2)/Power(3*c - Complex(0,1)*k0,2)))*Power(3*c - Complex(0,1)*k0,2) + 8*Power(k,2)*(5 - 4*Sqrt(1 + Power(k,2)/Power(3*c - Complex(0,1)*k0,2)))*Power(3*c - Complex(0,1)*k0,4) - 16*(-1 + Sqrt(1 + Power(k,2)/Power(3*c - Complex(0,1)*k0,2)))*Power(3*c - Complex(0,1)*k0,6))/(24.*Power(k,4)) + (5*Power(k,6) + 2*Power(k,4)*(15 - 8*Sqrt(1 + Power(k,2)/Power(4*c - Complex(0,1)*k0,2)))*Power(4*c - Complex(0,1)*k0,2) + 8*Power(k,2)*(5 - 4*Sqrt(1 + Power(k,2)/Power(4*c - Complex(0,1)*k0,2)))*Power(4*c - Complex(0,1)*k0,4) - 16*(-1 + Sqrt(1 + Power(k,2)/Power(4*c - Complex(0,1)*k0,2)))*Power(4*c - Complex(0,1)*k0,6))/(48.*Power(k,4)) - (5*Power(k,6) + 2*Power(k,4)*(15 - 8*Sqrt(1 + Power(k,2)/Power(5*c - Complex(0,1)*k0,2)))*Power(5*c - Complex(0,1)*k0,2) + 8*Power(k,2)*(5 - 4*Sqrt(1 + Power(k,2)/Power(5*c - Complex(0,1)*k0,2)))*Power(5*c - Complex(0,1)*k0,4) - 16*(-1 + Sqrt(1 + Power(k,2)/Power(5*c - Complex(0,1)*k0,2)))*Power(5*c - Complex(0,1)*k0,6))/(240.*Power(k,4)) + (5*Power(k,6) - 30*Power(k,4)*Power(k0,2) + 40*Power(k,2)*Power(k0,4) - 16*Power(k0,6) + Complex(0,16)*k0*Power(Power(k,2) - Power(k0,2),2.5))/(240.*Power(k,4)))/Power(k0,4) -SeriesData[k, Infinity, {(15*c^5)/k0^4, (-120*c^6)/k0^4 + ((48*I)*c^5)/k0^3, (35*(20*c^7 - (15*I)*c^6*k0 - 3*c^5*k0^2))/(2*k0^4), 0, (-105*(331*c^9 - (450*I)*c^8*k0 - 240*c^7*k0^2 + (60*I)*c^6*k0^3 + 6*c^5*k0^4))/(16*k0^4), 0, (33*(22430*c^11 - (42525*I)*c^10*k0 - 34755*c^9*k0^2 + (15750*I)*c^8*k0^3 + 4200*c^7*k0^4 - (630*I)*c^6*k0^5 - 42*c^5*k0^6))/(32*k0^4)}, 3, 11, 1] -(5*k^4*(-15 + 8*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^2 + 20*k^2*(-5 + 4*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^4 + 40*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^6 + 10*k^4*(15 - 8*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^2 + 40*k^2*(5 - 4*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^4 - 80*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^6 + 10*k^4*(-15 + 8*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^2 + 40*k^2*(-5 + 4*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^4 + 80*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^6 + 5*k^4*(15 - 8*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^2 + 20*k^2*(5 - 4*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^4 - 40*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^6 + k^4*(-15 + 8*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^2 + 4*k^2*(-5 + 4*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^4 + 8*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^6 - 15*k^4*k0^2 + 20*k^2*k0^4 - 8*k0^6 + (8*I)*k0*(k^2 - k0^2)^(5/2))/(120*k^4*k0^4) diff --git a/besseltransforms/klarge/5-4-5 b/besseltransforms/klarge/5-4-5 deleted file mode 100644 index d1a180e..0000000 --- a/besseltransforms/klarge/5-4-5 +++ /dev/null @@ -1,4 +0,0 @@ -(-(k^6*(-35 + 8*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0) + 20*k^4*(-7 + 4*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^3 + 8*k^2*(-21 + 17*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^5 + 64*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^7)/(168*k^5) + (k^6*(-35 + 8*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0) + 20*k^4*(-7 + 4*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^3 + 8*k^2*(-21 + 17*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^5 + 64*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^7)/(84*k^5) - (k^6*(-35 + 8*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0) + 20*k^4*(-7 + 4*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^3 + 8*k^2*(-21 + 17*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^5 + 64*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^7)/(84*k^5) + (k^6*(-35 + 8*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0) + 20*k^4*(-7 + 4*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^3 + 8*k^2*(-21 + 17*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^5 + 64*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^7)/(168*k^5) - (k^6*(-35 + 8*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0) + 20*k^4*(-7 + 4*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^3 + 8*k^2*(-21 + 17*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^5 + 64*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^7)/(840*k^5) + (8*k*(k^2 - 8*k0^2)*(k^2 - k0^2)^2*Sqrt[1 - k0^2/k^2] + I*(35*k^6*k0 - 140*k^4*k0^3 + 168*k^2*k0^5 - 64*k0^7))/(840*k^5))/k0^4 -(-(Power(k,6)*(-35 + 8*Sqrt(1 + Power(k,2)/Power(c - Complex(0,1)*k0,2)))*(c - Complex(0,1)*k0) + 20*Power(k,4)*(-7 + 4*Sqrt(1 + Power(k,2)/Power(c - Complex(0,1)*k0,2)))*Power(c - Complex(0,1)*k0,3) + 8*Power(k,2)*(-21 + 17*Sqrt(1 + Power(k,2)/Power(c - Complex(0,1)*k0,2)))*Power(c - Complex(0,1)*k0,5) + 64*(-1 + Sqrt(1 + Power(k,2)/Power(c - Complex(0,1)*k0,2)))*Power(c - Complex(0,1)*k0,7))/(168.*Power(k,5)) + (Power(k,6)*(-35 + 8*Sqrt(1 + Power(k,2)/Power(2*c - Complex(0,1)*k0,2)))*(2*c - Complex(0,1)*k0) + 20*Power(k,4)*(-7 + 4*Sqrt(1 + Power(k,2)/Power(2*c - Complex(0,1)*k0,2)))*Power(2*c - Complex(0,1)*k0,3) + 8*Power(k,2)*(-21 + 17*Sqrt(1 + Power(k,2)/Power(2*c - Complex(0,1)*k0,2)))*Power(2*c - Complex(0,1)*k0,5) + 64*(-1 + Sqrt(1 + Power(k,2)/Power(2*c - Complex(0,1)*k0,2)))*Power(2*c - Complex(0,1)*k0,7))/(84.*Power(k,5)) - (Power(k,6)*(-35 + 8*Sqrt(1 + Power(k,2)/Power(3*c - Complex(0,1)*k0,2)))*(3*c - Complex(0,1)*k0) + 20*Power(k,4)*(-7 + 4*Sqrt(1 + Power(k,2)/Power(3*c - Complex(0,1)*k0,2)))*Power(3*c - Complex(0,1)*k0,3) + 8*Power(k,2)*(-21 + 17*Sqrt(1 + Power(k,2)/Power(3*c - Complex(0,1)*k0,2)))*Power(3*c - Complex(0,1)*k0,5) + 64*(-1 + Sqrt(1 + Power(k,2)/Power(3*c - Complex(0,1)*k0,2)))*Power(3*c - Complex(0,1)*k0,7))/(84.*Power(k,5)) + (Power(k,6)*(-35 + 8*Sqrt(1 + Power(k,2)/Power(4*c - Complex(0,1)*k0,2)))*(4*c - Complex(0,1)*k0) + 20*Power(k,4)*(-7 + 4*Sqrt(1 + Power(k,2)/Power(4*c - Complex(0,1)*k0,2)))*Power(4*c - Complex(0,1)*k0,3) + 8*Power(k,2)*(-21 + 17*Sqrt(1 + Power(k,2)/Power(4*c - Complex(0,1)*k0,2)))*Power(4*c - Complex(0,1)*k0,5) + 64*(-1 + Sqrt(1 + Power(k,2)/Power(4*c - Complex(0,1)*k0,2)))*Power(4*c - Complex(0,1)*k0,7))/(168.*Power(k,5)) - (Power(k,6)*(-35 + 8*Sqrt(1 + Power(k,2)/Power(5*c - Complex(0,1)*k0,2)))*(5*c - Complex(0,1)*k0) + 20*Power(k,4)*(-7 + 4*Sqrt(1 + Power(k,2)/Power(5*c - Complex(0,1)*k0,2)))*Power(5*c - Complex(0,1)*k0,3) + 8*Power(k,2)*(-21 + 17*Sqrt(1 + Power(k,2)/Power(5*c - Complex(0,1)*k0,2)))*Power(5*c - Complex(0,1)*k0,5) + 64*(-1 + Sqrt(1 + Power(k,2)/Power(5*c - Complex(0,1)*k0,2)))*Power(5*c - Complex(0,1)*k0,7))/(840.*Power(k,5)) + (8*k*(Power(k,2) - 8*Power(k0,2))*Power(Power(k,2) - Power(k0,2),2)*Sqrt(1 - Power(k0,2)/Power(k,2)) + Complex(0,1)*(35*Power(k,6)*k0 - 140*Power(k,4)*Power(k0,3) + 168*Power(k,2)*Power(k0,5) - 64*Power(k0,7)))/(840.*Power(k,5)))/Power(k0,4) -SeriesData[k, Infinity, {(24*c^5)/k0^4, (-525*c^6)/(2*k0^4) + ((105*I)*c^5)/k0^3, (1280*c^7)/k0^4 - ((960*I)*c^6)/k0^3 - (192*c^5)/k0^2, (-315*(75*c^8 - (80*I)*c^7*k0 - 30*c^6*k0^2 + (4*I)*c^5*k0^3))/(8*k0^4), 0, (231*(2025*c^10 - (3310*I)*c^9*k0 - 2250*c^8*k0^2 + (800*I)*c^7*k0^3 + 150*c^6*k0^4 - (12*I)*c^5*k0^5))/(32*k0^4), 0, (-429*(20900*c^12 - (44860*I)*c^11*k0 - 42525*c^10*k0^2 + (23170*I)*c^9*k0^3 + 7875*c^8*k0^4 - (1680*I)*c^7*k0^5 - 210*c^6*k0^6 + (12*I)*c^5*k0^7))/(64*k0^4)}, 3, 11, 1] --(5*(k^6*(-35 + 8*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0) + 20*k^4*(-7 + 4*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^3 + 8*k^2*(-21 + 17*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^5 + 64*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^7) - 10*(k^6*(-35 + 8*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0) + 20*k^4*(-7 + 4*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^3 + 8*k^2*(-21 + 17*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^5 + 64*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^7) + 10*(k^6*(-35 + 8*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0) + 20*k^4*(-7 + 4*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^3 + 8*k^2*(-21 + 17*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^5 + 64*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^7) - 5*(k^6*(-35 + 8*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0) + 20*k^4*(-7 + 4*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^3 + 8*k^2*(-21 + 17*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^5 + 64*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^7) + k^6*(-35 + 8*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0) + 20*k^4*(-7 + 4*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^3 + 8*k^2*(-21 + 17*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^5 + 64*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^7 - 8*k*(k^2 - 8*k0^2)*(k^2 - k0^2)^2*Sqrt[1 - k0^2/k^2] - I*(35*k^6*k0 - 140*k^4*k0^3 + 168*k^2*k0^5 - 64*k0^7))/(840*k^5*k0^4) diff --git a/besseltransforms/klarge/5-5-0 b/besseltransforms/klarge/5-5-0 deleted file mode 100644 index 467046e..0000000 --- a/besseltransforms/klarge/5-5-0 +++ /dev/null @@ -1,13 +0,0 @@ -Integrate[(E^(I*k0*x)*(1 - E^(-(c*x)))^5*BesselJ[0, k*x])/(k0^5*x^4), {x, 0, Infinity}, Assumptions -> n == 0 && q == 5 && κ == 5 && k > k0 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0] -Integrate((Power(E,I*k0*x)*Power(1 - Power(E,-(c*x)),5)*BesselJ(0,k*x))/(Power(k0,5)*Power(x,4)),List(x,0,DirectedInfinity(1)),Rule(Assumptions,n == 0 && q == 5 && κ == 5 && k > k0 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0)) - - -5 c x + I k0 x c x 5 2 2 4 4 6 6 8 8 Pi 2 2 4 4 6 6 8 8 - E (-1 + E ) ((-418854310875 + 29682132480 k x - 3901685760 k x + 1258291200 k x - 2147483648 k x ) Cos[-- + k x] + 4 Sqrt[2] k x (13043905875 - 1229437440 k x + 240844800 k x - 150994944 k x + 2147483648 k x ) (Cos[k x] + Sin[k x])) - 4 -Integrate::idiv: Integral of ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ does not converge on {0, Infinity}. - 19/2 5 27/2 - 8589934592 k k0 Sqrt[2 Pi] x -Series[Integrate[(E^(I*k0*x)*(1 - E^(-(c*x)))^5*BesselJ[0, k*x])/(k0^5*x^4), {x, 0, Infinity}, Assumptions -> n == 0 && q == 5 && κ == 5 && k > k0 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0], {k, Infinity, 10}] - -Simplify::time: Time spent on a transformation exceeded 300. seconds, and the transformation was aborted. Increasing the value of TimeConstraint option may improve the result of simplification. -Integrate[(E^(I*k0*x)*(1 - E^(-(c*x)))^5*BesselJ[0, k*x])/(k0^5*x^4), {x, 0, Infinity}, Assumptions -> n == 0 && q == 5 && κ == 5] diff --git a/besseltransforms/klarge/5-5-1 b/besseltransforms/klarge/5-5-1 deleted file mode 100644 index 3f93e32..0000000 --- a/besseltransforms/klarge/5-5-1 +++ /dev/null @@ -1,13 +0,0 @@ -Integrate[(E^(I*k0*x)*(1 - E^(-(c*x)))^5*BesselJ[1, k*x])/(k0^5*x^4), {x, 0, Infinity}, Assumptions -> n == 1 && q == 5 && κ == 5 && k > k0 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0] -Integrate((Power(E,I*k0*x)*Power(1 - Power(E,-(c*x)),5)*BesselJ(1,k*x))/(Power(k0,5)*Power(x,4)),List(x,0,DirectedInfinity(1)),Rule(Assumptions,n == 1 && q == 5 && κ == 5 && k > k0 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0)) - - -5 c x + I k0 x c x 5 2 2 4 4 6 6 8 8 Pi 2 2 4 4 6 6 8 8 Pi - -(E (-1 + E ) (8 k x (-14783093325 + 1452971520 k x - 309657600 k x + 251658240 k x + 2147483648 k x ) Cos[-- + k x] - 3 (156043762875 - 11416204800 k x + 1589575680 k x - 587202560 k x + 2147483648 k x ) Sin[-- + k x])) - 4 4 -Integrate::idiv: Integral of ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ does not converge on {0, Infinity}. - 19/2 5 27/2 - 8589934592 k k0 Sqrt[2 Pi] x -Series[Integrate[(E^(I*k0*x)*(1 - E^(-(c*x)))^5*BesselJ[1, k*x])/(k0^5*x^4), {x, 0, Infinity}, Assumptions -> n == 1 && q == 5 && κ == 5 && k > k0 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0], {k, Infinity, 10}] - -Simplify::time: Time spent on a transformation exceeded 300. seconds, and the transformation was aborted. Increasing the value of TimeConstraint option may improve the result of simplification. -Integrate[(E^(I*k0*x)*(1 - E^(-(c*x)))^5*BesselJ[1, k*x])/(k0^5*x^4), {x, 0, Infinity}, Assumptions -> n == 1 && q == 5 && κ == 5] diff --git a/besseltransforms/klarge/5-5-2 b/besseltransforms/klarge/5-5-2 deleted file mode 100644 index 434adf3..0000000 --- a/besseltransforms/klarge/5-5-2 +++ /dev/null @@ -1,11 +0,0 @@ -Integrate[(E^(I*k0*x)*(1 - E^(-(c*x)))^5*BesselJ[2, k*x])/(k0^5*x^4), {x, 0, Infinity}, Assumptions -> n == 2 && q == 5 && κ == 5 && k > k0 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0] -Integrate((Power(E,I*k0*x)*Power(1 - Power(E,-(c*x)),5)*BesselJ(2,k*x))/(Power(k0,5)*Power(x,4)),List(x,0,DirectedInfinity(1)),Rule(Assumptions,n == 2 && q == 5 && κ == 5 && k > k0 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0)) - - -5 c x + I k0 x c x 5 2 2 4 4 6 6 8 8 Pi 2 2 4 4 6 6 8 8 - -(E (-1 + E ) (15 (-43692253605 + 3528645120 k x - 590413824 k x + 352321536 k x + 2147483648 k x ) Cos[-- + k x] + 4 Sqrt[2] k x (21606059475 - 2421619200 k x + 681246720 k x - 1761607680 k x + 2147483648 k x ) (Cos[k x] + Sin[k x]))) - 4 -Integrate::idiv: Integral of --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- does not converge on {0, Infinity}. - 19/2 5 27/2 - 8589934592 k k0 Sqrt[2 Pi] x -Series[Integrate[(E^(I*k0*x)*(1 - E^(-(c*x)))^5*BesselJ[2, k*x])/(k0^5*x^4), {x, 0, Infinity}, Assumptions -> n == 2 && q == 5 && κ == 5 && k > k0 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0], {k, Infinity, 10}] -Integrate[(E^(I*k0*x)*(1 - E^(-(c*x)))^5*BesselJ[2, k*x])/(k0^5*x^4), {x, 0, Infinity}, Assumptions -> n == 2 && q == 5 && κ == 5] diff --git a/besseltransforms/klarge/5-5-3 b/besseltransforms/klarge/5-5-3 deleted file mode 100644 index e64b420..0000000 --- a/besseltransforms/klarge/5-5-3 +++ /dev/null @@ -1,14 +0,0 @@ -Integrate[(E^(I*k0*x)*(1 - E^(-(c*x)))^5*BesselJ[3, k*x])/(k0^5*x^4), {x, 0, Infinity}, Assumptions -> n == 3 && q == 5 && κ == 5 && k > k0 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0] -Integrate((Power(E,I*k0*x)*Power(1 - Power(E,-(c*x)),5)*BesselJ(3,k*x))/(Power(k0,5)*Power(x,4)),List(x,0,DirectedInfinity(1)),Rule(Assumptions,n == 3 && q == 5 && κ == 5 && k > k0 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0)) - - 2 2 4 4 6 6 8 8 - -5 c x + I k0 x c x 5 2 2 4 4 6 6 8 8 Pi 35 (33129291195 - 3192583680 k x + 759103488 k x - 1660944384 k x + 2147483648 k x ) (Cos[k x] + Sin[k x]) - E (-1 + E ) (8 k x (-41247931725 + 5881075200 k x - 2952069120 k x - 15854469120 k x + 2147483648 k x ) Cos[-- + k x] - -----------------------------------------------------------------------------------------------------------------) - 4 Sqrt[2] -Integrate::idiv: Integral of ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- does not converge on {0, Infinity}. - 19/2 5 27/2 - 8589934592 k k0 Sqrt[2 Pi] x -Series[Integrate[(E^(I*k0*x)*(1 - E^(-(c*x)))^5*BesselJ[3, k*x])/(k0^5*x^4), {x, 0, Infinity}, Assumptions -> n == 3 && q == 5 && κ == 5 && k > k0 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0], {k, Infinity, 10}] - -Simplify::time: Time spent on a transformation exceeded 300. seconds, and the transformation was aborted. Increasing the value of TimeConstraint option may improve the result of simplification. -Integrate[(E^(I*k0*x)*(1 - E^(-(c*x)))^5*BesselJ[3, k*x])/(k0^5*x^4), {x, 0, Infinity}, Assumptions -> n == 3 && q == 5 && κ == 5] diff --git a/besseltransforms/klarge/5-5-4 b/besseltransforms/klarge/5-5-4 deleted file mode 100644 index c86eb6a..0000000 --- a/besseltransforms/klarge/5-5-4 +++ /dev/null @@ -1,4 +0,0 @@ -(-(k^6*(-35 + 16*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0) + 2*k^4*(-35 + 24*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^3 + 8*k^2*(-7 + 6*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^5 + 16*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^7)/(336*k^4) + (k^6*(-35 + 16*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0) + 2*k^4*(-35 + 24*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^3 + 8*k^2*(-7 + 6*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^5 + 16*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^7)/(168*k^4) - (k^6*(-35 + 16*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0) + 2*k^4*(-35 + 24*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^3 + 8*k^2*(-7 + 6*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^5 + 16*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^7)/(168*k^4) + (k^6*(-35 + 16*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0) + 2*k^4*(-35 + 24*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^3 + 8*k^2*(-7 + 6*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^5 + 16*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^7)/(336*k^4) - (k^6*(-35 + 16*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0) + 2*k^4*(-35 + 24*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^3 + 8*k^2*(-7 + 6*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^5 + 16*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^7)/(1680*k^4) + (16*(k^2 - k0^2)^(7/2) + I*(35*k^6*k0 - 70*k^4*k0^3 + 56*k^2*k0^5 - 16*k0^7))/(1680*k^4))/k0^5 -(-(Power(k,6)*(-35 + 16*Sqrt(1 + Power(k,2)/Power(c - Complex(0,1)*k0,2)))*(c - Complex(0,1)*k0) + 2*Power(k,4)*(-35 + 24*Sqrt(1 + Power(k,2)/Power(c - Complex(0,1)*k0,2)))*Power(c - Complex(0,1)*k0,3) + 8*Power(k,2)*(-7 + 6*Sqrt(1 + Power(k,2)/Power(c - Complex(0,1)*k0,2)))*Power(c - Complex(0,1)*k0,5) + 16*(-1 + Sqrt(1 + Power(k,2)/Power(c - Complex(0,1)*k0,2)))*Power(c - Complex(0,1)*k0,7))/(336.*Power(k,4)) + (Power(k,6)*(-35 + 16*Sqrt(1 + Power(k,2)/Power(2*c - Complex(0,1)*k0,2)))*(2*c - Complex(0,1)*k0) + 2*Power(k,4)*(-35 + 24*Sqrt(1 + Power(k,2)/Power(2*c - Complex(0,1)*k0,2)))*Power(2*c - Complex(0,1)*k0,3) + 8*Power(k,2)*(-7 + 6*Sqrt(1 + Power(k,2)/Power(2*c - Complex(0,1)*k0,2)))*Power(2*c - Complex(0,1)*k0,5) + 16*(-1 + Sqrt(1 + Power(k,2)/Power(2*c - Complex(0,1)*k0,2)))*Power(2*c - Complex(0,1)*k0,7))/(168.*Power(k,4)) - (Power(k,6)*(-35 + 16*Sqrt(1 + Power(k,2)/Power(3*c - Complex(0,1)*k0,2)))*(3*c - Complex(0,1)*k0) + 2*Power(k,4)*(-35 + 24*Sqrt(1 + Power(k,2)/Power(3*c - Complex(0,1)*k0,2)))*Power(3*c - Complex(0,1)*k0,3) + 8*Power(k,2)*(-7 + 6*Sqrt(1 + Power(k,2)/Power(3*c - Complex(0,1)*k0,2)))*Power(3*c - Complex(0,1)*k0,5) + 16*(-1 + Sqrt(1 + Power(k,2)/Power(3*c - Complex(0,1)*k0,2)))*Power(3*c - Complex(0,1)*k0,7))/(168.*Power(k,4)) + (Power(k,6)*(-35 + 16*Sqrt(1 + Power(k,2)/Power(4*c - Complex(0,1)*k0,2)))*(4*c - Complex(0,1)*k0) + 2*Power(k,4)*(-35 + 24*Sqrt(1 + Power(k,2)/Power(4*c - Complex(0,1)*k0,2)))*Power(4*c - Complex(0,1)*k0,3) + 8*Power(k,2)*(-7 + 6*Sqrt(1 + Power(k,2)/Power(4*c - Complex(0,1)*k0,2)))*Power(4*c - Complex(0,1)*k0,5) + 16*(-1 + Sqrt(1 + Power(k,2)/Power(4*c - Complex(0,1)*k0,2)))*Power(4*c - Complex(0,1)*k0,7))/(336.*Power(k,4)) - (Power(k,6)*(-35 + 16*Sqrt(1 + Power(k,2)/Power(5*c - Complex(0,1)*k0,2)))*(5*c - Complex(0,1)*k0) + 2*Power(k,4)*(-35 + 24*Sqrt(1 + Power(k,2)/Power(5*c - Complex(0,1)*k0,2)))*Power(5*c - Complex(0,1)*k0,3) + 8*Power(k,2)*(-7 + 6*Sqrt(1 + Power(k,2)/Power(5*c - Complex(0,1)*k0,2)))*Power(5*c - Complex(0,1)*k0,5) + 16*(-1 + Sqrt(1 + Power(k,2)/Power(5*c - Complex(0,1)*k0,2)))*Power(5*c - Complex(0,1)*k0,7))/(1680.*Power(k,4)) + (16*Power(Power(k,2) - Power(k0,2),3.5) + Complex(0,1)*(35*Power(k,6)*k0 - 70*Power(k,4)*Power(k0,3) + 56*Power(k,2)*Power(k0,5) - 16*Power(k0,7)))/(1680.*Power(k,4)))/Power(k0,5) -SeriesData[k, Infinity, {(4*c^5)/k0^5, (-75*c^6)/(2*k0^5) + ((15*I)*c^5)/k0^4, (160*c^7)/k0^5 - ((120*I)*c^6)/k0^4 - (24*c^5)/k0^3, (-35*(75*c^8 - (80*I)*c^7*k0 - 30*c^6*k0^2 + (4*I)*c^5*k0^3))/(8*k0^5), 0, (21*(2025*c^10 - (3310*I)*c^9*k0 - 2250*c^8*k0^2 + (800*I)*c^7*k0^3 + 150*c^6*k0^4 - (12*I)*c^5*k0^5))/(32*k0^5), 0, (-33*(20900*c^12 - (44860*I)*c^11*k0 - 42525*c^10*k0^2 + (23170*I)*c^9*k0^3 + 7875*c^8*k0^4 - (1680*I)*c^7*k0^5 - 210*c^6*k0^6 + (12*I)*c^5*k0^7))/(64*k0^5)}, 2, 11, 1] --(5*(k^6*(-35 + 16*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0) + 2*k^4*(-35 + 24*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^3 + 8*k^2*(-7 + 6*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^5 + 16*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^7) - 10*(k^6*(-35 + 16*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0) + 2*k^4*(-35 + 24*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^3 + 8*k^2*(-7 + 6*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^5 + 16*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^7) + 10*(k^6*(-35 + 16*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0) + 2*k^4*(-35 + 24*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^3 + 8*k^2*(-7 + 6*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^5 + 16*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^7) - 5*(k^6*(-35 + 16*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0) + 2*k^4*(-35 + 24*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^3 + 8*k^2*(-7 + 6*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^5 + 16*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^7) + k^6*(-35 + 16*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0) + 2*k^4*(-35 + 24*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^3 + 8*k^2*(-7 + 6*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^5 + 16*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^7 - 16*(k^2 - k0^2)^(7/2) - I*(35*k^6*k0 - 70*k^4*k0^3 + 56*k^2*k0^5 - 16*k0^7))/(1680*k^4*k0^5) diff --git a/besseltransforms/klarge/5-5-5 b/besseltransforms/klarge/5-5-5 deleted file mode 100644 index c3597ec..0000000 --- a/besseltransforms/klarge/5-5-5 +++ /dev/null @@ -1,4 +0,0 @@ -(-(35*k^8 + 8*k^6*(35 - 16*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^2 + 16*k^4*(35 - 24*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^4 + 64*k^2*(7 - 6*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^6 - 128*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^8)/(2688*k^5) + (35*k^8 + 8*k^6*(35 - 16*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^2 + 16*k^4*(35 - 24*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^4 + 64*k^2*(7 - 6*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^6 - 128*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^8)/(1344*k^5) - (35*k^8 + 8*k^6*(35 - 16*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^2 + 16*k^4*(35 - 24*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^4 + 64*k^2*(7 - 6*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^6 - 128*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^8)/(1344*k^5) + (35*k^8 + 8*k^6*(35 - 16*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^2 + 16*k^4*(35 - 24*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^4 + 64*k^2*(7 - 6*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^6 - 128*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^8)/(2688*k^5) - (35*k^8 + 8*k^6*(35 - 16*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^2 + 16*k^4*(35 - 24*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^4 + 64*k^2*(7 - 6*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^6 - 128*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^8)/(13440*k^5) + (35*k^8 - 280*k^6*k0^2 + 560*k^4*k0^4 - 448*k^2*k0^6 + 128*k0^8 + (128*I)*k0*(k^2 - k0^2)^(7/2))/(13440*k^5))/k0^5 -(-(35*Power(k,8) + 8*Power(k,6)*(35 - 16*Sqrt(1 + Power(k,2)/Power(c - Complex(0,1)*k0,2)))*Power(c - Complex(0,1)*k0,2) + 16*Power(k,4)*(35 - 24*Sqrt(1 + Power(k,2)/Power(c - Complex(0,1)*k0,2)))*Power(c - Complex(0,1)*k0,4) + 64*Power(k,2)*(7 - 6*Sqrt(1 + Power(k,2)/Power(c - Complex(0,1)*k0,2)))*Power(c - Complex(0,1)*k0,6) - 128*(-1 + Sqrt(1 + Power(k,2)/Power(c - Complex(0,1)*k0,2)))*Power(c - Complex(0,1)*k0,8))/(2688.*Power(k,5)) + (35*Power(k,8) + 8*Power(k,6)*(35 - 16*Sqrt(1 + Power(k,2)/Power(2*c - Complex(0,1)*k0,2)))*Power(2*c - Complex(0,1)*k0,2) + 16*Power(k,4)*(35 - 24*Sqrt(1 + Power(k,2)/Power(2*c - Complex(0,1)*k0,2)))*Power(2*c - Complex(0,1)*k0,4) + 64*Power(k,2)*(7 - 6*Sqrt(1 + Power(k,2)/Power(2*c - Complex(0,1)*k0,2)))*Power(2*c - Complex(0,1)*k0,6) - 128*(-1 + Sqrt(1 + Power(k,2)/Power(2*c - Complex(0,1)*k0,2)))*Power(2*c - Complex(0,1)*k0,8))/(1344.*Power(k,5)) - (35*Power(k,8) + 8*Power(k,6)*(35 - 16*Sqrt(1 + Power(k,2)/Power(3*c - Complex(0,1)*k0,2)))*Power(3*c - Complex(0,1)*k0,2) + 16*Power(k,4)*(35 - 24*Sqrt(1 + Power(k,2)/Power(3*c - Complex(0,1)*k0,2)))*Power(3*c - Complex(0,1)*k0,4) + 64*Power(k,2)*(7 - 6*Sqrt(1 + Power(k,2)/Power(3*c - Complex(0,1)*k0,2)))*Power(3*c - Complex(0,1)*k0,6) - 128*(-1 + Sqrt(1 + Power(k,2)/Power(3*c - Complex(0,1)*k0,2)))*Power(3*c - Complex(0,1)*k0,8))/(1344.*Power(k,5)) + (35*Power(k,8) + 8*Power(k,6)*(35 - 16*Sqrt(1 + Power(k,2)/Power(4*c - Complex(0,1)*k0,2)))*Power(4*c - Complex(0,1)*k0,2) + 16*Power(k,4)*(35 - 24*Sqrt(1 + Power(k,2)/Power(4*c - Complex(0,1)*k0,2)))*Power(4*c - Complex(0,1)*k0,4) + 64*Power(k,2)*(7 - 6*Sqrt(1 + Power(k,2)/Power(4*c - Complex(0,1)*k0,2)))*Power(4*c - Complex(0,1)*k0,6) - 128*(-1 + Sqrt(1 + Power(k,2)/Power(4*c - Complex(0,1)*k0,2)))*Power(4*c - Complex(0,1)*k0,8))/(2688.*Power(k,5)) - (35*Power(k,8) + 8*Power(k,6)*(35 - 16*Sqrt(1 + Power(k,2)/Power(5*c - Complex(0,1)*k0,2)))*Power(5*c - Complex(0,1)*k0,2) + 16*Power(k,4)*(35 - 24*Sqrt(1 + Power(k,2)/Power(5*c - Complex(0,1)*k0,2)))*Power(5*c - Complex(0,1)*k0,4) + 64*Power(k,2)*(7 - 6*Sqrt(1 + Power(k,2)/Power(5*c - Complex(0,1)*k0,2)))*Power(5*c - Complex(0,1)*k0,6) - 128*(-1 + Sqrt(1 + Power(k,2)/Power(5*c - Complex(0,1)*k0,2)))*Power(5*c - Complex(0,1)*k0,8))/(13440.*Power(k,5)) + (35*Power(k,8) - 280*Power(k,6)*Power(k0,2) + 560*Power(k,4)*Power(k0,4) - 448*Power(k,2)*Power(k0,6) + 128*Power(k0,8) + Complex(0,128)*k0*Power(Power(k,2) - Power(k0,2),3.5))/(13440.*Power(k,5)))/Power(k0,5) -SeriesData[k, Infinity, {(5*c^5)/k0^5, (-60*c^6)/k0^5 + ((24*I)*c^5)/k0^4, (35*(20*c^7 - (15*I)*c^6*k0 - 3*c^5*k0^2))/(2*k0^5), (-1200*c^8)/k0^5 + ((1280*I)*c^7)/k0^4 + (480*c^6)/k0^3 - ((64*I)*c^5)/k0^2, (105*(331*c^9 - (450*I)*c^8*k0 - 240*c^7*k0^2 + (60*I)*c^6*k0^3 + 6*c^5*k0^4))/(16*k0^5), 0, (-11*(22430*c^11 - (42525*I)*c^10*k0 - 34755*c^9*k0^2 + (15750*I)*c^8*k0^3 + 4200*c^7*k0^4 - (630*I)*c^6*k0^5 - 42*c^5*k0^6))/(32*k0^5), 0, (143*(52507*c^13 - (125400*I)*c^12*k0 - 134580*c^11*k0^2 + (85050*I)*c^10*k0^3 + 34755*c^9*k0^4 - (9450*I)*c^8*k0^5 - 1680*c^7*k0^6 + (180*I)*c^6*k0^7 + 9*c^5*k0^8))/(128*k0^5)}, 2, 11, 1] -(5*k^6*(-35 + 16*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^2 + 10*k^4*(-35 + 24*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^4 + 40*k^2*(-7 + 6*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^6 + 80*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^8 + 10*k^6*(35 - 16*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^2 + 20*k^4*(35 - 24*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^4 + 80*k^2*(7 - 6*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^6 - 160*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^8 + 10*k^6*(-35 + 16*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^2 + 20*k^4*(-35 + 24*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^4 + 80*k^2*(-7 + 6*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^6 + 160*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^8 + 5*k^6*(35 - 16*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^2 + 10*k^4*(35 - 24*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^4 + 40*k^2*(7 - 6*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^6 - 80*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^8 + k^6*(-35 + 16*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^2 + 2*k^4*(-35 + 24*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^4 + 8*k^2*(-7 + 6*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^6 + 16*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^8 - 35*k^6*k0^2 + 70*k^4*k0^4 - 56*k^2*k0^6 + 16*k0^8 + (16*I)*k0*(k^2 - k0^2)^(7/2))/(1680*k^5*k0^5) diff --git a/besseltransforms/klarge/runit.sh b/besseltransforms/klarge/runit.sh deleted file mode 100755 index d277388..0000000 --- a/besseltransforms/klarge/runit.sh +++ /dev/null @@ -1,11 +0,0 @@ -#!/bin/bash -K=$1 -Q=$2 -N=$3 -module load mathematica -cat - vzor.m <<<" -kk=$K; -qq=$Q; -nn=$N; -" | math -noprompt > "${K}-${Q}-${N}" - diff --git a/besseltransforms/klarge/vzor.m b/besseltransforms/klarge/vzor.m deleted file mode 100644 index 6803aa7..0000000 --- a/besseltransforms/klarge/vzor.m +++ /dev/null @@ -1,8 +0,0 @@ -$Assumptions = k >= 0 && k > k0 && k0 >= 0 && c >= 0 && n >= 0 ; -f = Refine[Integrate[(1 - Exp[-c x])^\[Kappa] (k0 x)^(-q) Exp[ - I k0 x] x BesselJ[n, k x], {x, - 0, \[Infinity]}], {\[Kappa] == kk, q == qq, n == nn}] -CForm[f] -Series[f, {k, \[Infinity], 10}] -Simplify[f] -Quit[ ] diff --git a/besseltransforms/ksmall/5-1-0 b/besseltransforms/ksmall/5-1-0 deleted file mode 100644 index 9b2b70d..0000000 --- a/besseltransforms/ksmall/5-1-0 +++ /dev/null @@ -1,4 +0,0 @@ -(-5/(Sqrt[1 + k^2/(c - I*k0)^2]*(c - I*k0)) + 10/(Sqrt[1 + k^2/(2*c - I*k0)^2]*(2*c - I*k0)) - 10/(Sqrt[1 + k^2/(3*c - I*k0)^2]*(3*c - I*k0)) + 5/(Sqrt[1 + k^2/(4*c - I*k0)^2]*(4*c - I*k0)) - 1/(Sqrt[1 + k^2/(5*c - I*k0)^2]*(5*c - I*k0)) + I/Sqrt[-k^2 + k0^2])/k0 -(-5/(Sqrt(1 + Power(k,2)/Power(c - Complex(0,1)*k0,2))*(c - Complex(0,1)*k0)) + 10/(Sqrt(1 + Power(k,2)/Power(2*c - Complex(0,1)*k0,2))*(2*c - Complex(0,1)*k0)) - 10/(Sqrt(1 + Power(k,2)/Power(3*c - Complex(0,1)*k0,2))*(3*c - Complex(0,1)*k0)) + 5/(Sqrt(1 + Power(k,2)/Power(4*c - Complex(0,1)*k0,2))*(4*c - Complex(0,1)*k0)) - 1/(Sqrt(1 + Power(k,2)/Power(5*c - Complex(0,1)*k0,2))*(5*c - Complex(0,1)*k0)) + Complex(0,1)/Sqrt(-Power(k,2) + Power(k0,2)))/k0 -SeriesData[k, Infinity, {-(1/(k*k0)), k0^(-1), -k0/(2*k), k0/2, ((-15*(c - I*k0)^3*(c/k - (I*k0)/k))/8 + (15*(2*c - I*k0)^3*((2*c)/k - (I*k0)/k))/4 - (15*(3*c - I*k0)^3*((3*c)/k - (I*k0)/k))/4 + (15*(4*c - I*k0)^3*((4*c)/k - (I*k0)/k))/8 - (3*(5*c - I*k0)^3*((5*c)/k - (I*k0)/k))/8)/k0, (3*k0^3)/8, ((25*(c - I*k0)^5*(c/k - (I*k0)/k))/16 - (25*(2*c - I*k0)^5*((2*c)/k - (I*k0)/k))/8 + (25*(3*c - I*k0)^5*((3*c)/k - (I*k0)/k))/8 - (25*(4*c - I*k0)^5*((4*c)/k - (I*k0)/k))/16 + (5*(5*c - I*k0)^5*((5*c)/k - (I*k0)/k))/16)/k0, (5*k0^5)/16, ((-175*(c - I*k0)^7*(c/k - (I*k0)/k))/128 + (175*(2*c - I*k0)^7*((2*c)/k - (I*k0)/k))/64 - (175*(3*c - I*k0)^7*((3*c)/k - (I*k0)/k))/64 + (175*(4*c - I*k0)^7*((4*c)/k - (I*k0)/k))/128 - (35*(5*c - I*k0)^7*((5*c)/k - (I*k0)/k))/128)/k0, (35*k0^7)/128, ((315*(c - I*k0)^9*(c/k - (I*k0)/k))/256 - (315*(2*c - I*k0)^9*((2*c)/k - (I*k0)/k))/128 + (315*(3*c - I*k0)^9*((3*c)/k - (I*k0)/k))/128 - (315*(4*c - I*k0)^9*((4*c)/k - (I*k0)/k))/256 + (63*(5*c - I*k0)^9*((5*c)/k - (I*k0)/k))/256)/k0}, 0, 11, 1] -(-5/(Sqrt[1 + k^2/(c - I*k0)^2]*(c - I*k0)) + 10/(Sqrt[1 + k^2/(2*c - I*k0)^2]*(2*c - I*k0)) - 10/(Sqrt[1 + k^2/(3*c - I*k0)^2]*(3*c - I*k0)) + 5/(Sqrt[1 + k^2/(4*c - I*k0)^2]*(4*c - I*k0)) - 1/(Sqrt[1 + k^2/(5*c - I*k0)^2]*(5*c - I*k0)) + I/Sqrt[-k^2 + k0^2])/k0 diff --git a/besseltransforms/ksmall/5-1-1 b/besseltransforms/ksmall/5-1-1 deleted file mode 100644 index 7cb5ee3..0000000 --- a/besseltransforms/ksmall/5-1-1 +++ /dev/null @@ -1,4 +0,0 @@ -(-k^(-1) - 5*(k^(-1) - 1/(k*Sqrt[1 + k^2/(c - I*k0)^2])) + 10*(k^(-1) - 1/(k*Sqrt[1 + k^2/(2*c - I*k0)^2])) - 10*(k^(-1) - 1/(k*Sqrt[1 + k^2/(3*c - I*k0)^2])) + 5*(k^(-1) - 1/(k*Sqrt[1 + k^2/(4*c - I*k0)^2])) + 1/(k*Sqrt[1 + k^2/(5*c - I*k0)^2]) + (1 - k0/Sqrt[-k^2 + k0^2])/k)/k0 -(-(1/k) - 5*(1/k - 1/(k*Sqrt(1 + Power(k,2)/Power(c - Complex(0,1)*k0,2)))) + 10*(1/k - 1/(k*Sqrt(1 + Power(k,2)/Power(2*c - Complex(0,1)*k0,2)))) - 10*(1/k - 1/(k*Sqrt(1 + Power(k,2)/Power(3*c - Complex(0,1)*k0,2)))) + 5*(1/k - 1/(k*Sqrt(1 + Power(k,2)/Power(4*c - Complex(0,1)*k0,2)))) + 1/(k*Sqrt(1 + Power(k,2)/Power(5*c - Complex(0,1)*k0,2))) + (1 - k0/Sqrt(-Power(k,2) + Power(k0,2)))/k)/k0 -SeriesData[k, Infinity, {-I/k, I, (-I/2*k0^2)/k, I/2*k0^2, (3*(120*c^5 - I*k0^5))/(8*k*k0), (3*I)/8*k0^4, (-5*(16800*c^7 - (12600*I)*c^6*k0 - 2520*c^5*k0^2 + I*k0^7))/(16*k*k0), (5*I)/16*k0^6, (35*(834120*c^9 - (1134000*I)*c^8*k0 - 604800*c^7*k0^2 + (151200*I)*c^6*k0^3 + 15120*c^5*k0^4 - I*k0^9))/(128*k*k0), (35*I)/128*k0^8}, 1, 11, 1] -(-5*(1 - 1/Sqrt[1 + k^2/(c - I*k0)^2]) + 10*(1 - 1/Sqrt[1 + k^2/(2*c - I*k0)^2]) - 10*(1 - 1/Sqrt[1 + k^2/(3*c - I*k0)^2]) + 5*(1 - 1/Sqrt[1 + k^2/(4*c - I*k0)^2]) + 1/Sqrt[1 + k^2/(5*c - I*k0)^2] - k0/Sqrt[-k^2 + k0^2])/(k*k0) diff --git a/besseltransforms/ksmall/5-1-2 b/besseltransforms/ksmall/5-1-2 deleted file mode 100644 index 2257754..0000000 --- a/besseltransforms/ksmall/5-1-2 +++ /dev/null @@ -1,4 +0,0 @@ -(-5*(1/(Sqrt[1 + k^2/(c - I*k0)^2]*(c - I*k0)) - (2*(c - I*k0))/k^2 + (2*(c - I*k0))/(k^2*Sqrt[1 + k^2/(c - I*k0)^2])) + 10*(1/(Sqrt[1 + k^2/(2*c - I*k0)^2]*(2*c - I*k0)) - (2*(2*c - I*k0))/k^2 + (2*(2*c - I*k0))/(k^2*Sqrt[1 + k^2/(2*c - I*k0)^2])) - 10*(1/(Sqrt[1 + k^2/(3*c - I*k0)^2]*(3*c - I*k0)) - (2*(3*c - I*k0))/k^2 + (2*(3*c - I*k0))/(k^2*Sqrt[1 + k^2/(3*c - I*k0)^2])) + 5*(1/(Sqrt[1 + k^2/(4*c - I*k0)^2]*(4*c - I*k0)) - (2*(4*c - I*k0))/k^2 + (2*(4*c - I*k0))/(k^2*Sqrt[1 + k^2/(4*c - I*k0)^2])) - 1/(Sqrt[1 + k^2/(5*c - I*k0)^2]*(5*c - I*k0)) + (2*(5*c - I*k0))/k^2 - (2*(5*c - I*k0))/(k^2*Sqrt[1 + k^2/(5*c - I*k0)^2]) + (I*(k^2 + 2*k0*(-k0 + Sqrt[-k^2 + k0^2])))/(k^2*Sqrt[-k^2 + k0^2]))/k0 -(-5*(1/(Sqrt(1 + Power(k,2)/Power(c - Complex(0,1)*k0,2))*(c - Complex(0,1)*k0)) - (2*(c - Complex(0,1)*k0))/Power(k,2) + (2*(c - Complex(0,1)*k0))/(Power(k,2)*Sqrt(1 + Power(k,2)/Power(c - Complex(0,1)*k0,2)))) + 10*(1/(Sqrt(1 + Power(k,2)/Power(2*c - Complex(0,1)*k0,2))*(2*c - Complex(0,1)*k0)) - (2*(2*c - Complex(0,1)*k0))/Power(k,2) + (2*(2*c - Complex(0,1)*k0))/(Power(k,2)*Sqrt(1 + Power(k,2)/Power(2*c - Complex(0,1)*k0,2)))) - 10*(1/(Sqrt(1 + Power(k,2)/Power(3*c - Complex(0,1)*k0,2))*(3*c - Complex(0,1)*k0)) - (2*(3*c - Complex(0,1)*k0))/Power(k,2) + (2*(3*c - Complex(0,1)*k0))/(Power(k,2)*Sqrt(1 + Power(k,2)/Power(3*c - Complex(0,1)*k0,2)))) + 5*(1/(Sqrt(1 + Power(k,2)/Power(4*c - Complex(0,1)*k0,2))*(4*c - Complex(0,1)*k0)) - (2*(4*c - Complex(0,1)*k0))/Power(k,2) + (2*(4*c - Complex(0,1)*k0))/(Power(k,2)*Sqrt(1 + Power(k,2)/Power(4*c - Complex(0,1)*k0,2)))) - 1/(Sqrt(1 + Power(k,2)/Power(5*c - Complex(0,1)*k0,2))*(5*c - Complex(0,1)*k0)) + (2*(5*c - Complex(0,1)*k0))/Power(k,2) - (2*(5*c - Complex(0,1)*k0))/(Power(k,2)*Sqrt(1 + Power(k,2)/Power(5*c - Complex(0,1)*k0,2))) + (Complex(0,1)*(Power(k,2) + 2*k0*(-k0 + Sqrt(-Power(k,2) + Power(k0,2)))))/(Power(k,2)*Sqrt(-Power(k,2) + Power(k0,2))))/k0 -SeriesData[k, Infinity, {-(1/(k*k0)), k0^(-1), (3*k0)/(2*k), (-3*k0)/2, ((5*c - I*k0)^4/k - (3*(5*c - I*k0)^3*((5*c)/k - (I*k0)/k))/8 - 5*(-((c - I*k0)^4/k) + (3*(c - I*k0)^3*(c/k - (I*k0)/k))/8) + 10*(-((2*c - I*k0)^4/k) + (3*(2*c - I*k0)^3*((2*c)/k - (I*k0)/k))/8) - 10*(-((3*c - I*k0)^4/k) + (3*(3*c - I*k0)^3*((3*c)/k - (I*k0)/k))/8) + 5*(-((4*c - I*k0)^4/k) + (3*(4*c - I*k0)^3*((4*c)/k - (I*k0)/k))/8))/k0, (-5*k0^3)/8, ((-3*(5*c - I*k0)^6)/(4*k) + (5*(5*c - I*k0)^5*((5*c)/k - (I*k0)/k))/16 - 5*((3*(c - I*k0)^6)/(4*k) - (5*(c - I*k0)^5*(c/k - (I*k0)/k))/16) + 10*((3*(2*c - I*k0)^6)/(4*k) - (5*(2*c - I*k0)^5*((2*c)/k - (I*k0)/k))/16) - 10*((3*(3*c - I*k0)^6)/(4*k) - (5*(3*c - I*k0)^5*((3*c)/k - (I*k0)/k))/16) + 5*((3*(4*c - I*k0)^6)/(4*k) - (5*(4*c - I*k0)^5*((4*c)/k - (I*k0)/k))/16))/k0, (-7*k0^5)/16, ((5*(5*c - I*k0)^8)/(8*k) - (35*(5*c - I*k0)^7*((5*c)/k - (I*k0)/k))/128 - 5*((-5*(c - I*k0)^8)/(8*k) + (35*(c - I*k0)^7*(c/k - (I*k0)/k))/128) + 10*((-5*(2*c - I*k0)^8)/(8*k) + (35*(2*c - I*k0)^7*((2*c)/k - (I*k0)/k))/128) - 10*((-5*(3*c - I*k0)^8)/(8*k) + (35*(3*c - I*k0)^7*((3*c)/k - (I*k0)/k))/128) + 5*((-5*(4*c - I*k0)^8)/(8*k) + (35*(4*c - I*k0)^7*((4*c)/k - (I*k0)/k))/128))/k0, (-45*k0^7)/128, ((-35*(5*c - I*k0)^10)/(64*k) + (63*(5*c - I*k0)^9*((5*c)/k - (I*k0)/k))/256 - 5*((35*(c - I*k0)^10)/(64*k) - (63*(c - I*k0)^9*(c/k - (I*k0)/k))/256) + 10*((35*(2*c - I*k0)^10)/(64*k) - (63*(2*c - I*k0)^9*((2*c)/k - (I*k0)/k))/256) - 10*((35*(3*c - I*k0)^10)/(64*k) - (63*(3*c - I*k0)^9*((3*c)/k - (I*k0)/k))/256) + 5*((35*(4*c - I*k0)^10)/(64*k) - (63*(4*c - I*k0)^9*((4*c)/k - (I*k0)/k))/256))/k0}, 0, 11, 1] -(-5*(1/(Sqrt[1 + k^2/(c - I*k0)^2]*(c - I*k0)) - (2*(c - I*k0))/k^2 + (2*(c - I*k0))/(k^2*Sqrt[1 + k^2/(c - I*k0)^2])) + 5*(1/(Sqrt[1 + k^2/(4*c - I*k0)^2]*(4*c - I*k0)) + (8*c - (2*I)*k0)/(k^2*Sqrt[1 + k^2/(4*c - I*k0)^2]) + (-8*c + (2*I)*k0)/k^2) - 10*(1/(Sqrt[1 + k^2/(3*c - I*k0)^2]*(3*c - I*k0)) + (6*c - (2*I)*k0)/(k^2*Sqrt[1 + k^2/(3*c - I*k0)^2]) + (-6*c + (2*I)*k0)/k^2) + 10*(1/(Sqrt[1 + k^2/(2*c - I*k0)^2]*(2*c - I*k0)) + (4*c - (2*I)*k0)/(k^2*Sqrt[1 + k^2/(2*c - I*k0)^2]) + (-4*c + (2*I)*k0)/k^2) - 1/(Sqrt[1 + k^2/(5*c - I*k0)^2]*(5*c - I*k0)) + (10*c - (2*I)*k0)/k^2 + (-10*c + (2*I)*k0)/(k^2*Sqrt[1 + k^2/(5*c - I*k0)^2]) + (I*(k^2 + 2*k0*(-k0 + Sqrt[-k^2 + k0^2])))/(k^2*Sqrt[-k^2 + k0^2]))/k0 diff --git a/besseltransforms/ksmall/5-1-3 b/besseltransforms/ksmall/5-1-3 deleted file mode 100644 index 277099c..0000000 --- a/besseltransforms/ksmall/5-1-3 +++ /dev/null @@ -1,4 +0,0 @@ -((-5*(k^2*(-3 + Sqrt[1 + k^2/(c - I*k0)^2]) + 4*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^2))/(k^3*Sqrt[1 + k^2/(c - I*k0)^2]) + (10*(k^2*(-3 + Sqrt[1 + k^2/(2*c - I*k0)^2]) + 4*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^2))/(k^3*Sqrt[1 + k^2/(2*c - I*k0)^2]) - (10*(k^2*(-3 + Sqrt[1 + k^2/(3*c - I*k0)^2]) + 4*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^2))/(k^3*Sqrt[1 + k^2/(3*c - I*k0)^2]) + (5*(k^2*(-3 + Sqrt[1 + k^2/(4*c - I*k0)^2]) + 4*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^2))/(k^3*Sqrt[1 + k^2/(4*c - I*k0)^2]) - (k^2*(-3 + Sqrt[1 + k^2/(5*c - I*k0)^2]) + 4*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^2)/(k^3*Sqrt[1 + k^2/(5*c - I*k0)^2]) + (k^2*(1 - (3*k0)/Sqrt[-k^2 + k0^2]) + 4*k0^2*(-1 + k0/Sqrt[-k^2 + k0^2]))/k^3)/k0 -((-5*(Power(k,2)*(-3 + Sqrt(1 + Power(k,2)/Power(c - Complex(0,1)*k0,2))) + 4*(-1 + Sqrt(1 + Power(k,2)/Power(c - Complex(0,1)*k0,2)))*Power(c - Complex(0,1)*k0,2)))/(Power(k,3)*Sqrt(1 + Power(k,2)/Power(c - Complex(0,1)*k0,2))) + (10*(Power(k,2)*(-3 + Sqrt(1 + Power(k,2)/Power(2*c - Complex(0,1)*k0,2))) + 4*(-1 + Sqrt(1 + Power(k,2)/Power(2*c - Complex(0,1)*k0,2)))*Power(2*c - Complex(0,1)*k0,2)))/(Power(k,3)*Sqrt(1 + Power(k,2)/Power(2*c - Complex(0,1)*k0,2))) - (10*(Power(k,2)*(-3 + Sqrt(1 + Power(k,2)/Power(3*c - Complex(0,1)*k0,2))) + 4*(-1 + Sqrt(1 + Power(k,2)/Power(3*c - Complex(0,1)*k0,2)))*Power(3*c - Complex(0,1)*k0,2)))/(Power(k,3)*Sqrt(1 + Power(k,2)/Power(3*c - Complex(0,1)*k0,2))) + (5*(Power(k,2)*(-3 + Sqrt(1 + Power(k,2)/Power(4*c - Complex(0,1)*k0,2))) + 4*(-1 + Sqrt(1 + Power(k,2)/Power(4*c - Complex(0,1)*k0,2)))*Power(4*c - Complex(0,1)*k0,2)))/(Power(k,3)*Sqrt(1 + Power(k,2)/Power(4*c - Complex(0,1)*k0,2))) - (Power(k,2)*(-3 + Sqrt(1 + Power(k,2)/Power(5*c - Complex(0,1)*k0,2))) + 4*(-1 + Sqrt(1 + Power(k,2)/Power(5*c - Complex(0,1)*k0,2)))*Power(5*c - Complex(0,1)*k0,2))/(Power(k,3)*Sqrt(1 + Power(k,2)/Power(5*c - Complex(0,1)*k0,2))) + (Power(k,2)*(1 - (3*k0)/Sqrt(-Power(k,2) + Power(k0,2))) + 4*Power(k0,2)*(-1 + k0/Sqrt(-Power(k,2) + Power(k0,2))))/Power(k,3))/k0 -SeriesData[k, Infinity, {-(1/(k*k0)), (k - (3*I)*k0)/(k*k0), (I*(3*k - (4*I)*k0))/k, (-8*k*k0 + (5*I)*k0^2)/(2*k), ((3*(5*c - I*k0)^4)/(8*k) - (5*I)/2*k0^3 - (3*(5*c - I*k0)^3*((5*c)/k - (I*k0)/k))/8 - 5*((-3*(c - I*k0)^4)/(8*k) + (3*(c - I*k0)^3*(c/k - (I*k0)/k))/8) + 10*((-3*(2*c - I*k0)^4)/(8*k) + (3*(2*c - I*k0)^3*((2*c)/k - (I*k0)/k))/8) - 10*((-3*(3*c - I*k0)^4)/(8*k) + (3*(3*c - I*k0)^3*((3*c)/k - (I*k0)/k))/8) + 5*((-3*(4*c - I*k0)^4)/(8*k) + (3*(4*c - I*k0)^3*((4*c)/k - (I*k0)/k))/8))/k0, ((-2*(5*c - I*k0)^5)/k + (9*(5*c - I*k0)^4*((5*c)/k - (I*k0)/k))/8 - 5*((2*(c - I*k0)^5)/k - (9*(c - I*k0)^4*(c/k - (I*k0)/k))/8) + 10*((2*(2*c - I*k0)^5)/k - (9*(2*c - I*k0)^4*((2*c)/k - (I*k0)/k))/8) - 10*((2*(3*c - I*k0)^5)/k - (9*(3*c - I*k0)^4*((3*c)/k - (I*k0)/k))/8) + 5*((2*(4*c - I*k0)^5)/k - (9*(4*c - I*k0)^4*((4*c)/k - (I*k0)/k))/8))/k0, ((11*(5*c - I*k0)^6)/(8*k) - (7*I)/8*k0^5 - (11*(5*c - I*k0)^5*((5*c)/k - (I*k0)/k))/8 - 5*((-11*(c - I*k0)^6)/(8*k) + (11*(c - I*k0)^5*(c/k - (I*k0)/k))/8) + 10*((-11*(2*c - I*k0)^6)/(8*k) + (11*(2*c - I*k0)^5*((2*c)/k - (I*k0)/k))/8) - 10*((-11*(3*c - I*k0)^6)/(8*k) + (11*(3*c - I*k0)^5*((3*c)/k - (I*k0)/k))/8) + 5*((-11*(4*c - I*k0)^6)/(8*k) + (11*(4*c - I*k0)^5*((4*c)/k - (I*k0)/k))/8))/k0, ((45*(c - I*k0)^6*(c/k - (I*k0)/k))/16 - (45*(2*c - I*k0)^6*((2*c)/k - (I*k0)/k))/8 + (45*(3*c - I*k0)^6*((3*c)/k - (I*k0)/k))/8 - (45*(4*c - I*k0)^6*((4*c)/k - (I*k0)/k))/16 + (9*(5*c - I*k0)^6*((5*c)/k - (I*k0)/k))/16)/k0, ((-55*(5*c - I*k0)^8)/(128*k) - (9*I)/16*k0^7 + (55*(5*c - I*k0)^7*((5*c)/k - (I*k0)/k))/128 - 5*((55*(c - I*k0)^8)/(128*k) - (55*(c - I*k0)^7*(c/k - (I*k0)/k))/128) + 10*((55*(2*c - I*k0)^8)/(128*k) - (55*(2*c - I*k0)^7*((2*c)/k - (I*k0)/k))/128) - 10*((55*(3*c - I*k0)^8)/(128*k) - (55*(3*c - I*k0)^7*((3*c)/k - (I*k0)/k))/128) + 5*((55*(4*c - I*k0)^8)/(128*k) - (55*(4*c - I*k0)^7*((4*c)/k - (I*k0)/k))/128))/k0, ((-275*(c - I*k0)^8*(c/k - (I*k0)/k))/128 + (275*(2*c - I*k0)^8*((2*c)/k - (I*k0)/k))/64 - (275*(3*c - I*k0)^8*((3*c)/k - (I*k0)/k))/64 + (275*(4*c - I*k0)^8*((4*c)/k - (I*k0)/k))/128 - (55*(5*c - I*k0)^8*((5*c)/k - (I*k0)/k))/128)/k0, ((15*(5*c - I*k0)^10)/(64*k) - (55*I)/128*k0^9 - (15*(5*c - I*k0)^9*((5*c)/k - (I*k0)/k))/64 - 5*((-15*(c - I*k0)^10)/(64*k) + (15*(c - I*k0)^9*(c/k - (I*k0)/k))/64) + 10*((-15*(2*c - I*k0)^10)/(64*k) + (15*(2*c - I*k0)^9*((2*c)/k - (I*k0)/k))/64) - 10*((-15*(3*c - I*k0)^10)/(64*k) + (15*(3*c - I*k0)^9*((3*c)/k - (I*k0)/k))/64) + 5*((-15*(4*c - I*k0)^10)/(64*k) + (15*(4*c - I*k0)^9*((4*c)/k - (I*k0)/k))/64))/k0}, 0, 11, 1] -((-5*(k^2*(-3 + Sqrt[1 + k^2/(c - I*k0)^2]) + 4*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^2))/Sqrt[1 + k^2/(c - I*k0)^2] + (10*(k^2*(-3 + Sqrt[1 + k^2/(2*c - I*k0)^2]) + 4*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^2))/Sqrt[1 + k^2/(2*c - I*k0)^2] - (10*(k^2*(-3 + Sqrt[1 + k^2/(3*c - I*k0)^2]) + 4*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^2))/Sqrt[1 + k^2/(3*c - I*k0)^2] + (5*(k^2*(-3 + Sqrt[1 + k^2/(4*c - I*k0)^2]) + 4*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^2))/Sqrt[1 + k^2/(4*c - I*k0)^2] - (k^2*(-3 + Sqrt[1 + k^2/(5*c - I*k0)^2]) + 4*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^2)/Sqrt[1 + k^2/(5*c - I*k0)^2] + k^2*(1 - (3*k0)/Sqrt[-k^2 + k0^2]) + 4*k0^2*(-1 + k0/Sqrt[-k^2 + k0^2]))/(k^3*k0) diff --git a/besseltransforms/ksmall/5-1-4 b/besseltransforms/ksmall/5-1-4 deleted file mode 100644 index 00c73ec..0000000 --- a/besseltransforms/ksmall/5-1-4 +++ /dev/null @@ -1,4 +0,0 @@ -((-5*(k^4 - 4*k^2*(-2 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^2 - 8*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^4))/(k^4*Sqrt[1 + k^2/(c - I*k0)^2]*(c - I*k0)) + (10*(k^4 - 4*k^2*(-2 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^2 - 8*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^4))/(k^4*Sqrt[1 + k^2/(2*c - I*k0)^2]*(2*c - I*k0)) - (10*(k^4 - 4*k^2*(-2 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^2 - 8*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^4))/(k^4*Sqrt[1 + k^2/(3*c - I*k0)^2]*(3*c - I*k0)) + (5*(k^4 - 4*k^2*(-2 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^2 - 8*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^4))/(k^4*Sqrt[1 + k^2/(4*c - I*k0)^2]*(4*c - I*k0)) - (k^4 - 4*k^2*(-2 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^2 - 8*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^4)/(k^4*Sqrt[1 + k^2/(5*c - I*k0)^2]*(5*c - I*k0)) + (I*(k^4 + 8*k0^3*(k0 - Sqrt[-k^2 + k0^2]) + 4*k^2*k0*(-2*k0 + Sqrt[-k^2 + k0^2])))/(k^4*Sqrt[-k^2 + k0^2]))/k0 -((-5*(Power(k,4) - 4*Power(k,2)*(-2 + Sqrt(1 + Power(k,2)/Power(c - Complex(0,1)*k0,2)))*Power(c - Complex(0,1)*k0,2) - 8*(-1 + Sqrt(1 + Power(k,2)/Power(c - Complex(0,1)*k0,2)))*Power(c - Complex(0,1)*k0,4)))/(Power(k,4)*Sqrt(1 + Power(k,2)/Power(c - Complex(0,1)*k0,2))*(c - Complex(0,1)*k0)) + (10*(Power(k,4) - 4*Power(k,2)*(-2 + Sqrt(1 + Power(k,2)/Power(2*c - Complex(0,1)*k0,2)))*Power(2*c - Complex(0,1)*k0,2) - 8*(-1 + Sqrt(1 + Power(k,2)/Power(2*c - Complex(0,1)*k0,2)))*Power(2*c - Complex(0,1)*k0,4)))/(Power(k,4)*Sqrt(1 + Power(k,2)/Power(2*c - Complex(0,1)*k0,2))*(2*c - Complex(0,1)*k0)) - (10*(Power(k,4) - 4*Power(k,2)*(-2 + Sqrt(1 + Power(k,2)/Power(3*c - Complex(0,1)*k0,2)))*Power(3*c - Complex(0,1)*k0,2) - 8*(-1 + Sqrt(1 + Power(k,2)/Power(3*c - Complex(0,1)*k0,2)))*Power(3*c - Complex(0,1)*k0,4)))/(Power(k,4)*Sqrt(1 + Power(k,2)/Power(3*c - Complex(0,1)*k0,2))*(3*c - Complex(0,1)*k0)) + (5*(Power(k,4) - 4*Power(k,2)*(-2 + Sqrt(1 + Power(k,2)/Power(4*c - Complex(0,1)*k0,2)))*Power(4*c - Complex(0,1)*k0,2) - 8*(-1 + Sqrt(1 + Power(k,2)/Power(4*c - Complex(0,1)*k0,2)))*Power(4*c - Complex(0,1)*k0,4)))/(Power(k,4)*Sqrt(1 + Power(k,2)/Power(4*c - Complex(0,1)*k0,2))*(4*c - Complex(0,1)*k0)) - (Power(k,4) - 4*Power(k,2)*(-2 + Sqrt(1 + Power(k,2)/Power(5*c - Complex(0,1)*k0,2)))*Power(5*c - Complex(0,1)*k0,2) - 8*(-1 + Sqrt(1 + Power(k,2)/Power(5*c - Complex(0,1)*k0,2)))*Power(5*c - Complex(0,1)*k0,4))/(Power(k,4)*Sqrt(1 + Power(k,2)/Power(5*c - Complex(0,1)*k0,2))*(5*c - Complex(0,1)*k0)) + (Complex(0,1)*(Power(k,4) + 8*Power(k0,3)*(k0 - Sqrt(-Power(k,2) + Power(k0,2))) + 4*Power(k,2)*k0*(-2*k0 + Sqrt(-Power(k,2) + Power(k0,2)))))/(Power(k,4)*Sqrt(-Power(k,2) + Power(k0,2))))/k0 -SeriesData[k, Infinity, {-(1/(k*k0)), (k - (4*I)*k0)/(k*k0), (I/2*(8*k - (15*I)*k0))/k, (-15*k*k0 + (16*I)*k0^2)/(2*k), ((-8*I)*k0^3 - (5*((4*(c - I*k0)^5)/k + (3*(c - I*k0)^4*(c/k - (I*k0)/k))/8))/(c - I*k0) + (10*((4*(2*c - I*k0)^5)/k + (3*(2*c - I*k0)^4*((2*c)/k - (I*k0)/k))/8))/(2*c - I*k0) - (10*((4*(3*c - I*k0)^5)/k + (3*(3*c - I*k0)^4*((3*c)/k - (I*k0)/k))/8))/(3*c - I*k0) + (5*((4*(4*c - I*k0)^5)/k + (3*(4*c - I*k0)^4*((4*c)/k - (I*k0)/k))/8))/(4*c - I*k0) + ((-4*(5*c - I*k0)^5)/k - (3*(5*c - I*k0)^4*((5*c)/k - (I*k0)/k))/8)/(5*c - I*k0))/k0, ((35*k0^4)/8 - (5*((3*(c - I*k0)^6)/(2*k) - (3*(c - I*k0)^5*(c/k - (I*k0)/k))/2))/(c - I*k0) + (10*((3*(2*c - I*k0)^6)/(2*k) - (3*(2*c - I*k0)^5*((2*c)/k - (I*k0)/k))/2))/(2*c - I*k0) - (10*((3*(3*c - I*k0)^6)/(2*k) - (3*(3*c - I*k0)^5*((3*c)/k - (I*k0)/k))/2))/(3*c - I*k0) + (5*((3*(4*c - I*k0)^6)/(2*k) - (3*(4*c - I*k0)^5*((4*c)/k - (I*k0)/k))/2))/(4*c - I*k0) + ((-3*(5*c - I*k0)^6)/(2*k) + (3*(5*c - I*k0)^5*((5*c)/k - (I*k0)/k))/2)/(5*c - I*k0))/k0, ((-5*((-4*(c - I*k0)^7)/k + (43*(c - I*k0)^6*(c/k - (I*k0)/k))/16))/(c - I*k0) + (10*((-4*(2*c - I*k0)^7)/k + (43*(2*c - I*k0)^6*((2*c)/k - (I*k0)/k))/16))/(2*c - I*k0) - (10*((-4*(3*c - I*k0)^7)/k + (43*(3*c - I*k0)^6*((3*c)/k - (I*k0)/k))/16))/(3*c - I*k0) + (5*((-4*(4*c - I*k0)^7)/k + (43*(4*c - I*k0)^6*((4*c)/k - (I*k0)/k))/16))/(4*c - I*k0) + ((4*(5*c - I*k0)^7)/k - (43*(5*c - I*k0)^6*((5*c)/k - (I*k0)/k))/16)/(5*c - I*k0))/k0, ((21*k0^6)/16 - (5*((5*(c - I*k0)^8)/(2*k) - (5*(c - I*k0)^7*(c/k - (I*k0)/k))/2))/(c - I*k0) + (10*((5*(2*c - I*k0)^8)/(2*k) - (5*(2*c - I*k0)^7*((2*c)/k - (I*k0)/k))/2))/(2*c - I*k0) - (10*((5*(3*c - I*k0)^8)/(2*k) - (5*(3*c - I*k0)^7*((3*c)/k - (I*k0)/k))/2))/(3*c - I*k0) + (5*((5*(4*c - I*k0)^8)/(2*k) - (5*(4*c - I*k0)^7*((4*c)/k - (I*k0)/k))/2))/(4*c - I*k0) + ((-5*(5*c - I*k0)^8)/(2*k) + (5*(5*c - I*k0)^7*((5*c)/k - (I*k0)/k))/2)/(5*c - I*k0))/k0, ((-495*(c - I*k0)^7*(c/k - (I*k0)/k))/128 + (495*(2*c - I*k0)^7*((2*c)/k - (I*k0)/k))/64 - (495*(3*c - I*k0)^7*((3*c)/k - (I*k0)/k))/64 + (495*(4*c - I*k0)^7*((4*c)/k - (I*k0)/k))/128 - (99*(5*c - I*k0)^7*((5*c)/k - (I*k0)/k))/128)/k0, ((99*k0^8)/128 - (5*((-23*(c - I*k0)^10)/(32*k) + (23*(c - I*k0)^9*(c/k - (I*k0)/k))/32))/(c - I*k0) + (10*((-23*(2*c - I*k0)^10)/(32*k) + (23*(2*c - I*k0)^9*((2*c)/k - (I*k0)/k))/32))/(2*c - I*k0) - (10*((-23*(3*c - I*k0)^10)/(32*k) + (23*(3*c - I*k0)^9*((3*c)/k - (I*k0)/k))/32))/(3*c - I*k0) + (5*((-23*(4*c - I*k0)^10)/(32*k) + (23*(4*c - I*k0)^9*((4*c)/k - (I*k0)/k))/32))/(4*c - I*k0) + ((23*(5*c - I*k0)^10)/(32*k) - (23*(5*c - I*k0)^9*((5*c)/k - (I*k0)/k))/32)/(5*c - I*k0))/k0, ((715*(c - I*k0)^9*(c/k - (I*k0)/k))/256 - (715*(2*c - I*k0)^9*((2*c)/k - (I*k0)/k))/128 + (715*(3*c - I*k0)^9*((3*c)/k - (I*k0)/k))/128 - (715*(4*c - I*k0)^9*((4*c)/k - (I*k0)/k))/256 + (143*(5*c - I*k0)^9*((5*c)/k - (I*k0)/k))/256)/k0}, 0, 11, 1] -((-5*(k^4 - 4*k^2*(-2 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^2 - 8*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^4))/(Sqrt[1 + k^2/(c - I*k0)^2]*(c - I*k0)) + (10*(k^4 - 4*k^2*(-2 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^2 - 8*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^4))/(Sqrt[1 + k^2/(2*c - I*k0)^2]*(2*c - I*k0)) - (10*(k^4 - 4*k^2*(-2 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^2 - 8*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^4))/(Sqrt[1 + k^2/(3*c - I*k0)^2]*(3*c - I*k0)) + (5*(k^4 - 4*k^2*(-2 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^2 - 8*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^4))/(Sqrt[1 + k^2/(4*c - I*k0)^2]*(4*c - I*k0)) - (k^4 - 4*k^2*(-2 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^2 - 8*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^4)/(Sqrt[1 + k^2/(5*c - I*k0)^2]*(5*c - I*k0)) + (I*(k^4 + 8*k0^3*(k0 - Sqrt[-k^2 + k0^2]) + 4*k^2*k0*(-2*k0 + Sqrt[-k^2 + k0^2])))/Sqrt[-k^2 + k0^2])/(k^4*k0) diff --git a/besseltransforms/ksmall/5-1-5 b/besseltransforms/ksmall/5-1-5 deleted file mode 100644 index 870caff..0000000 --- a/besseltransforms/ksmall/5-1-5 +++ /dev/null @@ -1,4 +0,0 @@ -((-5*(k^4*(-5 + Sqrt[1 + k^2/(c - I*k0)^2]) + 4*k^2*(-5 + 3*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^2 + 16*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^4))/(k^5*Sqrt[1 + k^2/(c - I*k0)^2]) + (10*(k^4*(-5 + Sqrt[1 + k^2/(2*c - I*k0)^2]) + 4*k^2*(-5 + 3*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^2 + 16*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^4))/(k^5*Sqrt[1 + k^2/(2*c - I*k0)^2]) - (10*(k^4*(-5 + Sqrt[1 + k^2/(3*c - I*k0)^2]) + 4*k^2*(-5 + 3*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^2 + 16*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^4))/(k^5*Sqrt[1 + k^2/(3*c - I*k0)^2]) + (5*(k^4*(-5 + Sqrt[1 + k^2/(4*c - I*k0)^2]) + 4*k^2*(-5 + 3*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^2 + 16*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^4))/(k^5*Sqrt[1 + k^2/(4*c - I*k0)^2]) - (k^4*(-5 + Sqrt[1 + k^2/(5*c - I*k0)^2]) + 4*k^2*(-5 + 3*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^2 + 16*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^4)/(k^5*Sqrt[1 + k^2/(5*c - I*k0)^2]) + (k^4*(1 - (5*k0)/Sqrt[-k^2 + k0^2]) + 16*k0^4*(1 - k0/Sqrt[-k^2 + k0^2]) + 4*k^2*k0^2*(-3 + (5*k0)/Sqrt[-k^2 + k0^2]))/k^5)/k0 -((-5*(Power(k,4)*(-5 + Sqrt(1 + Power(k,2)/Power(c - Complex(0,1)*k0,2))) + 4*Power(k,2)*(-5 + 3*Sqrt(1 + Power(k,2)/Power(c - Complex(0,1)*k0,2)))*Power(c - Complex(0,1)*k0,2) + 16*(-1 + Sqrt(1 + Power(k,2)/Power(c - Complex(0,1)*k0,2)))*Power(c - Complex(0,1)*k0,4)))/(Power(k,5)*Sqrt(1 + Power(k,2)/Power(c - Complex(0,1)*k0,2))) + (10*(Power(k,4)*(-5 + Sqrt(1 + Power(k,2)/Power(2*c - Complex(0,1)*k0,2))) + 4*Power(k,2)*(-5 + 3*Sqrt(1 + Power(k,2)/Power(2*c - Complex(0,1)*k0,2)))*Power(2*c - Complex(0,1)*k0,2) + 16*(-1 + Sqrt(1 + Power(k,2)/Power(2*c - Complex(0,1)*k0,2)))*Power(2*c - Complex(0,1)*k0,4)))/(Power(k,5)*Sqrt(1 + Power(k,2)/Power(2*c - Complex(0,1)*k0,2))) - (10*(Power(k,4)*(-5 + Sqrt(1 + Power(k,2)/Power(3*c - Complex(0,1)*k0,2))) + 4*Power(k,2)*(-5 + 3*Sqrt(1 + Power(k,2)/Power(3*c - Complex(0,1)*k0,2)))*Power(3*c - Complex(0,1)*k0,2) + 16*(-1 + Sqrt(1 + Power(k,2)/Power(3*c - Complex(0,1)*k0,2)))*Power(3*c - Complex(0,1)*k0,4)))/(Power(k,5)*Sqrt(1 + Power(k,2)/Power(3*c - Complex(0,1)*k0,2))) + (5*(Power(k,4)*(-5 + Sqrt(1 + Power(k,2)/Power(4*c - Complex(0,1)*k0,2))) + 4*Power(k,2)*(-5 + 3*Sqrt(1 + Power(k,2)/Power(4*c - Complex(0,1)*k0,2)))*Power(4*c - Complex(0,1)*k0,2) + 16*(-1 + Sqrt(1 + Power(k,2)/Power(4*c - Complex(0,1)*k0,2)))*Power(4*c - Complex(0,1)*k0,4)))/(Power(k,5)*Sqrt(1 + Power(k,2)/Power(4*c - Complex(0,1)*k0,2))) - (Power(k,4)*(-5 + Sqrt(1 + Power(k,2)/Power(5*c - Complex(0,1)*k0,2))) + 4*Power(k,2)*(-5 + 3*Sqrt(1 + Power(k,2)/Power(5*c - Complex(0,1)*k0,2)))*Power(5*c - Complex(0,1)*k0,2) + 16*(-1 + Sqrt(1 + Power(k,2)/Power(5*c - Complex(0,1)*k0,2)))*Power(5*c - Complex(0,1)*k0,4))/(Power(k,5)*Sqrt(1 + Power(k,2)/Power(5*c - Complex(0,1)*k0,2))) + (Power(k,4)*(1 - (5*k0)/Sqrt(-Power(k,2) + Power(k0,2))) + 16*Power(k0,4)*(1 - k0/Sqrt(-Power(k,2) + Power(k0,2))) + 4*Power(k,2)*Power(k0,2)*(-3 + (5*k0)/Sqrt(-Power(k,2) + Power(k0,2))))/Power(k,5))/k0 -SeriesData[k, Infinity, {-(1/(k*k0)), (k - (5*I)*k0)/(k*k0), (I*(5*k - (12*I)*k0))/k, (-24*k*k0 + (35*I)*k0^2)/(2*k), ((-125*(5*c - I*k0)^4)/(8*k) - (35*I)/2*k0^3 - (3*(5*c - I*k0)^3*((5*c)/k - (I*k0)/k))/8 - 5*((125*(c - I*k0)^4)/(8*k) + (3*(c - I*k0)^3*(c/k - (I*k0)/k))/8) + 10*((125*(2*c - I*k0)^4)/(8*k) + (3*(2*c - I*k0)^3*((2*c)/k - (I*k0)/k))/8) - 10*((125*(3*c - I*k0)^4)/(8*k) + (3*(3*c - I*k0)^3*((3*c)/k - (I*k0)/k))/8) + 5*((125*(4*c - I*k0)^4)/(8*k) + (3*(4*c - I*k0)^3*((4*c)/k - (I*k0)/k))/8))/k0, ((6*(5*c - I*k0)^5)/k + 16*k0^4 + (15*(5*c - I*k0)^4*((5*c)/k - (I*k0)/k))/8 - 5*((-6*(c - I*k0)^5)/k - (15*(c - I*k0)^4*(c/k - (I*k0)/k))/8) + 10*((-6*(2*c - I*k0)^5)/k - (15*(2*c - I*k0)^4*((2*c)/k - (I*k0)/k))/8) - 10*((-6*(3*c - I*k0)^5)/k - (15*(3*c - I*k0)^4*((3*c)/k - (I*k0)/k))/8) + 5*((-6*(4*c - I*k0)^5)/k - (15*(4*c - I*k0)^4*((4*c)/k - (I*k0)/k))/8))/k0, ((35*(5*c - I*k0)^6)/(8*k) + (63*I)/8*k0^5 - (35*(5*c - I*k0)^5*((5*c)/k - (I*k0)/k))/8 - 5*((-35*(c - I*k0)^6)/(8*k) + (35*(c - I*k0)^5*(c/k - (I*k0)/k))/8) + 10*((-35*(2*c - I*k0)^6)/(8*k) + (35*(2*c - I*k0)^5*((2*c)/k - (I*k0)/k))/8) - 10*((-35*(3*c - I*k0)^6)/(8*k) + (35*(3*c - I*k0)^5*((3*c)/k - (I*k0)/k))/8) + 5*((-35*(4*c - I*k0)^6)/(8*k) + (35*(4*c - I*k0)^5*((4*c)/k - (I*k0)/k))/8))/k0, ((-8*(5*c - I*k0)^7)/k + (95*(5*c - I*k0)^6*((5*c)/k - (I*k0)/k))/16 - 5*((8*(c - I*k0)^7)/k - (95*(c - I*k0)^6*(c/k - (I*k0)/k))/16) + 10*((8*(2*c - I*k0)^7)/k - (95*(2*c - I*k0)^6*((2*c)/k - (I*k0)/k))/16) - 10*((8*(3*c - I*k0)^7)/k - (95*(3*c - I*k0)^6*((3*c)/k - (I*k0)/k))/16) + 5*((8*(4*c - I*k0)^7)/k - (95*(4*c - I*k0)^6*((4*c)/k - (I*k0)/k))/16))/k0, ((585*(5*c - I*k0)^8)/(128*k) + (33*I)/16*k0^7 - (585*(5*c - I*k0)^7*((5*c)/k - (I*k0)/k))/128 - 5*((-585*(c - I*k0)^8)/(128*k) + (585*(c - I*k0)^7*(c/k - (I*k0)/k))/128) + 10*((-585*(2*c - I*k0)^8)/(128*k) + (585*(2*c - I*k0)^7*((2*c)/k - (I*k0)/k))/128) - 10*((-585*(3*c - I*k0)^8)/(128*k) + (585*(3*c - I*k0)^7*((3*c)/k - (I*k0)/k))/128) + 5*((-585*(4*c - I*k0)^8)/(128*k) + (585*(4*c - I*k0)^7*((4*c)/k - (I*k0)/k))/128))/k0, ((715*(c - I*k0)^8*(c/k - (I*k0)/k))/128 - (715*(2*c - I*k0)^8*((2*c)/k - (I*k0)/k))/64 + (715*(3*c - I*k0)^8*((3*c)/k - (I*k0)/k))/64 - (715*(4*c - I*k0)^8*((4*c)/k - (I*k0)/k))/128 + (143*(5*c - I*k0)^8*((5*c)/k - (I*k0)/k))/128)/k0, ((-77*(5*c - I*k0)^10)/(64*k) + (143*I)/128*k0^9 + (77*(5*c - I*k0)^9*((5*c)/k - (I*k0)/k))/64 - 5*((77*(c - I*k0)^10)/(64*k) - (77*(c - I*k0)^9*(c/k - (I*k0)/k))/64) + 10*((77*(2*c - I*k0)^10)/(64*k) - (77*(2*c - I*k0)^9*((2*c)/k - (I*k0)/k))/64) - 10*((77*(3*c - I*k0)^10)/(64*k) - (77*(3*c - I*k0)^9*((3*c)/k - (I*k0)/k))/64) + 5*((77*(4*c - I*k0)^10)/(64*k) - (77*(4*c - I*k0)^9*((4*c)/k - (I*k0)/k))/64))/k0}, 0, 11, 1] -((-5*(k^4*(-5 + Sqrt[1 + k^2/(c - I*k0)^2]) + 4*k^2*(-5 + 3*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^2 + 16*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^4))/Sqrt[1 + k^2/(c - I*k0)^2] + (10*(k^4*(-5 + Sqrt[1 + k^2/(2*c - I*k0)^2]) + 4*k^2*(-5 + 3*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^2 + 16*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^4))/Sqrt[1 + k^2/(2*c - I*k0)^2] - (10*(k^4*(-5 + Sqrt[1 + k^2/(3*c - I*k0)^2]) + 4*k^2*(-5 + 3*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^2 + 16*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^4))/Sqrt[1 + k^2/(3*c - I*k0)^2] + (5*(k^4*(-5 + Sqrt[1 + k^2/(4*c - I*k0)^2]) + 4*k^2*(-5 + 3*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^2 + 16*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^4))/Sqrt[1 + k^2/(4*c - I*k0)^2] - (k^4*(-5 + Sqrt[1 + k^2/(5*c - I*k0)^2]) + 4*k^2*(-5 + 3*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^2 + 16*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^4)/Sqrt[1 + k^2/(5*c - I*k0)^2] + k^4*(1 - (5*k0)/Sqrt[-k^2 + k0^2]) + 16*k0^4*(1 - k0/Sqrt[-k^2 + k0^2]) + 4*k^2*k0^2*(-3 + (5*k0)/Sqrt[-k^2 + k0^2]))/(k^5*k0) diff --git a/besseltransforms/ksmall/5-2-0 b/besseltransforms/ksmall/5-2-0 deleted file mode 100644 index 6ec1a7f..0000000 --- a/besseltransforms/ksmall/5-2-0 +++ /dev/null @@ -1,11 +0,0 @@ -Integrate[(E^(I*k0*x)*(1 - E^(-(c*x)))^5*BesselJ[0, k*x])/(k0^2*x), {x, 0, Infinity}, Assumptions -> n == 0 && q == 2 && κ == 5 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0 && k < k0] -Integrate((Power(E,I*k0*x)*Power(1 - Power(E,-(c*x)),5)*BesselJ(0,k*x))/(Power(k0,2)*x),List(x,0,DirectedInfinity(1)),Rule(Assumptions,n == 0 && q == 2 && κ == 5 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0 && k < k0)) - - -5 c x + I k0 x c x 5 2 2 4 4 6 6 8 8 Pi 2 2 4 4 6 6 8 8 - E (-1 + E ) ((-418854310875 + 29682132480 k x - 3901685760 k x + 1258291200 k x - 2147483648 k x ) Cos[-- + k x] + 4 Sqrt[2] k x (13043905875 - 1229437440 k x + 240844800 k x - 150994944 k x + 2147483648 k x ) (Cos[k x] + Sin[k x])) - 4 -Integrate::idiv: Integral of ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ does not converge on {0, Infinity}. - 19/2 2 21/2 - 8589934592 k k0 Sqrt[2 Pi] x -Series[Integrate[(E^(I*k0*x)*(1 - E^(-(c*x)))^5*BesselJ[0, k*x])/(k0^2*x), {x, 0, Infinity}, Assumptions -> n == 0 && q == 2 && κ == 5 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0 && k < k0], {k, Infinity, 10}] -Integrate[(E^(I*k0*x)*(1 - E^(-(c*x)))^5*BesselJ[0, k*x])/(k0^2*x), {x, 0, Infinity}, Assumptions -> n == 0 && q == 2 && κ == 5] diff --git a/besseltransforms/ksmall/5-2-1 b/besseltransforms/ksmall/5-2-1 deleted file mode 100644 index a248614..0000000 --- a/besseltransforms/ksmall/5-2-1 +++ /dev/null @@ -1,4 +0,0 @@ -(-5*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0) + 10*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0) - 10*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0) + 5*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0) - (-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0) + I*(k0 - Sqrt[-k^2 + k0^2]))/(k*k0^2) -(-5*(-1 + Sqrt(1 + Power(k,2)/Power(c - Complex(0,1)*k0,2)))*(c - Complex(0,1)*k0) + 10*(-1 + Sqrt(1 + Power(k,2)/Power(2*c - Complex(0,1)*k0,2)))*(2*c - Complex(0,1)*k0) - 10*(-1 + Sqrt(1 + Power(k,2)/Power(3*c - Complex(0,1)*k0,2)))*(3*c - Complex(0,1)*k0) + 5*(-1 + Sqrt(1 + Power(k,2)/Power(4*c - Complex(0,1)*k0,2)))*(4*c - Complex(0,1)*k0) - (-1 + Sqrt(1 + Power(k,2)/Power(5*c - Complex(0,1)*k0,2)))*(5*c - Complex(0,1)*k0) + Complex(0,1)*(k0 - Sqrt(-Power(k,2) + Power(k0,2))))/(k*Power(k0,2)) -SeriesData[k, Infinity, {(-225*c^6)/(2*k0^2) + ((45*I)*c^5)/k0, 0, (-7875*c^6)/4 + (39375*c^8)/(8*k0^2) - ((5250*I)*c^7)/k0 + (525*I)/2*c^5*k0, 0, (-2205*(2025*c^10 - (3310*I)*c^9*k0 - 2250*c^8*k0^2 + (800*I)*c^7*k0^3 + 150*c^6*k0^4 - (12*I)*c^5*k0^5))/(32*k0^2)}, 6, 11, 1] -(-5*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0) + 10*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0) - 10*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0) + 5*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0) - (-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0) + I*(k0 - Sqrt[-k^2 + k0^2]))/(k*k0^2) diff --git a/besseltransforms/ksmall/5-2-2 b/besseltransforms/ksmall/5-2-2 deleted file mode 100644 index a9a4158..0000000 --- a/besseltransforms/ksmall/5-2-2 +++ /dev/null @@ -1,4 +0,0 @@ -(5*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^2 - 10*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^2 + 10*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^2 - 5*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^2 + (-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^2 - k0*(k0 - Sqrt[-k^2 + k0^2]))/(k^2*k0^2) -(5*(-1 + Sqrt(1 + Power(k,2)/Power(c - Complex(0,1)*k0,2)))*Power(c - Complex(0,1)*k0,2) - 10*(-1 + Sqrt(1 + Power(k,2)/Power(2*c - Complex(0,1)*k0,2)))*Power(2*c - Complex(0,1)*k0,2) + 10*(-1 + Sqrt(1 + Power(k,2)/Power(3*c - Complex(0,1)*k0,2)))*Power(3*c - Complex(0,1)*k0,2) - 5*(-1 + Sqrt(1 + Power(k,2)/Power(4*c - Complex(0,1)*k0,2)))*Power(4*c - Complex(0,1)*k0,2) + (-1 + Sqrt(1 + Power(k,2)/Power(5*c - Complex(0,1)*k0,2)))*Power(5*c - Complex(0,1)*k0,2) - k0*(k0 - Sqrt(-Power(k,2) + Power(k0,2))))/(Power(k,2)*Power(k0,2)) -SeriesData[k, Infinity, {(-15*c^5)/k0^2, 0, (-315*c^5)/2 + (1050*c^7)/k0^2 - ((1575*I)/2*c^6)/k0, 0, (-1575*(331*c^9 - (450*I)*c^8*k0 - 240*c^7*k0^2 + (60*I)*c^6*k0^3 + 6*c^5*k0^4))/(16*k0^2)}, 5, 11, 1] -(5*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^2 - 10*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^2 + 10*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^2 - 5*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^2 + (-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^2 - k0*(k0 - Sqrt[-k^2 + k0^2]))/(k^2*k0^2) diff --git a/besseltransforms/ksmall/5-2-3 b/besseltransforms/ksmall/5-2-3 deleted file mode 100644 index 01380aa..0000000 --- a/besseltransforms/ksmall/5-2-3 +++ /dev/null @@ -1,4 +0,0 @@ -((-5*(k^2*(-3 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0) + 4*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^3))/(3*k^3) + (10*(k^2*(-3 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0) + 4*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^3))/(3*k^3) - (10*(k^2*(-3 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0) + 4*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^3))/(3*k^3) + (5*(k^2*(-3 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0) + 4*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^3))/(3*k^3) - (k^2*(-3 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0) + 4*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^3)/(3*k^3) - (I/3*(4*k0^2*(k0 - Sqrt[-k^2 + k0^2]) + k^2*(-3*k0 + Sqrt[-k^2 + k0^2])))/k^3)/k0^2 -((-5*(Power(k,2)*(-3 + Sqrt(1 + Power(k,2)/Power(c - Complex(0,1)*k0,2)))*(c - Complex(0,1)*k0) + 4*(-1 + Sqrt(1 + Power(k,2)/Power(c - Complex(0,1)*k0,2)))*Power(c - Complex(0,1)*k0,3)))/(3.*Power(k,3)) + (10*(Power(k,2)*(-3 + Sqrt(1 + Power(k,2)/Power(2*c - Complex(0,1)*k0,2)))*(2*c - Complex(0,1)*k0) + 4*(-1 + Sqrt(1 + Power(k,2)/Power(2*c - Complex(0,1)*k0,2)))*Power(2*c - Complex(0,1)*k0,3)))/(3.*Power(k,3)) - (10*(Power(k,2)*(-3 + Sqrt(1 + Power(k,2)/Power(3*c - Complex(0,1)*k0,2)))*(3*c - Complex(0,1)*k0) + 4*(-1 + Sqrt(1 + Power(k,2)/Power(3*c - Complex(0,1)*k0,2)))*Power(3*c - Complex(0,1)*k0,3)))/(3.*Power(k,3)) + (5*(Power(k,2)*(-3 + Sqrt(1 + Power(k,2)/Power(4*c - Complex(0,1)*k0,2)))*(4*c - Complex(0,1)*k0) + 4*(-1 + Sqrt(1 + Power(k,2)/Power(4*c - Complex(0,1)*k0,2)))*Power(4*c - Complex(0,1)*k0,3)))/(3.*Power(k,3)) - (Power(k,2)*(-3 + Sqrt(1 + Power(k,2)/Power(5*c - Complex(0,1)*k0,2)))*(5*c - Complex(0,1)*k0) + 4*(-1 + Sqrt(1 + Power(k,2)/Power(5*c - Complex(0,1)*k0,2)))*Power(5*c - Complex(0,1)*k0,3))/(3.*Power(k,3)) - (Complex(0,0.3333333333333333)*(4*Power(k0,2)*(k0 - Sqrt(-Power(k,2) + Power(k0,2))) + Power(k,2)*(-3*k0 + Sqrt(-Power(k,2) + Power(k0,2)))))/Power(k,3))/Power(k0,2) -SeriesData[k, Infinity, {(525*c^6)/(2*k0^2) - ((105*I)*c^5)/k0, 0, (14175*c^6)/4 - (70875*c^8)/(8*k0^2) + ((9450*I)*c^7)/k0 - (945*I)/2*c^5*k0, 0, (3465*(2025*c^10 - (3310*I)*c^9*k0 - 2250*c^8*k0^2 + (800*I)*c^7*k0^3 + 150*c^6*k0^4 - (12*I)*c^5*k0^5))/(32*k0^2)}, 6, 11, 1] --(5*k^2*(-3 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0) + 20*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^3 - 10*k^2*(-3 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0) - 40*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^3 + 10*k^2*(-3 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0) + 40*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^3 - 5*k^2*(-3 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0) - 20*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^3 + k^2*(-3 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0) + 4*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^3 + (4*I)*k0^2*(k0 - Sqrt[-k^2 + k0^2]) + I*k^2*(-3*k0 + Sqrt[-k^2 + k0^2]))/(3*k^3*k0^2) diff --git a/besseltransforms/ksmall/5-2-4 b/besseltransforms/ksmall/5-2-4 deleted file mode 100644 index 953be74..0000000 --- a/besseltransforms/ksmall/5-2-4 +++ /dev/null @@ -1,4 +0,0 @@ -(-5*(1/4 - ((-2 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^2)/k^2 - (2*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^4)/k^4) + 10*(1/4 - ((-2 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^2)/k^2 - (2*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^4)/k^4) - 10*(1/4 - ((-2 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^2)/k^2 - (2*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^4)/k^4) + 5*(1/4 - ((-2 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^2)/k^2 - (2*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^4)/k^4) + ((-2 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^2)/k^2 + (2*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^4)/k^4 + (2*k0^3*(k0 - Sqrt[-k^2 + k0^2]))/k^4 + (k0*(-2*k0 + Sqrt[-k^2 + k0^2]))/k^2)/k0^2 -(-5*(0.25 - ((-2 + Sqrt(1 + Power(k,2)/Power(c - Complex(0,1)*k0,2)))*Power(c - Complex(0,1)*k0,2))/Power(k,2) - (2*(-1 + Sqrt(1 + Power(k,2)/Power(c - Complex(0,1)*k0,2)))*Power(c - Complex(0,1)*k0,4))/Power(k,4)) + 10*(0.25 - ((-2 + Sqrt(1 + Power(k,2)/Power(2*c - Complex(0,1)*k0,2)))*Power(2*c - Complex(0,1)*k0,2))/Power(k,2) - (2*(-1 + Sqrt(1 + Power(k,2)/Power(2*c - Complex(0,1)*k0,2)))*Power(2*c - Complex(0,1)*k0,4))/Power(k,4)) - 10*(0.25 - ((-2 + Sqrt(1 + Power(k,2)/Power(3*c - Complex(0,1)*k0,2)))*Power(3*c - Complex(0,1)*k0,2))/Power(k,2) - (2*(-1 + Sqrt(1 + Power(k,2)/Power(3*c - Complex(0,1)*k0,2)))*Power(3*c - Complex(0,1)*k0,4))/Power(k,4)) + 5*(0.25 - ((-2 + Sqrt(1 + Power(k,2)/Power(4*c - Complex(0,1)*k0,2)))*Power(4*c - Complex(0,1)*k0,2))/Power(k,2) - (2*(-1 + Sqrt(1 + Power(k,2)/Power(4*c - Complex(0,1)*k0,2)))*Power(4*c - Complex(0,1)*k0,4))/Power(k,4)) + ((-2 + Sqrt(1 + Power(k,2)/Power(5*c - Complex(0,1)*k0,2)))*Power(5*c - Complex(0,1)*k0,2))/Power(k,2) + (2*(-1 + Sqrt(1 + Power(k,2)/Power(5*c - Complex(0,1)*k0,2)))*Power(5*c - Complex(0,1)*k0,4))/Power(k,4) + (2*Power(k0,3)*(k0 - Sqrt(-Power(k,2) + Power(k0,2))))/Power(k,4) + (k0*(-2*k0 + Sqrt(-Power(k,2) + Power(k0,2))))/Power(k,2))/Power(k0,2) -SeriesData[k, Infinity, {(105*c^5)/k0^2, 0, (945*c^5)/2 - (3150*c^7)/k0^2 + ((4725*I)/2*c^6)/k0, 0, (3465*(331*c^9 - (450*I)*c^8*k0 - 240*c^7*k0^2 + (60*I)*c^6*k0^3 + 6*c^5*k0^4))/(16*k0^2)}, 5, 11, 1] -(5*k^2*(-2 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^2 + 10*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^4 - 10*k^2*(-2 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^2 - 20*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^4 + 10*k^2*(-2 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^2 + 20*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^4 - 5*k^2*(-2 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^2 - 10*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^4 + k^2*(-2 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^2 + 2*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^4 + 2*k0^3*(k0 - Sqrt[-k^2 + k0^2]) - k^2*k0*(2*k0 - Sqrt[-k^2 + k0^2]))/(k^4*k0^2) diff --git a/besseltransforms/ksmall/5-2-5 b/besseltransforms/ksmall/5-2-5 deleted file mode 100644 index 50ad5ce..0000000 --- a/besseltransforms/ksmall/5-2-5 +++ /dev/null @@ -1,4 +0,0 @@ -(-((k^4*(-5 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0) + 4*k^2*(-5 + 3*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^3 + 16*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^5)/k^5) + (2*(k^4*(-5 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0) + 4*k^2*(-5 + 3*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^3 + 16*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^5))/k^5 - (2*(k^4*(-5 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0) + 4*k^2*(-5 + 3*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^3 + 16*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^5))/k^5 + (k^4*(-5 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0) + 4*k^2*(-5 + 3*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^3 + 16*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^5)/k^5 - (k^4*(-5 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0) + 4*k^2*(-5 + 3*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^3 + 16*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^5)/(5*k^5) + (I/5*(16*k0^4*(k0 - Sqrt[-k^2 + k0^2]) - k^4*(-5*k0 + Sqrt[-k^2 + k0^2]) + 4*k^2*k0^2*(-5*k0 + 3*Sqrt[-k^2 + k0^2])))/k^5)/k0^2 -(-((Power(k,4)*(-5 + Sqrt(1 + Power(k,2)/Power(c - Complex(0,1)*k0,2)))*(c - Complex(0,1)*k0) + 4*Power(k,2)*(-5 + 3*Sqrt(1 + Power(k,2)/Power(c - Complex(0,1)*k0,2)))*Power(c - Complex(0,1)*k0,3) + 16*(-1 + Sqrt(1 + Power(k,2)/Power(c - Complex(0,1)*k0,2)))*Power(c - Complex(0,1)*k0,5))/Power(k,5)) + (2*(Power(k,4)*(-5 + Sqrt(1 + Power(k,2)/Power(2*c - Complex(0,1)*k0,2)))*(2*c - Complex(0,1)*k0) + 4*Power(k,2)*(-5 + 3*Sqrt(1 + Power(k,2)/Power(2*c - Complex(0,1)*k0,2)))*Power(2*c - Complex(0,1)*k0,3) + 16*(-1 + Sqrt(1 + Power(k,2)/Power(2*c - Complex(0,1)*k0,2)))*Power(2*c - Complex(0,1)*k0,5)))/Power(k,5) - (2*(Power(k,4)*(-5 + Sqrt(1 + Power(k,2)/Power(3*c - Complex(0,1)*k0,2)))*(3*c - Complex(0,1)*k0) + 4*Power(k,2)*(-5 + 3*Sqrt(1 + Power(k,2)/Power(3*c - Complex(0,1)*k0,2)))*Power(3*c - Complex(0,1)*k0,3) + 16*(-1 + Sqrt(1 + Power(k,2)/Power(3*c - Complex(0,1)*k0,2)))*Power(3*c - Complex(0,1)*k0,5)))/Power(k,5) + (Power(k,4)*(-5 + Sqrt(1 + Power(k,2)/Power(4*c - Complex(0,1)*k0,2)))*(4*c - Complex(0,1)*k0) + 4*Power(k,2)*(-5 + 3*Sqrt(1 + Power(k,2)/Power(4*c - Complex(0,1)*k0,2)))*Power(4*c - Complex(0,1)*k0,3) + 16*(-1 + Sqrt(1 + Power(k,2)/Power(4*c - Complex(0,1)*k0,2)))*Power(4*c - Complex(0,1)*k0,5))/Power(k,5) - (Power(k,4)*(-5 + Sqrt(1 + Power(k,2)/Power(5*c - Complex(0,1)*k0,2)))*(5*c - Complex(0,1)*k0) + 4*Power(k,2)*(-5 + 3*Sqrt(1 + Power(k,2)/Power(5*c - Complex(0,1)*k0,2)))*Power(5*c - Complex(0,1)*k0,3) + 16*(-1 + Sqrt(1 + Power(k,2)/Power(5*c - Complex(0,1)*k0,2)))*Power(5*c - Complex(0,1)*k0,5))/(5.*Power(k,5)) + (Complex(0,0.2)*(16*Power(k0,4)*(k0 - Sqrt(-Power(k,2) + Power(k0,2))) - Power(k,4)*(-5*k0 + Sqrt(-Power(k,2) + Power(k0,2))) + 4*Power(k,2)*Power(k0,2)*(-5*k0 + 3*Sqrt(-Power(k,2) + Power(k0,2)))))/Power(k,5))/Power(k0,2) -SeriesData[k, Infinity, {(384*c^5)/k0^2, (-4725*c^6)/(2*k0^2) + ((945*I)*c^5)/k0, 0, (-51975*c^6)/4 + (259875*c^8)/(8*k0^2) - ((34650*I)*c^7)/k0 + (3465*I)/2*c^5*k0, 0, (-9009*(2025*c^10 - (3310*I)*c^9*k0 - 2250*c^8*k0^2 + (800*I)*c^7*k0^3 + 150*c^6*k0^4 - (12*I)*c^5*k0^5))/(32*k0^2)}, 5, 11, 1] --(5*(k^4*(-5 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0) + 4*k^2*(-5 + 3*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^3 + 16*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^5) - 10*(k^4*(-5 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0) + 4*k^2*(-5 + 3*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^3 + 16*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^5) + 10*(k^4*(-5 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0) + 4*k^2*(-5 + 3*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^3 + 16*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^5) - 5*(k^4*(-5 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0) + 4*k^2*(-5 + 3*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^3 + 16*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^5) + k^4*(-5 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0) + 4*k^2*(-5 + 3*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^3 + 16*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^5 - I*(16*k0^4*(k0 - Sqrt[-k^2 + k0^2]) - k^4*(-5*k0 + Sqrt[-k^2 + k0^2]) + 4*k^2*k0^2*(-5*k0 + 3*Sqrt[-k^2 + k0^2])))/(5*k^5*k0^2) diff --git a/besseltransforms/ksmall/5-3-0 b/besseltransforms/ksmall/5-3-0 deleted file mode 100644 index 6915a00..0000000 --- a/besseltransforms/ksmall/5-3-0 +++ /dev/null @@ -1,11 +0,0 @@ -Integrate[(E^(I*k0*x)*(1 - E^(-(c*x)))^5*BesselJ[0, k*x])/(k0^3*x^2), {x, 0, Infinity}, Assumptions -> n == 0 && q == 3 && κ == 5 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0 && k < k0] -Integrate((Power(E,I*k0*x)*Power(1 - Power(E,-(c*x)),5)*BesselJ(0,k*x))/(Power(k0,3)*Power(x,2)),List(x,0,DirectedInfinity(1)),Rule(Assumptions,n == 0 && q == 3 && κ == 5 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0 && k < k0)) - - I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi I k0 x 2 Pi -5 c x + I k0 x 2 Pi -4 c x + I k0 x 2 Pi -3 c x + I k0 x 2 Pi -2 c x + I k0 x 2 Pi -(c x) + I k0 x 2 Pi I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi - 13043905875 E Cos[-- - k x] 13043905875 E Cos[-- - k x] 65219529375 E Cos[-- - k x] 65219529375 E Cos[-- - k x] 65219529375 E Cos[-- - k x] 65219529375 E Cos[-- - k x] 2401245 E Cos[-- - k x] 2401245 E Cos[-- - k x] 12006225 E Cos[-- - k x] 12006225 E Cos[-- - k x] 12006225 E Cos[-- - k x] 12006225 E Cos[-- - k x] 3675 E Cos[-- - k x] 3675 E Cos[-- - k x] 18375 E Cos[-- - k x] 18375 E Cos[-- - k x] 18375 E Cos[-- - k x] 18375 E Cos[-- - k x] 9 E Cos[-- - k x] 9 E Cos[-- - k x] 45 E Cos[-- - k x] 45 E Cos[-- - k x] 45 E Cos[-- - k x] 45 E Cos[-- - k x] E Sqrt[--] Cos[-- - k x] E Sqrt[--] Cos[-- - k x] 5 E Sqrt[--] Cos[-- - k x] 10 E Sqrt[--] Cos[-- - k x] 10 E Sqrt[--] Cos[-- - k x] 5 E Sqrt[--] Cos[-- - k x] 418854310875 E Sin[-- - k x] 418854310875 E Sin[-- - k x] 2094271554375 E Sin[-- - k x] 2094271554375 E Sin[-- - k x] 2094271554375 E Sin[-- - k x] 2094271554375 E Sin[-- - k x] 57972915 E Sin[-- - k x] 57972915 E Sin[-- - k x] 289864575 E Sin[-- - k x] 289864575 E Sin[-- - k x] 289864575 E Sin[-- - k x] 289864575 E Sin[-- - k x] 59535 E Sin[-- - k x] 59535 E Sin[-- - k x] 297675 E Sin[-- - k x] 297675 E Sin[-- - k x] 297675 E Sin[-- - k x] 297675 E Sin[-- - k x] 75 E Sin[-- - k x] 75 E Sin[-- - k x] 375 E Sin[-- - k x] 375 E Sin[-- - k x] 375 E Sin[-- - k x] 375 E Sin[-- - k x] E Sin[-- - k x] E Sin[-- - k x] 5 E Sin[-- - k x] 5 E Sin[-- - k x] 5 E Sin[-- - k x] 5 E Sin[-- - k x] - 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 Pi 4 Pi 4 Pi 4 Pi 4 Pi 4 Pi 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 -Integrate::idiv: Integral of ------------------------------------- - ------------------------------------------ + ------------------------------------------ - ------------------------------------------ + ------------------------------------------ - ------------------------------------------ - ---------------------------------- + -------------------------------------- - --------------------------------------- + --------------------------------------- - --------------------------------------- + --------------------------------------- + ------------------------------- - ----------------------------------- + ------------------------------------ - ------------------------------------ + ------------------------------------ - ------------------------------------ - --------------------------- + -------------------------------- - --------------------------------- + --------------------------------- - --------------------------------- + --------------------------------- + ------------------------------ - --------------------------------------- + ----------------------------------------- - ------------------------------------------ + ------------------------------------------ - ----------------------------------------- - ------------------------------------- + ------------------------------------------- - -------------------------------------------- + -------------------------------------------- - -------------------------------------------- + -------------------------------------------- + ----------------------------------- - --------------------------------------- + ---------------------------------------- - ---------------------------------------- + ---------------------------------------- - ---------------------------------------- - --------------------------------- + ------------------------------------ - ------------------------------------- + ------------------------------------- - ------------------------------------- + ------------------------------------- + ----------------------------- - --------------------------------- + ---------------------------------- - ---------------------------------- + ---------------------------------- - ---------------------------------- - -------------------------- + ------------------------------ - -------------------------------- + -------------------------------- - -------------------------------- + -------------------------------- does not converge on {0, Infinity}. - 17/2 3 21/2 17/2 3 21/2 17/2 3 21/2 17/2 3 21/2 17/2 3 21/2 17/2 3 21/2 13/2 3 17/2 13/2 3 17/2 13/2 3 17/2 13/2 3 17/2 13/2 3 17/2 13/2 3 17/2 9/2 3 13/2 9/2 3 13/2 9/2 3 13/2 9/2 3 13/2 9/2 3 13/2 9/2 3 13/2 5/2 3 9/2 5/2 3 9/2 5/2 3 9/2 5/2 3 9/2 5/2 3 9/2 5/2 3 9/2 3 5/2 3 5/2 3 5/2 3 5/2 3 5/2 3 5/2 19/2 3 23/2 19/2 3 23/2 19/2 3 23/2 19/2 3 23/2 19/2 3 23/2 19/2 3 23/2 15/2 3 19/2 15/2 3 19/2 15/2 3 19/2 15/2 3 19/2 15/2 3 19/2 15/2 3 19/2 11/2 3 15/2 11/2 3 15/2 11/2 3 15/2 11/2 3 15/2 11/2 3 15/2 11/2 3 15/2 7/2 3 11/2 7/2 3 11/2 7/2 3 11/2 7/2 3 11/2 7/2 3 11/2 7/2 3 11/2 3/2 3 7/2 3/2 3 7/2 3/2 3 7/2 3/2 3 7/2 3/2 3 7/2 3/2 3 7/2 - 1073741824 k k0 Sqrt[2 Pi] x 1073741824 k k0 Sqrt[2 Pi] x 1073741824 k k0 Sqrt[2 Pi] x 536870912 k k0 Sqrt[2 Pi] x 536870912 k k0 Sqrt[2 Pi] x 1073741824 k k0 Sqrt[2 Pi] x 2097152 k k0 Sqrt[2 Pi] x 2097152 k k0 Sqrt[2 Pi] x 2097152 k k0 Sqrt[2 Pi] x 1048576 k k0 Sqrt[2 Pi] x 1048576 k k0 Sqrt[2 Pi] x 2097152 k k0 Sqrt[2 Pi] x 16384 k k0 Sqrt[2 Pi] x 16384 k k0 Sqrt[2 Pi] x 16384 k k0 Sqrt[2 Pi] x 8192 k k0 Sqrt[2 Pi] x 8192 k k0 Sqrt[2 Pi] x 16384 k k0 Sqrt[2 Pi] x 64 k k0 Sqrt[2 Pi] x 64 k k0 Sqrt[2 Pi] x 64 k k0 Sqrt[2 Pi] x 32 k k0 Sqrt[2 Pi] x 32 k k0 Sqrt[2 Pi] x 64 k k0 Sqrt[2 Pi] x Sqrt[k] k0 x Sqrt[k] k0 x Sqrt[k] k0 x Sqrt[k] k0 x Sqrt[k] k0 x Sqrt[k] k0 x 8589934592 k k0 Sqrt[2 Pi] x 8589934592 k k0 Sqrt[2 Pi] x 8589934592 k k0 Sqrt[2 Pi] x 4294967296 k k0 Sqrt[2 Pi] x 4294967296 k k0 Sqrt[2 Pi] x 8589934592 k k0 Sqrt[2 Pi] x 16777216 k k0 Sqrt[2 Pi] x 16777216 k k0 Sqrt[2 Pi] x 16777216 k k0 Sqrt[2 Pi] x 8388608 k k0 Sqrt[2 Pi] x 8388608 k k0 Sqrt[2 Pi] x 16777216 k k0 Sqrt[2 Pi] x 131072 k k0 Sqrt[2 Pi] x 131072 k k0 Sqrt[2 Pi] x 131072 k k0 Sqrt[2 Pi] x 65536 k k0 Sqrt[2 Pi] x 65536 k k0 Sqrt[2 Pi] x 131072 k k0 Sqrt[2 Pi] x 512 k k0 Sqrt[2 Pi] x 512 k k0 Sqrt[2 Pi] x 512 k k0 Sqrt[2 Pi] x 256 k k0 Sqrt[2 Pi] x 256 k k0 Sqrt[2 Pi] x 512 k k0 Sqrt[2 Pi] x 4 k k0 Sqrt[2 Pi] x 4 k k0 Sqrt[2 Pi] x 4 k k0 Sqrt[2 Pi] x 2 k k0 Sqrt[2 Pi] x 2 k k0 Sqrt[2 Pi] x 4 k k0 Sqrt[2 Pi] x -Series[Integrate[(E^(I*k0*x)*(1 - E^(-(c*x)))^5*BesselJ[0, k*x])/(k0^3*x^2), {x, 0, Infinity}, Assumptions -> n == 0 && q == 3 && κ == 5 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0 && k < k0], {k, Infinity, 10}] -Integrate[(E^(I*k0*x)*(1 - E^(-(c*x)))^5*BesselJ[0, k*x])/(k0^3*x^2), {x, 0, Infinity}, Assumptions -> n == 0 && q == 3 && κ == 5] diff --git a/besseltransforms/ksmall/5-3-1 b/besseltransforms/ksmall/5-3-1 deleted file mode 100644 index 9b83b0e..0000000 --- a/besseltransforms/ksmall/5-3-1 +++ /dev/null @@ -1,11 +0,0 @@ -Integrate[(E^(I*k0*x)*(1 - E^(-(c*x)))^5*BesselJ[1, k*x])/(k0^3*x^2), {x, 0, Infinity}, Assumptions -> n == 1 && q == 3 && κ == 5 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0 && k < k0] -Integrate((Power(E,I*k0*x)*Power(1 - Power(E,-(c*x)),5)*BesselJ(1,k*x))/(Power(k0,3)*Power(x,2)),List(x,0,DirectedInfinity(1)),Rule(Assumptions,n == 1 && q == 3 && κ == 5 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0 && k < k0)) - - I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi I k0 x 2 Pi -5 c x + I k0 x 2 Pi -4 c x + I k0 x 2 Pi -3 c x + I k0 x 2 Pi -2 c x + I k0 x 2 Pi -(c x) + I k0 x 2 Pi I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi - 14783093325 E Cos[-- + k x] 14783093325 E Cos[-- + k x] 73915466625 E Cos[-- + k x] 73915466625 E Cos[-- + k x] 73915466625 E Cos[-- + k x] 73915466625 E Cos[-- + k x] 2837835 E Cos[-- + k x] 2837835 E Cos[-- + k x] 14189175 E Cos[-- + k x] 14189175 E Cos[-- + k x] 14189175 E Cos[-- + k x] 14189175 E Cos[-- + k x] 4725 E Cos[-- + k x] 4725 E Cos[-- + k x] 23625 E Cos[-- + k x] 23625 E Cos[-- + k x] 23625 E Cos[-- + k x] 23625 E Cos[-- + k x] 15 E Cos[-- + k x] 15 E Cos[-- + k x] 75 E Cos[-- + k x] 75 E Cos[-- + k x] 75 E Cos[-- + k x] 75 E Cos[-- + k x] E Sqrt[--] Cos[-- + k x] E Sqrt[--] Cos[-- + k x] 5 E Sqrt[--] Cos[-- + k x] 10 E Sqrt[--] Cos[-- + k x] 10 E Sqrt[--] Cos[-- + k x] 5 E Sqrt[--] Cos[-- + k x] 468131288625 E Sin[-- + k x] 468131288625 E Sin[-- + k x] 2340656443125 E Sin[-- + k x] 2340656443125 E Sin[-- + k x] 2340656443125 E Sin[-- + k x] 2340656443125 E Sin[-- + k x] 66891825 E Sin[-- + k x] 66891825 E Sin[-- + k x] 334459125 E Sin[-- + k x] 334459125 E Sin[-- + k x] 334459125 E Sin[-- + k x] 334459125 E Sin[-- + k x] 72765 E Sin[-- + k x] 72765 E Sin[-- + k x] 363825 E Sin[-- + k x] 363825 E Sin[-- + k x] 363825 E Sin[-- + k x] 363825 E Sin[-- + k x] 105 E Sin[-- + k x] 105 E Sin[-- + k x] 525 E Sin[-- + k x] 525 E Sin[-- + k x] 525 E Sin[-- + k x] 525 E Sin[-- + k x] 3 E Sin[-- + k x] 3 E Sin[-- + k x] 15 E Sin[-- + k x] 15 E Sin[-- + k x] 15 E Sin[-- + k x] 15 E Sin[-- + k x] - 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 Pi 4 Pi 4 Pi 4 Pi 4 Pi 4 Pi 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 -Integrate::idiv: Integral of ------------------------------------- - ------------------------------------------ + ------------------------------------------ - ------------------------------------------ + ------------------------------------------ - ------------------------------------------ - ---------------------------------- + -------------------------------------- - --------------------------------------- + --------------------------------------- - --------------------------------------- + --------------------------------------- + ------------------------------- - ----------------------------------- + ------------------------------------ - ------------------------------------ + ------------------------------------ - ------------------------------------ - --------------------------- + --------------------------------- - --------------------------------- + --------------------------------- - --------------------------------- + --------------------------------- - ------------------------------ + --------------------------------------- - ----------------------------------------- + ------------------------------------------ - ------------------------------------------ + ----------------------------------------- + ------------------------------------- - ------------------------------------------- + -------------------------------------------- - -------------------------------------------- + -------------------------------------------- - -------------------------------------------- - ----------------------------------- + --------------------------------------- - ---------------------------------------- + ---------------------------------------- - ---------------------------------------- + ---------------------------------------- + --------------------------------- - ------------------------------------ + ------------------------------------- - ------------------------------------- + ------------------------------------- - ------------------------------------- - ----------------------------- + ---------------------------------- - ---------------------------------- + ---------------------------------- - ---------------------------------- + ---------------------------------- + -------------------------- - -------------------------------- + --------------------------------- - --------------------------------- + --------------------------------- - --------------------------------- does not converge on {0, Infinity}. - 17/2 3 21/2 17/2 3 21/2 17/2 3 21/2 17/2 3 21/2 17/2 3 21/2 17/2 3 21/2 13/2 3 17/2 13/2 3 17/2 13/2 3 17/2 13/2 3 17/2 13/2 3 17/2 13/2 3 17/2 9/2 3 13/2 9/2 3 13/2 9/2 3 13/2 9/2 3 13/2 9/2 3 13/2 9/2 3 13/2 5/2 3 9/2 5/2 3 9/2 5/2 3 9/2 5/2 3 9/2 5/2 3 9/2 5/2 3 9/2 3 5/2 3 5/2 3 5/2 3 5/2 3 5/2 3 5/2 19/2 3 23/2 19/2 3 23/2 19/2 3 23/2 19/2 3 23/2 19/2 3 23/2 19/2 3 23/2 15/2 3 19/2 15/2 3 19/2 15/2 3 19/2 15/2 3 19/2 15/2 3 19/2 15/2 3 19/2 11/2 3 15/2 11/2 3 15/2 11/2 3 15/2 11/2 3 15/2 11/2 3 15/2 11/2 3 15/2 7/2 3 11/2 7/2 3 11/2 7/2 3 11/2 7/2 3 11/2 7/2 3 11/2 7/2 3 11/2 3/2 3 7/2 3/2 3 7/2 3/2 3 7/2 3/2 3 7/2 3/2 3 7/2 3/2 3 7/2 - 1073741824 k k0 Sqrt[2 Pi] x 1073741824 k k0 Sqrt[2 Pi] x 1073741824 k k0 Sqrt[2 Pi] x 536870912 k k0 Sqrt[2 Pi] x 536870912 k k0 Sqrt[2 Pi] x 1073741824 k k0 Sqrt[2 Pi] x 2097152 k k0 Sqrt[2 Pi] x 2097152 k k0 Sqrt[2 Pi] x 2097152 k k0 Sqrt[2 Pi] x 1048576 k k0 Sqrt[2 Pi] x 1048576 k k0 Sqrt[2 Pi] x 2097152 k k0 Sqrt[2 Pi] x 16384 k k0 Sqrt[2 Pi] x 16384 k k0 Sqrt[2 Pi] x 16384 k k0 Sqrt[2 Pi] x 8192 k k0 Sqrt[2 Pi] x 8192 k k0 Sqrt[2 Pi] x 16384 k k0 Sqrt[2 Pi] x 64 k k0 Sqrt[2 Pi] x 64 k k0 Sqrt[2 Pi] x 64 k k0 Sqrt[2 Pi] x 32 k k0 Sqrt[2 Pi] x 32 k k0 Sqrt[2 Pi] x 64 k k0 Sqrt[2 Pi] x Sqrt[k] k0 x Sqrt[k] k0 x Sqrt[k] k0 x Sqrt[k] k0 x Sqrt[k] k0 x Sqrt[k] k0 x 8589934592 k k0 Sqrt[2 Pi] x 8589934592 k k0 Sqrt[2 Pi] x 8589934592 k k0 Sqrt[2 Pi] x 4294967296 k k0 Sqrt[2 Pi] x 4294967296 k k0 Sqrt[2 Pi] x 8589934592 k k0 Sqrt[2 Pi] x 16777216 k k0 Sqrt[2 Pi] x 16777216 k k0 Sqrt[2 Pi] x 16777216 k k0 Sqrt[2 Pi] x 8388608 k k0 Sqrt[2 Pi] x 8388608 k k0 Sqrt[2 Pi] x 16777216 k k0 Sqrt[2 Pi] x 131072 k k0 Sqrt[2 Pi] x 131072 k k0 Sqrt[2 Pi] x 131072 k k0 Sqrt[2 Pi] x 65536 k k0 Sqrt[2 Pi] x 65536 k k0 Sqrt[2 Pi] x 131072 k k0 Sqrt[2 Pi] x 512 k k0 Sqrt[2 Pi] x 512 k k0 Sqrt[2 Pi] x 512 k k0 Sqrt[2 Pi] x 256 k k0 Sqrt[2 Pi] x 256 k k0 Sqrt[2 Pi] x 512 k k0 Sqrt[2 Pi] x 4 k k0 Sqrt[2 Pi] x 4 k k0 Sqrt[2 Pi] x 4 k k0 Sqrt[2 Pi] x 2 k k0 Sqrt[2 Pi] x 2 k k0 Sqrt[2 Pi] x 4 k k0 Sqrt[2 Pi] x -Series[Integrate[(E^(I*k0*x)*(1 - E^(-(c*x)))^5*BesselJ[1, k*x])/(k0^3*x^2), {x, 0, Infinity}, Assumptions -> n == 1 && q == 3 && κ == 5 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0 && k < k0], {k, Infinity, 10}] -Integrate[(E^(I*k0*x)*(1 - E^(-(c*x)))^5*BesselJ[1, k*x])/(k0^3*x^2), {x, 0, Infinity}, Assumptions -> n == 1 && q == 3 && κ == 5] diff --git a/besseltransforms/ksmall/5-3-2 b/besseltransforms/ksmall/5-3-2 deleted file mode 100644 index 443b081..0000000 --- a/besseltransforms/ksmall/5-3-2 +++ /dev/null @@ -1,4 +0,0 @@ -(-5*(((-3 + 2*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0))/6 + ((-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^3)/(3*k^2)) + 10*(((-3 + 2*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0))/6 + ((-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^3)/(3*k^2)) - 10*(((-3 + 2*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0))/6 + ((-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^3)/(3*k^2)) + 5*(((-3 + 2*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0))/6 + ((-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^3)/(3*k^2)) - ((-3 + 2*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0))/6 - ((-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^3)/(3*k^2) + I/6*(3*k0 - (2*k0^3)/k^2 - 2*Sqrt[-k^2 + k0^2] + (2*k0^2*Sqrt[-k^2 + k0^2])/k^2))/k0^3 -(-5*(((-3 + 2*Sqrt(1 + Power(k,2)/Power(c - Complex(0,1)*k0,2)))*(c - Complex(0,1)*k0))/6. + ((-1 + Sqrt(1 + Power(k,2)/Power(c - Complex(0,1)*k0,2)))*Power(c - Complex(0,1)*k0,3))/(3.*Power(k,2))) + 10*(((-3 + 2*Sqrt(1 + Power(k,2)/Power(2*c - Complex(0,1)*k0,2)))*(2*c - Complex(0,1)*k0))/6. + ((-1 + Sqrt(1 + Power(k,2)/Power(2*c - Complex(0,1)*k0,2)))*Power(2*c - Complex(0,1)*k0,3))/(3.*Power(k,2))) - 10*(((-3 + 2*Sqrt(1 + Power(k,2)/Power(3*c - Complex(0,1)*k0,2)))*(3*c - Complex(0,1)*k0))/6. + ((-1 + Sqrt(1 + Power(k,2)/Power(3*c - Complex(0,1)*k0,2)))*Power(3*c - Complex(0,1)*k0,3))/(3.*Power(k,2))) + 5*(((-3 + 2*Sqrt(1 + Power(k,2)/Power(4*c - Complex(0,1)*k0,2)))*(4*c - Complex(0,1)*k0))/6. + ((-1 + Sqrt(1 + Power(k,2)/Power(4*c - Complex(0,1)*k0,2)))*Power(4*c - Complex(0,1)*k0,3))/(3.*Power(k,2))) - ((-3 + 2*Sqrt(1 + Power(k,2)/Power(5*c - Complex(0,1)*k0,2)))*(5*c - Complex(0,1)*k0))/6. - ((-1 + Sqrt(1 + Power(k,2)/Power(5*c - Complex(0,1)*k0,2)))*Power(5*c - Complex(0,1)*k0,3))/(3.*Power(k,2)) + Complex(0,0.16666666666666666)*(3*k0 - (2*Power(k0,3))/Power(k,2) - 2*Sqrt(-Power(k,2) + Power(k0,2)) + (2*Power(k0,2)*Sqrt(-Power(k,2) + Power(k0,2)))/Power(k,2)))/Power(k0,3) -SeriesData[k, Infinity, {(75*c^6)/(2*k0^3) - ((15*I)*c^5)/k0^2, 0, (-105*(75*c^8 - (80*I)*c^7*k0 - 30*c^6*k0^2 + (4*I)*c^5*k0^3))/(8*k0^3), 0, (315*(2025*c^10 - (3310*I)*c^9*k0 - 2250*c^8*k0^2 + (800*I)*c^7*k0^3 + 150*c^6*k0^4 - (12*I)*c^5*k0^5))/(32*k0^3)}, 5, 11, 1] -(5*k^2*(3 - 2*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0) - 10*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^3 + 10*k^2*(-3 + 2*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0) + 20*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^3 + 10*k^2*(3 - 2*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0) - 20*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^3 + 5*k^2*(-3 + 2*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0) + 10*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^3 + k^2*(3 - 2*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0) - 2*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^3 + I*(k^2*(3*k0 - 2*Sqrt[-k^2 + k0^2]) + 2*k0^2*(-k0 + Sqrt[-k^2 + k0^2])))/(6*k^2*k0^3) diff --git a/besseltransforms/ksmall/5-3-3 b/besseltransforms/ksmall/5-3-3 deleted file mode 100644 index f2c32f7..0000000 --- a/besseltransforms/ksmall/5-3-3 +++ /dev/null @@ -1,4 +0,0 @@ -((-5*(3*k^4 + 4*k^2*(3 - 2*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^2 - 8*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^4))/(24*k^3) + (5*(3*k^4 + 4*k^2*(3 - 2*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^2 - 8*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^4))/(12*k^3) - (5*(3*k^4 + 4*k^2*(3 - 2*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^2 - 8*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^4))/(12*k^3) + (5*(3*k^4 + 4*k^2*(3 - 2*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^2 - 8*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^4))/(24*k^3) - (3*k^4 + 4*k^2*(3 - 2*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^2 - 8*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^4)/(24*k^3) + (3*k^4 + 8*k0^3*(k0 - Sqrt[-k^2 + k0^2]) + 4*k^2*k0*(-3*k0 + 2*Sqrt[-k^2 + k0^2]))/(24*k^3))/k0^3 -((-5*(3*Power(k,4) + 4*Power(k,2)*(3 - 2*Sqrt(1 + Power(k,2)/Power(c - Complex(0,1)*k0,2)))*Power(c - Complex(0,1)*k0,2) - 8*(-1 + Sqrt(1 + Power(k,2)/Power(c - Complex(0,1)*k0,2)))*Power(c - Complex(0,1)*k0,4)))/(24.*Power(k,3)) + (5*(3*Power(k,4) + 4*Power(k,2)*(3 - 2*Sqrt(1 + Power(k,2)/Power(2*c - Complex(0,1)*k0,2)))*Power(2*c - Complex(0,1)*k0,2) - 8*(-1 + Sqrt(1 + Power(k,2)/Power(2*c - Complex(0,1)*k0,2)))*Power(2*c - Complex(0,1)*k0,4)))/(12.*Power(k,3)) - (5*(3*Power(k,4) + 4*Power(k,2)*(3 - 2*Sqrt(1 + Power(k,2)/Power(3*c - Complex(0,1)*k0,2)))*Power(3*c - Complex(0,1)*k0,2) - 8*(-1 + Sqrt(1 + Power(k,2)/Power(3*c - Complex(0,1)*k0,2)))*Power(3*c - Complex(0,1)*k0,4)))/(12.*Power(k,3)) + (5*(3*Power(k,4) + 4*Power(k,2)*(3 - 2*Sqrt(1 + Power(k,2)/Power(4*c - Complex(0,1)*k0,2)))*Power(4*c - Complex(0,1)*k0,2) - 8*(-1 + Sqrt(1 + Power(k,2)/Power(4*c - Complex(0,1)*k0,2)))*Power(4*c - Complex(0,1)*k0,4)))/(24.*Power(k,3)) - (3*Power(k,4) + 4*Power(k,2)*(3 - 2*Sqrt(1 + Power(k,2)/Power(5*c - Complex(0,1)*k0,2)))*Power(5*c - Complex(0,1)*k0,2) - 8*(-1 + Sqrt(1 + Power(k,2)/Power(5*c - Complex(0,1)*k0,2)))*Power(5*c - Complex(0,1)*k0,4))/(24.*Power(k,3)) + (3*Power(k,4) + 8*Power(k0,3)*(k0 - Sqrt(-Power(k,2) + Power(k0,2))) + 4*Power(k,2)*k0*(-3*k0 + 2*Sqrt(-Power(k,2) + Power(k0,2))))/(24.*Power(k,3)))/Power(k0,3) -SeriesData[k, Infinity, {(15*c^5)/k0^3, 0, (-35*(20*c^7 - (15*I)*c^6*k0 - 3*c^5*k0^2))/(2*k0^3), 0, (315*(331*c^9 - (450*I)*c^8*k0 - 240*c^7*k0^2 + (60*I)*c^6*k0^3 + 6*c^5*k0^4))/(16*k0^3), 0, (-165*(22430*c^11 - (42525*I)*c^10*k0 - 34755*c^9*k0^2 + (15750*I)*c^8*k0^3 + 4200*c^7*k0^4 - (630*I)*c^6*k0^5 - 42*c^5*k0^6))/(32*k0^3)}, 4, 11, 1] -(5*k^2*(-3 + 2*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^2 + 10*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^4 + 10*k^2*(3 - 2*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^2 - 20*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^4 + 10*k^2*(-3 + 2*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^2 + 20*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^4 + 5*k^2*(3 - 2*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^2 - 10*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^4 + k^2*(-3 + 2*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^2 + 2*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^4 + 2*k0^3*(k0 - Sqrt[-k^2 + k0^2]) + k^2*k0*(-3*k0 + 2*Sqrt[-k^2 + k0^2]))/(6*k^3*k0^3) diff --git a/besseltransforms/ksmall/5-3-4 b/besseltransforms/ksmall/5-3-4 deleted file mode 100644 index 8b02869..0000000 --- a/besseltransforms/ksmall/5-3-4 +++ /dev/null @@ -1,4 +0,0 @@ -(-(k^4*(-15 + 4*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0) + 4*k^2*(-10 + 7*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^3 + 24*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^5)/(12*k^4) + (k^4*(-15 + 4*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0) + 4*k^2*(-10 + 7*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^3 + 24*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^5)/(6*k^4) - (k^4*(-15 + 4*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0) + 4*k^2*(-10 + 7*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^3 + 24*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^5)/(6*k^4) + (k^4*(-15 + 4*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0) + 4*k^2*(-10 + 7*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^3 + 24*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^5)/(12*k^4) - (k^4*(-15 + 4*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0) + 4*k^2*(-10 + 7*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^3 + 24*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^5)/(60*k^4) + (I/60*(k^4*(15*k0 - 4*Sqrt[-k^2 + k0^2]) + 24*k0^4*(k0 - Sqrt[-k^2 + k0^2]) + 4*k^2*k0^2*(-10*k0 + 7*Sqrt[-k^2 + k0^2])))/k^4)/k0^3 -(-(Power(k,4)*(-15 + 4*Sqrt(1 + Power(k,2)/Power(c - Complex(0,1)*k0,2)))*(c - Complex(0,1)*k0) + 4*Power(k,2)*(-10 + 7*Sqrt(1 + Power(k,2)/Power(c - Complex(0,1)*k0,2)))*Power(c - Complex(0,1)*k0,3) + 24*(-1 + Sqrt(1 + Power(k,2)/Power(c - Complex(0,1)*k0,2)))*Power(c - Complex(0,1)*k0,5))/(12.*Power(k,4)) + (Power(k,4)*(-15 + 4*Sqrt(1 + Power(k,2)/Power(2*c - Complex(0,1)*k0,2)))*(2*c - Complex(0,1)*k0) + 4*Power(k,2)*(-10 + 7*Sqrt(1 + Power(k,2)/Power(2*c - Complex(0,1)*k0,2)))*Power(2*c - Complex(0,1)*k0,3) + 24*(-1 + Sqrt(1 + Power(k,2)/Power(2*c - Complex(0,1)*k0,2)))*Power(2*c - Complex(0,1)*k0,5))/(6.*Power(k,4)) - (Power(k,4)*(-15 + 4*Sqrt(1 + Power(k,2)/Power(3*c - Complex(0,1)*k0,2)))*(3*c - Complex(0,1)*k0) + 4*Power(k,2)*(-10 + 7*Sqrt(1 + Power(k,2)/Power(3*c - Complex(0,1)*k0,2)))*Power(3*c - Complex(0,1)*k0,3) + 24*(-1 + Sqrt(1 + Power(k,2)/Power(3*c - Complex(0,1)*k0,2)))*Power(3*c - Complex(0,1)*k0,5))/(6.*Power(k,4)) + (Power(k,4)*(-15 + 4*Sqrt(1 + Power(k,2)/Power(4*c - Complex(0,1)*k0,2)))*(4*c - Complex(0,1)*k0) + 4*Power(k,2)*(-10 + 7*Sqrt(1 + Power(k,2)/Power(4*c - Complex(0,1)*k0,2)))*Power(4*c - Complex(0,1)*k0,3) + 24*(-1 + Sqrt(1 + Power(k,2)/Power(4*c - Complex(0,1)*k0,2)))*Power(4*c - Complex(0,1)*k0,5))/(12.*Power(k,4)) - (Power(k,4)*(-15 + 4*Sqrt(1 + Power(k,2)/Power(5*c - Complex(0,1)*k0,2)))*(5*c - Complex(0,1)*k0) + 4*Power(k,2)*(-10 + 7*Sqrt(1 + Power(k,2)/Power(5*c - Complex(0,1)*k0,2)))*Power(5*c - Complex(0,1)*k0,3) + 24*(-1 + Sqrt(1 + Power(k,2)/Power(5*c - Complex(0,1)*k0,2)))*Power(5*c - Complex(0,1)*k0,5))/(60.*Power(k,4)) + (Complex(0,0.016666666666666666)*(Power(k,4)*(15*k0 - 4*Sqrt(-Power(k,2) + Power(k0,2))) + 24*Power(k0,4)*(k0 - Sqrt(-Power(k,2) + Power(k0,2))) + 4*Power(k,2)*Power(k0,2)*(-10*k0 + 7*Sqrt(-Power(k,2) + Power(k0,2)))))/Power(k,4))/Power(k0,3) -SeriesData[k, Infinity, {(48*c^5)/k0^3, (-525*c^6)/(2*k0^3) + ((105*I)*c^5)/k0^2, 0, (315*(75*c^8 - (80*I)*c^7*k0 - 30*c^6*k0^2 + (4*I)*c^5*k0^3))/(8*k0^3), 0, (-693*(2025*c^10 - (3310*I)*c^9*k0 - 2250*c^8*k0^2 + (800*I)*c^7*k0^3 + 150*c^6*k0^4 - (12*I)*c^5*k0^5))/(32*k0^3)}, 4, 11, 1] --(5*(k^4*(-15 + 4*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0) + 4*k^2*(-10 + 7*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^3 + 24*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^5) - 10*(k^4*(-15 + 4*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0) + 4*k^2*(-10 + 7*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^3 + 24*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^5) + 10*(k^4*(-15 + 4*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0) + 4*k^2*(-10 + 7*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^3 + 24*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^5) - 5*(k^4*(-15 + 4*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0) + 4*k^2*(-10 + 7*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^3 + 24*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^5) + k^4*(-15 + 4*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0) + 4*k^2*(-10 + 7*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^3 + 24*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^5 - I*(k^4*(15*k0 - 4*Sqrt[-k^2 + k0^2]) + 24*k0^4*(k0 - Sqrt[-k^2 + k0^2]) + 4*k^2*k0^2*(-10*k0 + 7*Sqrt[-k^2 + k0^2])))/(60*k^4*k0^3) diff --git a/besseltransforms/ksmall/5-3-5 b/besseltransforms/ksmall/5-3-5 deleted file mode 100644 index f388a57..0000000 --- a/besseltransforms/ksmall/5-3-5 +++ /dev/null @@ -1,4 +0,0 @@ -(-(5*k^6 + 12*k^4*(5 - 2*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^2 + 8*k^2*(15 - 11*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^4 - 64*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^6)/(24*k^5) + (5*k^6 + 12*k^4*(5 - 2*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^2 + 8*k^2*(15 - 11*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^4 - 64*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^6)/(12*k^5) - (5*k^6 + 12*k^4*(5 - 2*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^2 + 8*k^2*(15 - 11*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^4 - 64*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^6)/(12*k^5) + (5*k^6 + 12*k^4*(5 - 2*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^2 + 8*k^2*(15 - 11*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^4 - 64*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^6)/(24*k^5) - (5*k^6 + 12*k^4*(5 - 2*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^2 + 8*k^2*(15 - 11*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^4 - 64*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^6)/(120*k^5) + (5*k^6 + 8*k^2*k0^3*(15*k0 - 11*Sqrt[-k^2 + k0^2]) + 64*k0^5*(-k0 + Sqrt[-k^2 + k0^2]) + 12*k^4*k0*(-5*k0 + 2*Sqrt[-k^2 + k0^2]))/(120*k^5))/k0^3 -(-(5*Power(k,6) + 12*Power(k,4)*(5 - 2*Sqrt(1 + Power(k,2)/Power(c - Complex(0,1)*k0,2)))*Power(c - Complex(0,1)*k0,2) + 8*Power(k,2)*(15 - 11*Sqrt(1 + Power(k,2)/Power(c - Complex(0,1)*k0,2)))*Power(c - Complex(0,1)*k0,4) - 64*(-1 + Sqrt(1 + Power(k,2)/Power(c - Complex(0,1)*k0,2)))*Power(c - Complex(0,1)*k0,6))/(24.*Power(k,5)) + (5*Power(k,6) + 12*Power(k,4)*(5 - 2*Sqrt(1 + Power(k,2)/Power(2*c - Complex(0,1)*k0,2)))*Power(2*c - Complex(0,1)*k0,2) + 8*Power(k,2)*(15 - 11*Sqrt(1 + Power(k,2)/Power(2*c - Complex(0,1)*k0,2)))*Power(2*c - Complex(0,1)*k0,4) - 64*(-1 + Sqrt(1 + Power(k,2)/Power(2*c - Complex(0,1)*k0,2)))*Power(2*c - Complex(0,1)*k0,6))/(12.*Power(k,5)) - (5*Power(k,6) + 12*Power(k,4)*(5 - 2*Sqrt(1 + Power(k,2)/Power(3*c - Complex(0,1)*k0,2)))*Power(3*c - Complex(0,1)*k0,2) + 8*Power(k,2)*(15 - 11*Sqrt(1 + Power(k,2)/Power(3*c - Complex(0,1)*k0,2)))*Power(3*c - Complex(0,1)*k0,4) - 64*(-1 + Sqrt(1 + Power(k,2)/Power(3*c - Complex(0,1)*k0,2)))*Power(3*c - Complex(0,1)*k0,6))/(12.*Power(k,5)) + (5*Power(k,6) + 12*Power(k,4)*(5 - 2*Sqrt(1 + Power(k,2)/Power(4*c - Complex(0,1)*k0,2)))*Power(4*c - Complex(0,1)*k0,2) + 8*Power(k,2)*(15 - 11*Sqrt(1 + Power(k,2)/Power(4*c - Complex(0,1)*k0,2)))*Power(4*c - Complex(0,1)*k0,4) - 64*(-1 + Sqrt(1 + Power(k,2)/Power(4*c - Complex(0,1)*k0,2)))*Power(4*c - Complex(0,1)*k0,6))/(24.*Power(k,5)) - (5*Power(k,6) + 12*Power(k,4)*(5 - 2*Sqrt(1 + Power(k,2)/Power(5*c - Complex(0,1)*k0,2)))*Power(5*c - Complex(0,1)*k0,2) + 8*Power(k,2)*(15 - 11*Sqrt(1 + Power(k,2)/Power(5*c - Complex(0,1)*k0,2)))*Power(5*c - Complex(0,1)*k0,4) - 64*(-1 + Sqrt(1 + Power(k,2)/Power(5*c - Complex(0,1)*k0,2)))*Power(5*c - Complex(0,1)*k0,6))/(120.*Power(k,5)) + (5*Power(k,6) + 8*Power(k,2)*Power(k0,3)*(15*k0 - 11*Sqrt(-Power(k,2) + Power(k0,2))) + 64*Power(k0,5)*(-k0 + Sqrt(-Power(k,2) + Power(k0,2))) + 12*Power(k,4)*k0*(-5*k0 + 2*Sqrt(-Power(k,2) + Power(k0,2))))/(120.*Power(k,5)))/Power(k0,3) -SeriesData[k, Infinity, {(105*c^5)/k0^3, (-960*c^6)/k0^3 + ((384*I)*c^5)/k0^2, (315*(20*c^7 - (15*I)*c^6*k0 - 3*c^5*k0^2))/(2*k0^3), 0, (-1155*(331*c^9 - (450*I)*c^8*k0 - 240*c^7*k0^2 + (60*I)*c^6*k0^3 + 6*c^5*k0^4))/(16*k0^3), 0, (429*(22430*c^11 - (42525*I)*c^10*k0 - 34755*c^9*k0^2 + (15750*I)*c^8*k0^3 + 4200*c^7*k0^4 - (630*I)*c^6*k0^5 - 42*c^5*k0^6))/(32*k0^3)}, 4, 11, 1] -(15*k^4*(-5 + 2*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^2 + 10*k^2*(-15 + 11*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^4 + 80*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^6 + 30*k^4*(5 - 2*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^2 + 20*k^2*(15 - 11*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^4 - 160*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^6 + 30*k^4*(-5 + 2*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^2 + 20*k^2*(-15 + 11*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^4 + 160*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^6 + 15*k^4*(5 - 2*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^2 + 10*k^2*(15 - 11*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^4 - 80*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^6 + 3*k^4*(-5 + 2*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^2 + 2*k^2*(-15 + 11*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^4 + 16*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^6 + 2*k^2*k0^3*(15*k0 - 11*Sqrt[-k^2 + k0^2]) + 16*k0^5*(-k0 + Sqrt[-k^2 + k0^2]) + 3*k^4*k0*(-5*k0 + 2*Sqrt[-k^2 + k0^2]))/(30*k^5*k0^3) diff --git a/besseltransforms/ksmall/5-4-0 b/besseltransforms/ksmall/5-4-0 deleted file mode 100644 index d9ebba2..0000000 --- a/besseltransforms/ksmall/5-4-0 +++ /dev/null @@ -1,13 +0,0 @@ -Integrate[(E^(I*k0*x)*(1 - E^(-(c*x)))^5*BesselJ[0, k*x])/(k0^4*x^3), {x, 0, Infinity}, Assumptions -> n == 0 && q == 4 && κ == 5 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0 && k < k0] -Integrate((Power(E,I*k0*x)*Power(1 - Power(E,-(c*x)),5)*BesselJ(0,k*x))/(Power(k0,4)*Power(x,3)),List(x,0,DirectedInfinity(1)),Rule(Assumptions,n == 0 && q == 4 && κ == 5 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0 && k < k0)) - - I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi I k0 x 2 Pi -5 c x + I k0 x 2 Pi -4 c x + I k0 x 2 Pi -3 c x + I k0 x 2 Pi -2 c x + I k0 x 2 Pi -(c x) + I k0 x 2 Pi I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi - 13043905875 E Cos[-- - k x] 13043905875 E Cos[-- - k x] 65219529375 E Cos[-- - k x] 65219529375 E Cos[-- - k x] 65219529375 E Cos[-- - k x] 65219529375 E Cos[-- - k x] 2401245 E Cos[-- - k x] 2401245 E Cos[-- - k x] 12006225 E Cos[-- - k x] 12006225 E Cos[-- - k x] 12006225 E Cos[-- - k x] 12006225 E Cos[-- - k x] 3675 E Cos[-- - k x] 3675 E Cos[-- - k x] 18375 E Cos[-- - k x] 18375 E Cos[-- - k x] 18375 E Cos[-- - k x] 18375 E Cos[-- - k x] 9 E Cos[-- - k x] 9 E Cos[-- - k x] 45 E Cos[-- - k x] 45 E Cos[-- - k x] 45 E Cos[-- - k x] 45 E Cos[-- - k x] E Sqrt[--] Cos[-- - k x] E Sqrt[--] Cos[-- - k x] 5 E Sqrt[--] Cos[-- - k x] 10 E Sqrt[--] Cos[-- - k x] 10 E Sqrt[--] Cos[-- - k x] 5 E Sqrt[--] Cos[-- - k x] 418854310875 E Sin[-- - k x] 418854310875 E Sin[-- - k x] 2094271554375 E Sin[-- - k x] 2094271554375 E Sin[-- - k x] 2094271554375 E Sin[-- - k x] 2094271554375 E Sin[-- - k x] 57972915 E Sin[-- - k x] 57972915 E Sin[-- - k x] 289864575 E Sin[-- - k x] 289864575 E Sin[-- - k x] 289864575 E Sin[-- - k x] 289864575 E Sin[-- - k x] 59535 E Sin[-- - k x] 59535 E Sin[-- - k x] 297675 E Sin[-- - k x] 297675 E Sin[-- - k x] 297675 E Sin[-- - k x] 297675 E Sin[-- - k x] 75 E Sin[-- - k x] 75 E Sin[-- - k x] 375 E Sin[-- - k x] 375 E Sin[-- - k x] 375 E Sin[-- - k x] 375 E Sin[-- - k x] E Sin[-- - k x] E Sin[-- - k x] 5 E Sin[-- - k x] 5 E Sin[-- - k x] 5 E Sin[-- - k x] 5 E Sin[-- - k x] - 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 Pi 4 Pi 4 Pi 4 Pi 4 Pi 4 Pi 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 -Integrate::idiv: Integral of ------------------------------------- - ------------------------------------------ + ------------------------------------------ - ------------------------------------------ + ------------------------------------------ - ------------------------------------------ - ---------------------------------- + -------------------------------------- - --------------------------------------- + --------------------------------------- - --------------------------------------- + --------------------------------------- + ------------------------------- - ----------------------------------- + ------------------------------------ - ------------------------------------ + ------------------------------------ - ------------------------------------ - ---------------------------- + -------------------------------- - --------------------------------- + --------------------------------- - --------------------------------- + --------------------------------- + ------------------------------ - --------------------------------------- + ----------------------------------------- - ------------------------------------------ + ------------------------------------------ - ----------------------------------------- - ------------------------------------- + ------------------------------------------- - -------------------------------------------- + -------------------------------------------- - -------------------------------------------- + -------------------------------------------- + ----------------------------------- - --------------------------------------- + ---------------------------------------- - ---------------------------------------- + ---------------------------------------- - ---------------------------------------- - --------------------------------- + ------------------------------------ - ------------------------------------- + ------------------------------------- - ------------------------------------- + ------------------------------------- + ----------------------------- - --------------------------------- + ---------------------------------- - ---------------------------------- + ---------------------------------- - ---------------------------------- - -------------------------- + ------------------------------ - -------------------------------- + -------------------------------- - -------------------------------- + -------------------------------- does not converge on {0, Infinity}. - 17/2 4 23/2 17/2 4 23/2 17/2 4 23/2 17/2 4 23/2 17/2 4 23/2 17/2 4 23/2 13/2 4 19/2 13/2 4 19/2 13/2 4 19/2 13/2 4 19/2 13/2 4 19/2 13/2 4 19/2 9/2 4 15/2 9/2 4 15/2 9/2 4 15/2 9/2 4 15/2 9/2 4 15/2 9/2 4 15/2 5/2 4 11/2 5/2 4 11/2 5/2 4 11/2 5/2 4 11/2 5/2 4 11/2 5/2 4 11/2 4 7/2 4 7/2 4 7/2 4 7/2 4 7/2 4 7/2 19/2 4 25/2 19/2 4 25/2 19/2 4 25/2 19/2 4 25/2 19/2 4 25/2 19/2 4 25/2 15/2 4 21/2 15/2 4 21/2 15/2 4 21/2 15/2 4 21/2 15/2 4 21/2 15/2 4 21/2 11/2 4 17/2 11/2 4 17/2 11/2 4 17/2 11/2 4 17/2 11/2 4 17/2 11/2 4 17/2 7/2 4 13/2 7/2 4 13/2 7/2 4 13/2 7/2 4 13/2 7/2 4 13/2 7/2 4 13/2 3/2 4 9/2 3/2 4 9/2 3/2 4 9/2 3/2 4 9/2 3/2 4 9/2 3/2 4 9/2 - 1073741824 k k0 Sqrt[2 Pi] x 1073741824 k k0 Sqrt[2 Pi] x 1073741824 k k0 Sqrt[2 Pi] x 536870912 k k0 Sqrt[2 Pi] x 536870912 k k0 Sqrt[2 Pi] x 1073741824 k k0 Sqrt[2 Pi] x 2097152 k k0 Sqrt[2 Pi] x 2097152 k k0 Sqrt[2 Pi] x 2097152 k k0 Sqrt[2 Pi] x 1048576 k k0 Sqrt[2 Pi] x 1048576 k k0 Sqrt[2 Pi] x 2097152 k k0 Sqrt[2 Pi] x 16384 k k0 Sqrt[2 Pi] x 16384 k k0 Sqrt[2 Pi] x 16384 k k0 Sqrt[2 Pi] x 8192 k k0 Sqrt[2 Pi] x 8192 k k0 Sqrt[2 Pi] x 16384 k k0 Sqrt[2 Pi] x 64 k k0 Sqrt[2 Pi] x 64 k k0 Sqrt[2 Pi] x 64 k k0 Sqrt[2 Pi] x 32 k k0 Sqrt[2 Pi] x 32 k k0 Sqrt[2 Pi] x 64 k k0 Sqrt[2 Pi] x Sqrt[k] k0 x Sqrt[k] k0 x Sqrt[k] k0 x Sqrt[k] k0 x Sqrt[k] k0 x Sqrt[k] k0 x 8589934592 k k0 Sqrt[2 Pi] x 8589934592 k k0 Sqrt[2 Pi] x 8589934592 k k0 Sqrt[2 Pi] x 4294967296 k k0 Sqrt[2 Pi] x 4294967296 k k0 Sqrt[2 Pi] x 8589934592 k k0 Sqrt[2 Pi] x 16777216 k k0 Sqrt[2 Pi] x 16777216 k k0 Sqrt[2 Pi] x 16777216 k k0 Sqrt[2 Pi] x 8388608 k k0 Sqrt[2 Pi] x 8388608 k k0 Sqrt[2 Pi] x 16777216 k k0 Sqrt[2 Pi] x 131072 k k0 Sqrt[2 Pi] x 131072 k k0 Sqrt[2 Pi] x 131072 k k0 Sqrt[2 Pi] x 65536 k k0 Sqrt[2 Pi] x 65536 k k0 Sqrt[2 Pi] x 131072 k k0 Sqrt[2 Pi] x 512 k k0 Sqrt[2 Pi] x 512 k k0 Sqrt[2 Pi] x 512 k k0 Sqrt[2 Pi] x 256 k k0 Sqrt[2 Pi] x 256 k k0 Sqrt[2 Pi] x 512 k k0 Sqrt[2 Pi] x 4 k k0 Sqrt[2 Pi] x 4 k k0 Sqrt[2 Pi] x 4 k k0 Sqrt[2 Pi] x 2 k k0 Sqrt[2 Pi] x 2 k k0 Sqrt[2 Pi] x 4 k k0 Sqrt[2 Pi] x -Series[Integrate[(E^(I*k0*x)*(1 - E^(-(c*x)))^5*BesselJ[0, k*x])/(k0^4*x^3), {x, 0, Infinity}, Assumptions -> n == 0 && q == 4 && κ == 5 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0 && k < k0], {k, Infinity, 10}] - -Simplify::time: Time spent on a transformation exceeded 300. seconds, and the transformation was aborted. Increasing the value of TimeConstraint option may improve the result of simplification. -Integrate[(E^(I*k0*x)*(1 - E^(-(c*x)))^5*BesselJ[0, k*x])/(k0^4*x^3), {x, 0, Infinity}, Assumptions -> n == 0 && q == 4 && κ == 5] diff --git a/besseltransforms/ksmall/5-4-1 b/besseltransforms/ksmall/5-4-1 deleted file mode 100644 index fbdea74..0000000 --- a/besseltransforms/ksmall/5-4-1 +++ /dev/null @@ -1,11 +0,0 @@ -Integrate[(E^(I*k0*x)*(1 - E^(-(c*x)))^5*BesselJ[1, k*x])/(k0^4*x^3), {x, 0, Infinity}, Assumptions -> n == 1 && q == 4 && κ == 5 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0 && k < k0] -Integrate((Power(E,I*k0*x)*Power(1 - Power(E,-(c*x)),5)*BesselJ(1,k*x))/(Power(k0,4)*Power(x,3)),List(x,0,DirectedInfinity(1)),Rule(Assumptions,n == 1 && q == 4 && κ == 5 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0 && k < k0)) - - I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi I k0 x 2 Pi -5 c x + I k0 x 2 Pi -4 c x + I k0 x 2 Pi -3 c x + I k0 x 2 Pi -2 c x + I k0 x 2 Pi -(c x) + I k0 x 2 Pi I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi - 14783093325 E Cos[-- + k x] 14783093325 E Cos[-- + k x] 73915466625 E Cos[-- + k x] 73915466625 E Cos[-- + k x] 73915466625 E Cos[-- + k x] 73915466625 E Cos[-- + k x] 2837835 E Cos[-- + k x] 2837835 E Cos[-- + k x] 14189175 E Cos[-- + k x] 14189175 E Cos[-- + k x] 14189175 E Cos[-- + k x] 14189175 E Cos[-- + k x] 4725 E Cos[-- + k x] 4725 E Cos[-- + k x] 23625 E Cos[-- + k x] 23625 E Cos[-- + k x] 23625 E Cos[-- + k x] 23625 E Cos[-- + k x] 15 E Cos[-- + k x] 15 E Cos[-- + k x] 75 E Cos[-- + k x] 75 E Cos[-- + k x] 75 E Cos[-- + k x] 75 E Cos[-- + k x] E Sqrt[--] Cos[-- + k x] E Sqrt[--] Cos[-- + k x] 5 E Sqrt[--] Cos[-- + k x] 10 E Sqrt[--] Cos[-- + k x] 10 E Sqrt[--] Cos[-- + k x] 5 E Sqrt[--] Cos[-- + k x] 468131288625 E Sin[-- + k x] 468131288625 E Sin[-- + k x] 2340656443125 E Sin[-- + k x] 2340656443125 E Sin[-- + k x] 2340656443125 E Sin[-- + k x] 2340656443125 E Sin[-- + k x] 66891825 E Sin[-- + k x] 66891825 E Sin[-- + k x] 334459125 E Sin[-- + k x] 334459125 E Sin[-- + k x] 334459125 E Sin[-- + k x] 334459125 E Sin[-- + k x] 72765 E Sin[-- + k x] 72765 E Sin[-- + k x] 363825 E Sin[-- + k x] 363825 E Sin[-- + k x] 363825 E Sin[-- + k x] 363825 E Sin[-- + k x] 105 E Sin[-- + k x] 105 E Sin[-- + k x] 525 E Sin[-- + k x] 525 E Sin[-- + k x] 525 E Sin[-- + k x] 525 E Sin[-- + k x] 3 E Sin[-- + k x] 3 E Sin[-- + k x] 15 E Sin[-- + k x] 15 E Sin[-- + k x] 15 E Sin[-- + k x] 15 E Sin[-- + k x] - 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 Pi 4 Pi 4 Pi 4 Pi 4 Pi 4 Pi 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 -Integrate::idiv: Integral of ------------------------------------- - ------------------------------------------ + ------------------------------------------ - ------------------------------------------ + ------------------------------------------ - ------------------------------------------ - ---------------------------------- + -------------------------------------- - --------------------------------------- + --------------------------------------- - --------------------------------------- + --------------------------------------- + ------------------------------- - ----------------------------------- + ------------------------------------ - ------------------------------------ + ------------------------------------ - ------------------------------------ - ---------------------------- + --------------------------------- - --------------------------------- + --------------------------------- - --------------------------------- + --------------------------------- - ------------------------------ + --------------------------------------- - ----------------------------------------- + ------------------------------------------ - ------------------------------------------ + ----------------------------------------- + ------------------------------------- - ------------------------------------------- + -------------------------------------------- - -------------------------------------------- + -------------------------------------------- - -------------------------------------------- - ----------------------------------- + --------------------------------------- - ---------------------------------------- + ---------------------------------------- - ---------------------------------------- + ---------------------------------------- + --------------------------------- - ------------------------------------ + ------------------------------------- - ------------------------------------- + ------------------------------------- - ------------------------------------- - ----------------------------- + ---------------------------------- - ---------------------------------- + ---------------------------------- - ---------------------------------- + ---------------------------------- + -------------------------- - -------------------------------- + --------------------------------- - --------------------------------- + --------------------------------- - --------------------------------- does not converge on {0, Infinity}. - 17/2 4 23/2 17/2 4 23/2 17/2 4 23/2 17/2 4 23/2 17/2 4 23/2 17/2 4 23/2 13/2 4 19/2 13/2 4 19/2 13/2 4 19/2 13/2 4 19/2 13/2 4 19/2 13/2 4 19/2 9/2 4 15/2 9/2 4 15/2 9/2 4 15/2 9/2 4 15/2 9/2 4 15/2 9/2 4 15/2 5/2 4 11/2 5/2 4 11/2 5/2 4 11/2 5/2 4 11/2 5/2 4 11/2 5/2 4 11/2 4 7/2 4 7/2 4 7/2 4 7/2 4 7/2 4 7/2 19/2 4 25/2 19/2 4 25/2 19/2 4 25/2 19/2 4 25/2 19/2 4 25/2 19/2 4 25/2 15/2 4 21/2 15/2 4 21/2 15/2 4 21/2 15/2 4 21/2 15/2 4 21/2 15/2 4 21/2 11/2 4 17/2 11/2 4 17/2 11/2 4 17/2 11/2 4 17/2 11/2 4 17/2 11/2 4 17/2 7/2 4 13/2 7/2 4 13/2 7/2 4 13/2 7/2 4 13/2 7/2 4 13/2 7/2 4 13/2 3/2 4 9/2 3/2 4 9/2 3/2 4 9/2 3/2 4 9/2 3/2 4 9/2 3/2 4 9/2 - 1073741824 k k0 Sqrt[2 Pi] x 1073741824 k k0 Sqrt[2 Pi] x 1073741824 k k0 Sqrt[2 Pi] x 536870912 k k0 Sqrt[2 Pi] x 536870912 k k0 Sqrt[2 Pi] x 1073741824 k k0 Sqrt[2 Pi] x 2097152 k k0 Sqrt[2 Pi] x 2097152 k k0 Sqrt[2 Pi] x 2097152 k k0 Sqrt[2 Pi] x 1048576 k k0 Sqrt[2 Pi] x 1048576 k k0 Sqrt[2 Pi] x 2097152 k k0 Sqrt[2 Pi] x 16384 k k0 Sqrt[2 Pi] x 16384 k k0 Sqrt[2 Pi] x 16384 k k0 Sqrt[2 Pi] x 8192 k k0 Sqrt[2 Pi] x 8192 k k0 Sqrt[2 Pi] x 16384 k k0 Sqrt[2 Pi] x 64 k k0 Sqrt[2 Pi] x 64 k k0 Sqrt[2 Pi] x 64 k k0 Sqrt[2 Pi] x 32 k k0 Sqrt[2 Pi] x 32 k k0 Sqrt[2 Pi] x 64 k k0 Sqrt[2 Pi] x Sqrt[k] k0 x Sqrt[k] k0 x Sqrt[k] k0 x Sqrt[k] k0 x Sqrt[k] k0 x Sqrt[k] k0 x 8589934592 k k0 Sqrt[2 Pi] x 8589934592 k k0 Sqrt[2 Pi] x 8589934592 k k0 Sqrt[2 Pi] x 4294967296 k k0 Sqrt[2 Pi] x 4294967296 k k0 Sqrt[2 Pi] x 8589934592 k k0 Sqrt[2 Pi] x 16777216 k k0 Sqrt[2 Pi] x 16777216 k k0 Sqrt[2 Pi] x 16777216 k k0 Sqrt[2 Pi] x 8388608 k k0 Sqrt[2 Pi] x 8388608 k k0 Sqrt[2 Pi] x 16777216 k k0 Sqrt[2 Pi] x 131072 k k0 Sqrt[2 Pi] x 131072 k k0 Sqrt[2 Pi] x 131072 k k0 Sqrt[2 Pi] x 65536 k k0 Sqrt[2 Pi] x 65536 k k0 Sqrt[2 Pi] x 131072 k k0 Sqrt[2 Pi] x 512 k k0 Sqrt[2 Pi] x 512 k k0 Sqrt[2 Pi] x 512 k k0 Sqrt[2 Pi] x 256 k k0 Sqrt[2 Pi] x 256 k k0 Sqrt[2 Pi] x 512 k k0 Sqrt[2 Pi] x 4 k k0 Sqrt[2 Pi] x 4 k k0 Sqrt[2 Pi] x 4 k k0 Sqrt[2 Pi] x 2 k k0 Sqrt[2 Pi] x 2 k k0 Sqrt[2 Pi] x 4 k k0 Sqrt[2 Pi] x -Series[Integrate[(E^(I*k0*x)*(1 - E^(-(c*x)))^5*BesselJ[1, k*x])/(k0^4*x^3), {x, 0, Infinity}, Assumptions -> n == 1 && q == 4 && κ == 5 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0 && k < k0], {k, Infinity, 10}] -Integrate[(E^(I*k0*x)*(1 - E^(-(c*x)))^5*BesselJ[1, k*x])/(k0^4*x^3), {x, 0, Infinity}, Assumptions -> n == 1 && q == 4 && κ == 5] diff --git a/besseltransforms/ksmall/5-4-2 b/besseltransforms/ksmall/5-4-2 deleted file mode 100644 index 73502e7..0000000 --- a/besseltransforms/ksmall/5-4-2 +++ /dev/null @@ -1,11 +0,0 @@ -Integrate[(E^(I*k0*x)*(1 - E^(-(c*x)))^5*BesselJ[2, k*x])/(k0^4*x^3), {x, 0, Infinity}, Assumptions -> n == 2 && q == 4 && κ == 5 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0 && k < k0] -Integrate((Power(E,I*k0*x)*Power(1 - Power(E,-(c*x)),5)*BesselJ(2,k*x))/(Power(k0,4)*Power(x,3)),List(x,0,DirectedInfinity(1)),Rule(Assumptions,n == 2 && q == 4 && κ == 5 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0 && k < k0)) - - I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi I k0 x 2 Pi -5 c x + I k0 x 2 Pi -4 c x + I k0 x 2 Pi -3 c x + I k0 x 2 Pi -2 c x + I k0 x 2 Pi -(c x) + I k0 x 2 Pi I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi - -21606059475 E Cos[-- - k x] 21606059475 E Cos[-- - k x] 108030297375 E Cos[-- - k x] 108030297375 E Cos[-- - k x] 108030297375 E Cos[-- - k x] 108030297375 E Cos[-- - k x] 4729725 E Cos[-- - k x] 4729725 E Cos[-- - k x] 23648625 E Cos[-- - k x] 23648625 E Cos[-- - k x] 23648625 E Cos[-- - k x] 23648625 E Cos[-- - k x] 10395 E Cos[-- - k x] 10395 E Cos[-- - k x] 51975 E Cos[-- - k x] 51975 E Cos[-- - k x] 51975 E Cos[-- - k x] 51975 E Cos[-- - k x] 105 E Cos[-- - k x] 105 E Cos[-- - k x] 525 E Cos[-- - k x] 525 E Cos[-- - k x] 525 E Cos[-- - k x] 525 E Cos[-- - k x] E Sqrt[--] Cos[-- - k x] E Sqrt[--] Cos[-- - k x] 5 E Sqrt[--] Cos[-- - k x] 10 E Sqrt[--] Cos[-- - k x] 10 E Sqrt[--] Cos[-- - k x] 5 E Sqrt[--] Cos[-- - k x] 655383804075 E Sin[-- - k x] 655383804075 E Sin[-- - k x] 3276919020375 E Sin[-- - k x] 3276919020375 E Sin[-- - k x] 3276919020375 E Sin[-- - k x] 3276919020375 E Sin[-- - k x] 103378275 E Sin[-- - k x] 103378275 E Sin[-- - k x] 516891375 E Sin[-- - k x] 516891375 E Sin[-- - k x] 516891375 E Sin[-- - k x] 516891375 E Sin[-- - k x] 135135 E Sin[-- - k x] 135135 E Sin[-- - k x] 675675 E Sin[-- - k x] 675675 E Sin[-- - k x] 675675 E Sin[-- - k x] 675675 E Sin[-- - k x] 315 E Sin[-- - k x] 315 E Sin[-- - k x] 1575 E Sin[-- - k x] 1575 E Sin[-- - k x] 1575 E Sin[-- - k x] 1575 E Sin[-- - k x] 15 E Sin[-- - k x] 15 E Sin[-- - k x] 75 E Sin[-- - k x] 75 E Sin[-- - k x] 75 E Sin[-- - k x] 75 E Sin[-- - k x] - 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 Pi 4 Pi 4 Pi 4 Pi 4 Pi 4 Pi 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 -Integrate::idiv: Integral of ------------------------------------- + ------------------------------------------ - ------------------------------------------- + ------------------------------------------- - ------------------------------------------- + ------------------------------------------- + ---------------------------------- - -------------------------------------- + --------------------------------------- - --------------------------------------- + --------------------------------------- - --------------------------------------- - ------------------------------- + ------------------------------------ - ------------------------------------ + ------------------------------------ - ------------------------------------ + ------------------------------------ + ---------------------------- - ---------------------------------- + ---------------------------------- - ---------------------------------- + ---------------------------------- - ---------------------------------- - ------------------------------ + --------------------------------------- - ----------------------------------------- + ------------------------------------------ - ------------------------------------------ + ----------------------------------------- + ------------------------------------- - ------------------------------------------- + -------------------------------------------- - -------------------------------------------- + -------------------------------------------- - -------------------------------------------- - ----------------------------------- + ---------------------------------------- - ---------------------------------------- + ---------------------------------------- - ---------------------------------------- + ---------------------------------------- + --------------------------------- - ------------------------------------- + ------------------------------------- - ------------------------------------- + ------------------------------------- - ------------------------------------- - ----------------------------- + ---------------------------------- - ----------------------------------- + ----------------------------------- - ----------------------------------- + ----------------------------------- - -------------------------- + --------------------------------- - --------------------------------- + --------------------------------- - --------------------------------- + --------------------------------- does not converge on {0, Infinity}. - 17/2 4 23/2 17/2 4 23/2 17/2 4 23/2 17/2 4 23/2 17/2 4 23/2 17/2 4 23/2 13/2 4 19/2 13/2 4 19/2 13/2 4 19/2 13/2 4 19/2 13/2 4 19/2 13/2 4 19/2 9/2 4 15/2 9/2 4 15/2 9/2 4 15/2 9/2 4 15/2 9/2 4 15/2 9/2 4 15/2 5/2 4 11/2 5/2 4 11/2 5/2 4 11/2 5/2 4 11/2 5/2 4 11/2 5/2 4 11/2 4 7/2 4 7/2 4 7/2 4 7/2 4 7/2 4 7/2 19/2 4 25/2 19/2 4 25/2 19/2 4 25/2 19/2 4 25/2 19/2 4 25/2 19/2 4 25/2 15/2 4 21/2 15/2 4 21/2 15/2 4 21/2 15/2 4 21/2 15/2 4 21/2 15/2 4 21/2 11/2 4 17/2 11/2 4 17/2 11/2 4 17/2 11/2 4 17/2 11/2 4 17/2 11/2 4 17/2 7/2 4 13/2 7/2 4 13/2 7/2 4 13/2 7/2 4 13/2 7/2 4 13/2 7/2 4 13/2 3/2 4 9/2 3/2 4 9/2 3/2 4 9/2 3/2 4 9/2 3/2 4 9/2 3/2 4 9/2 - 1073741824 k k0 Sqrt[2 Pi] x 1073741824 k k0 Sqrt[2 Pi] x 1073741824 k k0 Sqrt[2 Pi] x 536870912 k k0 Sqrt[2 Pi] x 536870912 k k0 Sqrt[2 Pi] x 1073741824 k k0 Sqrt[2 Pi] x 2097152 k k0 Sqrt[2 Pi] x 2097152 k k0 Sqrt[2 Pi] x 2097152 k k0 Sqrt[2 Pi] x 1048576 k k0 Sqrt[2 Pi] x 1048576 k k0 Sqrt[2 Pi] x 2097152 k k0 Sqrt[2 Pi] x 16384 k k0 Sqrt[2 Pi] x 16384 k k0 Sqrt[2 Pi] x 16384 k k0 Sqrt[2 Pi] x 8192 k k0 Sqrt[2 Pi] x 8192 k k0 Sqrt[2 Pi] x 16384 k k0 Sqrt[2 Pi] x 64 k k0 Sqrt[2 Pi] x 64 k k0 Sqrt[2 Pi] x 64 k k0 Sqrt[2 Pi] x 32 k k0 Sqrt[2 Pi] x 32 k k0 Sqrt[2 Pi] x 64 k k0 Sqrt[2 Pi] x Sqrt[k] k0 x Sqrt[k] k0 x Sqrt[k] k0 x Sqrt[k] k0 x Sqrt[k] k0 x Sqrt[k] k0 x 8589934592 k k0 Sqrt[2 Pi] x 8589934592 k k0 Sqrt[2 Pi] x 8589934592 k k0 Sqrt[2 Pi] x 4294967296 k k0 Sqrt[2 Pi] x 4294967296 k k0 Sqrt[2 Pi] x 8589934592 k k0 Sqrt[2 Pi] x 16777216 k k0 Sqrt[2 Pi] x 16777216 k k0 Sqrt[2 Pi] x 16777216 k k0 Sqrt[2 Pi] x 8388608 k k0 Sqrt[2 Pi] x 8388608 k k0 Sqrt[2 Pi] x 16777216 k k0 Sqrt[2 Pi] x 131072 k k0 Sqrt[2 Pi] x 131072 k k0 Sqrt[2 Pi] x 131072 k k0 Sqrt[2 Pi] x 65536 k k0 Sqrt[2 Pi] x 65536 k k0 Sqrt[2 Pi] x 131072 k k0 Sqrt[2 Pi] x 512 k k0 Sqrt[2 Pi] x 512 k k0 Sqrt[2 Pi] x 512 k k0 Sqrt[2 Pi] x 256 k k0 Sqrt[2 Pi] x 256 k k0 Sqrt[2 Pi] x 512 k k0 Sqrt[2 Pi] x 4 k k0 Sqrt[2 Pi] x 4 k k0 Sqrt[2 Pi] x 4 k k0 Sqrt[2 Pi] x 2 k k0 Sqrt[2 Pi] x 2 k k0 Sqrt[2 Pi] x 4 k k0 Sqrt[2 Pi] x -Series[Integrate[(E^(I*k0*x)*(1 - E^(-(c*x)))^5*BesselJ[2, k*x])/(k0^4*x^3), {x, 0, Infinity}, Assumptions -> n == 2 && q == 4 && κ == 5 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0 && k < k0], {k, Infinity, 10}] -Integrate[(E^(I*k0*x)*(1 - E^(-(c*x)))^5*BesselJ[2, k*x])/(k0^4*x^3), {x, 0, Infinity}, Assumptions -> n == 2 && q == 4 && κ == 5] diff --git a/besseltransforms/ksmall/5-4-3 b/besseltransforms/ksmall/5-4-3 deleted file mode 100644 index 0040fd9..0000000 --- a/besseltransforms/ksmall/5-4-3 +++ /dev/null @@ -1,4 +0,0 @@ -(-(k^4*(-15 + 8*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0) + 4*k^2*(-5 + 4*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^3 + 8*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^5)/(24*k^3) + (k^4*(-15 + 8*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0) + 4*k^2*(-5 + 4*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^3 + 8*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^5)/(12*k^3) - (k^4*(-15 + 8*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0) + 4*k^2*(-5 + 4*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^3 + 8*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^5)/(12*k^3) + (k^4*(-15 + 8*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0) + 4*k^2*(-5 + 4*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^3 + 8*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^5)/(24*k^3) - (k^4*(-15 + 8*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0) + 4*k^2*(-5 + 4*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^3 + 8*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^5)/(120*k^3) + (I/120*(k^4*(15*k0 - 8*Sqrt[-k^2 + k0^2]) + 8*k0^4*(k0 - Sqrt[-k^2 + k0^2]) + 4*k^2*k0^2*(-5*k0 + 4*Sqrt[-k^2 + k0^2])))/k^3)/k0^4 -(-(Power(k,4)*(-15 + 8*Sqrt(1 + Power(k,2)/Power(c - Complex(0,1)*k0,2)))*(c - Complex(0,1)*k0) + 4*Power(k,2)*(-5 + 4*Sqrt(1 + Power(k,2)/Power(c - Complex(0,1)*k0,2)))*Power(c - Complex(0,1)*k0,3) + 8*(-1 + Sqrt(1 + Power(k,2)/Power(c - Complex(0,1)*k0,2)))*Power(c - Complex(0,1)*k0,5))/(24.*Power(k,3)) + (Power(k,4)*(-15 + 8*Sqrt(1 + Power(k,2)/Power(2*c - Complex(0,1)*k0,2)))*(2*c - Complex(0,1)*k0) + 4*Power(k,2)*(-5 + 4*Sqrt(1 + Power(k,2)/Power(2*c - Complex(0,1)*k0,2)))*Power(2*c - Complex(0,1)*k0,3) + 8*(-1 + Sqrt(1 + Power(k,2)/Power(2*c - Complex(0,1)*k0,2)))*Power(2*c - Complex(0,1)*k0,5))/(12.*Power(k,3)) - (Power(k,4)*(-15 + 8*Sqrt(1 + Power(k,2)/Power(3*c - Complex(0,1)*k0,2)))*(3*c - Complex(0,1)*k0) + 4*Power(k,2)*(-5 + 4*Sqrt(1 + Power(k,2)/Power(3*c - Complex(0,1)*k0,2)))*Power(3*c - Complex(0,1)*k0,3) + 8*(-1 + Sqrt(1 + Power(k,2)/Power(3*c - Complex(0,1)*k0,2)))*Power(3*c - Complex(0,1)*k0,5))/(12.*Power(k,3)) + (Power(k,4)*(-15 + 8*Sqrt(1 + Power(k,2)/Power(4*c - Complex(0,1)*k0,2)))*(4*c - Complex(0,1)*k0) + 4*Power(k,2)*(-5 + 4*Sqrt(1 + Power(k,2)/Power(4*c - Complex(0,1)*k0,2)))*Power(4*c - Complex(0,1)*k0,3) + 8*(-1 + Sqrt(1 + Power(k,2)/Power(4*c - Complex(0,1)*k0,2)))*Power(4*c - Complex(0,1)*k0,5))/(24.*Power(k,3)) - (Power(k,4)*(-15 + 8*Sqrt(1 + Power(k,2)/Power(5*c - Complex(0,1)*k0,2)))*(5*c - Complex(0,1)*k0) + 4*Power(k,2)*(-5 + 4*Sqrt(1 + Power(k,2)/Power(5*c - Complex(0,1)*k0,2)))*Power(5*c - Complex(0,1)*k0,3) + 8*(-1 + Sqrt(1 + Power(k,2)/Power(5*c - Complex(0,1)*k0,2)))*Power(5*c - Complex(0,1)*k0,5))/(120.*Power(k,3)) + (Complex(0,0.008333333333333333)*(Power(k,4)*(15*k0 - 8*Sqrt(-Power(k,2) + Power(k0,2))) + 8*Power(k0,4)*(k0 - Sqrt(-Power(k,2) + Power(k0,2))) + 4*Power(k,2)*Power(k0,2)*(-5*k0 + 4*Sqrt(-Power(k,2) + Power(k0,2)))))/Power(k,3))/Power(k0,4) -SeriesData[k, Infinity, {(8*c^5)/k0^4, (-75*c^6)/(2*k0^4) + ((15*I)*c^5)/k0^3, 0, (35*(75*c^8 - (80*I)*c^7*k0 - 30*c^6*k0^2 + (4*I)*c^5*k0^3))/(8*k0^4), 0, (-63*(2025*c^10 - (3310*I)*c^9*k0 - 2250*c^8*k0^2 + (800*I)*c^7*k0^3 + 150*c^6*k0^4 - (12*I)*c^5*k0^5))/(32*k0^4), 0, (165*(20900*c^12 - (44860*I)*c^11*k0 - 42525*c^10*k0^2 + (23170*I)*c^9*k0^3 + 7875*c^8*k0^4 - (1680*I)*c^7*k0^5 - 210*c^6*k0^6 + (12*I)*c^5*k0^7))/(64*k0^4)}, 3, 11, 1] --(5*(k^4*(-15 + 8*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0) + 4*k^2*(-5 + 4*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^3 + 8*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^5) - 10*(k^4*(-15 + 8*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0) + 4*k^2*(-5 + 4*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^3 + 8*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^5) + 10*(k^4*(-15 + 8*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0) + 4*k^2*(-5 + 4*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^3 + 8*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^5) - 5*(k^4*(-15 + 8*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0) + 4*k^2*(-5 + 4*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^3 + 8*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^5) + k^4*(-15 + 8*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0) + 4*k^2*(-5 + 4*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^3 + 8*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^5 - I*(k^4*(15*k0 - 8*Sqrt[-k^2 + k0^2]) + 8*k0^4*(k0 - Sqrt[-k^2 + k0^2]) + 4*k^2*k0^2*(-5*k0 + 4*Sqrt[-k^2 + k0^2])))/(120*k^3*k0^4) diff --git a/besseltransforms/ksmall/5-4-4 b/besseltransforms/ksmall/5-4-4 deleted file mode 100644 index a67f0e3..0000000 --- a/besseltransforms/ksmall/5-4-4 +++ /dev/null @@ -1,4 +0,0 @@ -(-(5*k^6 + 2*k^4*(15 - 8*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^2 + 8*k^2*(5 - 4*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^4 - 16*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^6)/(48*k^4) + (5*k^6 + 2*k^4*(15 - 8*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^2 + 8*k^2*(5 - 4*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^4 - 16*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^6)/(24*k^4) - (5*k^6 + 2*k^4*(15 - 8*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^2 + 8*k^2*(5 - 4*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^4 - 16*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^6)/(24*k^4) + (5*k^6 + 2*k^4*(15 - 8*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^2 + 8*k^2*(5 - 4*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^4 - 16*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^6)/(48*k^4) - (5*k^6 + 2*k^4*(15 - 8*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^2 + 8*k^2*(5 - 4*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^4 - 16*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^6)/(240*k^4) + (5*k^6 + 16*k0^5*(-k0 + Sqrt[-k^2 + k0^2]) - 8*k^2*k0^3*(-5*k0 + 4*Sqrt[-k^2 + k0^2]) + 2*k^4*k0*(-15*k0 + 8*Sqrt[-k^2 + k0^2]))/(240*k^4))/k0^4 -(-(5*Power(k,6) + 2*Power(k,4)*(15 - 8*Sqrt(1 + Power(k,2)/Power(c - Complex(0,1)*k0,2)))*Power(c - Complex(0,1)*k0,2) + 8*Power(k,2)*(5 - 4*Sqrt(1 + Power(k,2)/Power(c - Complex(0,1)*k0,2)))*Power(c - Complex(0,1)*k0,4) - 16*(-1 + Sqrt(1 + Power(k,2)/Power(c - Complex(0,1)*k0,2)))*Power(c - Complex(0,1)*k0,6))/(48.*Power(k,4)) + (5*Power(k,6) + 2*Power(k,4)*(15 - 8*Sqrt(1 + Power(k,2)/Power(2*c - Complex(0,1)*k0,2)))*Power(2*c - Complex(0,1)*k0,2) + 8*Power(k,2)*(5 - 4*Sqrt(1 + Power(k,2)/Power(2*c - Complex(0,1)*k0,2)))*Power(2*c - Complex(0,1)*k0,4) - 16*(-1 + Sqrt(1 + Power(k,2)/Power(2*c - Complex(0,1)*k0,2)))*Power(2*c - Complex(0,1)*k0,6))/(24.*Power(k,4)) - (5*Power(k,6) + 2*Power(k,4)*(15 - 8*Sqrt(1 + Power(k,2)/Power(3*c - Complex(0,1)*k0,2)))*Power(3*c - Complex(0,1)*k0,2) + 8*Power(k,2)*(5 - 4*Sqrt(1 + Power(k,2)/Power(3*c - Complex(0,1)*k0,2)))*Power(3*c - Complex(0,1)*k0,4) - 16*(-1 + Sqrt(1 + Power(k,2)/Power(3*c - Complex(0,1)*k0,2)))*Power(3*c - Complex(0,1)*k0,6))/(24.*Power(k,4)) + (5*Power(k,6) + 2*Power(k,4)*(15 - 8*Sqrt(1 + Power(k,2)/Power(4*c - Complex(0,1)*k0,2)))*Power(4*c - Complex(0,1)*k0,2) + 8*Power(k,2)*(5 - 4*Sqrt(1 + Power(k,2)/Power(4*c - Complex(0,1)*k0,2)))*Power(4*c - Complex(0,1)*k0,4) - 16*(-1 + Sqrt(1 + Power(k,2)/Power(4*c - Complex(0,1)*k0,2)))*Power(4*c - Complex(0,1)*k0,6))/(48.*Power(k,4)) - (5*Power(k,6) + 2*Power(k,4)*(15 - 8*Sqrt(1 + Power(k,2)/Power(5*c - Complex(0,1)*k0,2)))*Power(5*c - Complex(0,1)*k0,2) + 8*Power(k,2)*(5 - 4*Sqrt(1 + Power(k,2)/Power(5*c - Complex(0,1)*k0,2)))*Power(5*c - Complex(0,1)*k0,4) - 16*(-1 + Sqrt(1 + Power(k,2)/Power(5*c - Complex(0,1)*k0,2)))*Power(5*c - Complex(0,1)*k0,6))/(240.*Power(k,4)) + (5*Power(k,6) + 16*Power(k0,5)*(-k0 + Sqrt(-Power(k,2) + Power(k0,2))) - 8*Power(k,2)*Power(k0,3)*(-5*k0 + 4*Sqrt(-Power(k,2) + Power(k0,2))) + 2*Power(k,4)*k0*(-15*k0 + 8*Sqrt(-Power(k,2) + Power(k0,2))))/(240.*Power(k,4)))/Power(k0,4) -SeriesData[k, Infinity, {(15*c^5)/k0^4, (-120*c^6)/k0^4 + ((48*I)*c^5)/k0^3, (35*(20*c^7 - (15*I)*c^6*k0 - 3*c^5*k0^2))/(2*k0^4), 0, (-105*(331*c^9 - (450*I)*c^8*k0 - 240*c^7*k0^2 + (60*I)*c^6*k0^3 + 6*c^5*k0^4))/(16*k0^4), 0, (33*(22430*c^11 - (42525*I)*c^10*k0 - 34755*c^9*k0^2 + (15750*I)*c^8*k0^3 + 4200*c^7*k0^4 - (630*I)*c^6*k0^5 - 42*c^5*k0^6))/(32*k0^4)}, 3, 11, 1] -(5*k^4*(-15 + 8*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^2 + 20*k^2*(-5 + 4*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^4 + 40*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^6 + 10*k^4*(15 - 8*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^2 + 40*k^2*(5 - 4*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^4 - 80*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^6 + 10*k^4*(-15 + 8*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^2 + 40*k^2*(-5 + 4*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^4 + 80*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^6 + 5*k^4*(15 - 8*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^2 + 20*k^2*(5 - 4*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^4 - 40*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^6 + k^4*(-15 + 8*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^2 + 4*k^2*(-5 + 4*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^4 + 8*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^6 + 8*k0^5*(-k0 + Sqrt[-k^2 + k0^2]) - 4*k^2*k0^3*(-5*k0 + 4*Sqrt[-k^2 + k0^2]) + k^4*k0*(-15*k0 + 8*Sqrt[-k^2 + k0^2]))/(120*k^4*k0^4) diff --git a/besseltransforms/ksmall/5-4-5 b/besseltransforms/ksmall/5-4-5 deleted file mode 100644 index 06d2457..0000000 --- a/besseltransforms/ksmall/5-4-5 +++ /dev/null @@ -1,4 +0,0 @@ -(-(k^6*(-35 + 8*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0) + 20*k^4*(-7 + 4*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^3 + 8*k^2*(-21 + 17*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^5 + 64*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^7)/(168*k^5) + (k^6*(-35 + 8*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0) + 20*k^4*(-7 + 4*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^3 + 8*k^2*(-21 + 17*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^5 + 64*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^7)/(84*k^5) - (k^6*(-35 + 8*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0) + 20*k^4*(-7 + 4*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^3 + 8*k^2*(-21 + 17*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^5 + 64*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^7)/(84*k^5) + (k^6*(-35 + 8*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0) + 20*k^4*(-7 + 4*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^3 + 8*k^2*(-21 + 17*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^5 + 64*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^7)/(168*k^5) - (k^6*(-35 + 8*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0) + 20*k^4*(-7 + 4*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^3 + 8*k^2*(-21 + 17*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^5 + 64*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^7)/(840*k^5) + (I/840*(k^6*(35*k0 - 8*Sqrt[-k^2 + k0^2]) + 64*k0^6*(-k0 + Sqrt[-k^2 + k0^2]) + 20*k^4*k0^2*(-7*k0 + 4*Sqrt[-k^2 + k0^2]) - 8*k^2*k0^4*(-21*k0 + 17*Sqrt[-k^2 + k0^2])))/k^5)/k0^4 -(-(Power(k,6)*(-35 + 8*Sqrt(1 + Power(k,2)/Power(c - Complex(0,1)*k0,2)))*(c - Complex(0,1)*k0) + 20*Power(k,4)*(-7 + 4*Sqrt(1 + Power(k,2)/Power(c - Complex(0,1)*k0,2)))*Power(c - Complex(0,1)*k0,3) + 8*Power(k,2)*(-21 + 17*Sqrt(1 + Power(k,2)/Power(c - Complex(0,1)*k0,2)))*Power(c - Complex(0,1)*k0,5) + 64*(-1 + Sqrt(1 + Power(k,2)/Power(c - Complex(0,1)*k0,2)))*Power(c - Complex(0,1)*k0,7))/(168.*Power(k,5)) + (Power(k,6)*(-35 + 8*Sqrt(1 + Power(k,2)/Power(2*c - Complex(0,1)*k0,2)))*(2*c - Complex(0,1)*k0) + 20*Power(k,4)*(-7 + 4*Sqrt(1 + Power(k,2)/Power(2*c - Complex(0,1)*k0,2)))*Power(2*c - Complex(0,1)*k0,3) + 8*Power(k,2)*(-21 + 17*Sqrt(1 + Power(k,2)/Power(2*c - Complex(0,1)*k0,2)))*Power(2*c - Complex(0,1)*k0,5) + 64*(-1 + Sqrt(1 + Power(k,2)/Power(2*c - Complex(0,1)*k0,2)))*Power(2*c - Complex(0,1)*k0,7))/(84.*Power(k,5)) - (Power(k,6)*(-35 + 8*Sqrt(1 + Power(k,2)/Power(3*c - Complex(0,1)*k0,2)))*(3*c - Complex(0,1)*k0) + 20*Power(k,4)*(-7 + 4*Sqrt(1 + Power(k,2)/Power(3*c - Complex(0,1)*k0,2)))*Power(3*c - Complex(0,1)*k0,3) + 8*Power(k,2)*(-21 + 17*Sqrt(1 + Power(k,2)/Power(3*c - Complex(0,1)*k0,2)))*Power(3*c - Complex(0,1)*k0,5) + 64*(-1 + Sqrt(1 + Power(k,2)/Power(3*c - Complex(0,1)*k0,2)))*Power(3*c - Complex(0,1)*k0,7))/(84.*Power(k,5)) + (Power(k,6)*(-35 + 8*Sqrt(1 + Power(k,2)/Power(4*c - Complex(0,1)*k0,2)))*(4*c - Complex(0,1)*k0) + 20*Power(k,4)*(-7 + 4*Sqrt(1 + Power(k,2)/Power(4*c - Complex(0,1)*k0,2)))*Power(4*c - Complex(0,1)*k0,3) + 8*Power(k,2)*(-21 + 17*Sqrt(1 + Power(k,2)/Power(4*c - Complex(0,1)*k0,2)))*Power(4*c - Complex(0,1)*k0,5) + 64*(-1 + Sqrt(1 + Power(k,2)/Power(4*c - Complex(0,1)*k0,2)))*Power(4*c - Complex(0,1)*k0,7))/(168.*Power(k,5)) - (Power(k,6)*(-35 + 8*Sqrt(1 + Power(k,2)/Power(5*c - Complex(0,1)*k0,2)))*(5*c - Complex(0,1)*k0) + 20*Power(k,4)*(-7 + 4*Sqrt(1 + Power(k,2)/Power(5*c - Complex(0,1)*k0,2)))*Power(5*c - Complex(0,1)*k0,3) + 8*Power(k,2)*(-21 + 17*Sqrt(1 + Power(k,2)/Power(5*c - Complex(0,1)*k0,2)))*Power(5*c - Complex(0,1)*k0,5) + 64*(-1 + Sqrt(1 + Power(k,2)/Power(5*c - Complex(0,1)*k0,2)))*Power(5*c - Complex(0,1)*k0,7))/(840.*Power(k,5)) + (Complex(0,0.0011904761904761906)*(Power(k,6)*(35*k0 - 8*Sqrt(-Power(k,2) + Power(k0,2))) + 64*Power(k0,6)*(-k0 + Sqrt(-Power(k,2) + Power(k0,2))) + 20*Power(k,4)*Power(k0,2)*(-7*k0 + 4*Sqrt(-Power(k,2) + Power(k0,2))) - 8*Power(k,2)*Power(k0,4)*(-21*k0 + 17*Sqrt(-Power(k,2) + Power(k0,2)))))/Power(k,5))/Power(k0,4) -SeriesData[k, Infinity, {(24*c^5)/k0^4, (-525*c^6)/(2*k0^4) + ((105*I)*c^5)/k0^3, (1280*c^7)/k0^4 - ((960*I)*c^6)/k0^3 - (192*c^5)/k0^2, (-315*(75*c^8 - (80*I)*c^7*k0 - 30*c^6*k0^2 + (4*I)*c^5*k0^3))/(8*k0^4), 0, (231*(2025*c^10 - (3310*I)*c^9*k0 - 2250*c^8*k0^2 + (800*I)*c^7*k0^3 + 150*c^6*k0^4 - (12*I)*c^5*k0^5))/(32*k0^4), 0, (-429*(20900*c^12 - (44860*I)*c^11*k0 - 42525*c^10*k0^2 + (23170*I)*c^9*k0^3 + 7875*c^8*k0^4 - (1680*I)*c^7*k0^5 - 210*c^6*k0^6 + (12*I)*c^5*k0^7))/(64*k0^4)}, 3, 11, 1] --(5*(k^6*(-35 + 8*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0) + 20*k^4*(-7 + 4*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^3 + 8*k^2*(-21 + 17*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^5 + 64*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^7) - 10*(k^6*(-35 + 8*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0) + 20*k^4*(-7 + 4*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^3 + 8*k^2*(-21 + 17*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^5 + 64*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^7) + 10*(k^6*(-35 + 8*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0) + 20*k^4*(-7 + 4*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^3 + 8*k^2*(-21 + 17*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^5 + 64*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^7) - 5*(k^6*(-35 + 8*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0) + 20*k^4*(-7 + 4*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^3 + 8*k^2*(-21 + 17*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^5 + 64*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^7) + k^6*(-35 + 8*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0) + 20*k^4*(-7 + 4*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^3 + 8*k^2*(-21 + 17*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^5 + 64*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^7 - I*(k^6*(35*k0 - 8*Sqrt[-k^2 + k0^2]) + 64*k0^6*(-k0 + Sqrt[-k^2 + k0^2]) + 20*k^4*k0^2*(-7*k0 + 4*Sqrt[-k^2 + k0^2]) - 8*k^2*k0^4*(-21*k0 + 17*Sqrt[-k^2 + k0^2])))/(840*k^5*k0^4) diff --git a/besseltransforms/ksmall/5-5-0 b/besseltransforms/ksmall/5-5-0 deleted file mode 100644 index 5038b60..0000000 --- a/besseltransforms/ksmall/5-5-0 +++ /dev/null @@ -1,13 +0,0 @@ -Integrate[(E^(I*k0*x)*(1 - E^(-(c*x)))^5*BesselJ[0, k*x])/(k0^5*x^4), {x, 0, Infinity}, Assumptions -> n == 0 && q == 5 && κ == 5 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0 && k < k0] -Integrate((Power(E,I*k0*x)*Power(1 - Power(E,-(c*x)),5)*BesselJ(0,k*x))/(Power(k0,5)*Power(x,4)),List(x,0,DirectedInfinity(1)),Rule(Assumptions,n == 0 && q == 5 && κ == 5 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0 && k < k0)) - - I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi I k0 x 2 Pi -5 c x + I k0 x 2 Pi -4 c x + I k0 x 2 Pi -3 c x + I k0 x 2 Pi -2 c x + I k0 x 2 Pi -(c x) + I k0 x 2 Pi I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi - 13043905875 E Cos[-- - k x] 13043905875 E Cos[-- - k x] 65219529375 E Cos[-- - k x] 65219529375 E Cos[-- - k x] 65219529375 E Cos[-- - k x] 65219529375 E Cos[-- - k x] 2401245 E Cos[-- - k x] 2401245 E Cos[-- - k x] 12006225 E Cos[-- - k x] 12006225 E Cos[-- - k x] 12006225 E Cos[-- - k x] 12006225 E Cos[-- - k x] 3675 E Cos[-- - k x] 3675 E Cos[-- - k x] 18375 E Cos[-- - k x] 18375 E Cos[-- - k x] 18375 E Cos[-- - k x] 18375 E Cos[-- - k x] 9 E Cos[-- - k x] 9 E Cos[-- - k x] 45 E Cos[-- - k x] 45 E Cos[-- - k x] 45 E Cos[-- - k x] 45 E Cos[-- - k x] E Sqrt[--] Cos[-- - k x] E Sqrt[--] Cos[-- - k x] 5 E Sqrt[--] Cos[-- - k x] 10 E Sqrt[--] Cos[-- - k x] 10 E Sqrt[--] Cos[-- - k x] 5 E Sqrt[--] Cos[-- - k x] 418854310875 E Sin[-- - k x] 418854310875 E Sin[-- - k x] 2094271554375 E Sin[-- - k x] 2094271554375 E Sin[-- - k x] 2094271554375 E Sin[-- - k x] 2094271554375 E Sin[-- - k x] 57972915 E Sin[-- - k x] 57972915 E Sin[-- - k x] 289864575 E Sin[-- - k x] 289864575 E Sin[-- - k x] 289864575 E Sin[-- - k x] 289864575 E Sin[-- - k x] 59535 E Sin[-- - k x] 59535 E Sin[-- - k x] 297675 E Sin[-- - k x] 297675 E Sin[-- - k x] 297675 E Sin[-- - k x] 297675 E Sin[-- - k x] 75 E Sin[-- - k x] 75 E Sin[-- - k x] 375 E Sin[-- - k x] 375 E Sin[-- - k x] 375 E Sin[-- - k x] 375 E Sin[-- - k x] E Sin[-- - k x] E Sin[-- - k x] 5 E Sin[-- - k x] 5 E Sin[-- - k x] 5 E Sin[-- - k x] 5 E Sin[-- - k x] - 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 Pi 4 Pi 4 Pi 4 Pi 4 Pi 4 Pi 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 -Integrate::idiv: Integral of ------------------------------------- - ------------------------------------------ + ------------------------------------------ - ------------------------------------------ + ------------------------------------------ - ------------------------------------------ - ---------------------------------- + -------------------------------------- - --------------------------------------- + --------------------------------------- - --------------------------------------- + --------------------------------------- + ------------------------------- - ----------------------------------- + ------------------------------------ - ------------------------------------ + ------------------------------------ - ------------------------------------ - ---------------------------- + -------------------------------- - --------------------------------- + --------------------------------- - --------------------------------- + --------------------------------- + ------------------------------ - --------------------------------------- + ----------------------------------------- - ------------------------------------------ + ------------------------------------------ - ----------------------------------------- - ------------------------------------- + ------------------------------------------- - -------------------------------------------- + -------------------------------------------- - -------------------------------------------- + -------------------------------------------- + ----------------------------------- - --------------------------------------- + ---------------------------------------- - ---------------------------------------- + ---------------------------------------- - ---------------------------------------- - --------------------------------- + ------------------------------------ - ------------------------------------- + ------------------------------------- - ------------------------------------- + ------------------------------------- + ----------------------------- - --------------------------------- + ---------------------------------- - ---------------------------------- + ---------------------------------- - ---------------------------------- - --------------------------- + ------------------------------ - -------------------------------- + -------------------------------- - -------------------------------- + -------------------------------- does not converge on {0, Infinity}. - 17/2 5 25/2 17/2 5 25/2 17/2 5 25/2 17/2 5 25/2 17/2 5 25/2 17/2 5 25/2 13/2 5 21/2 13/2 5 21/2 13/2 5 21/2 13/2 5 21/2 13/2 5 21/2 13/2 5 21/2 9/2 5 17/2 9/2 5 17/2 9/2 5 17/2 9/2 5 17/2 9/2 5 17/2 9/2 5 17/2 5/2 5 13/2 5/2 5 13/2 5/2 5 13/2 5/2 5 13/2 5/2 5 13/2 5/2 5 13/2 5 9/2 5 9/2 5 9/2 5 9/2 5 9/2 5 9/2 19/2 5 27/2 19/2 5 27/2 19/2 5 27/2 19/2 5 27/2 19/2 5 27/2 19/2 5 27/2 15/2 5 23/2 15/2 5 23/2 15/2 5 23/2 15/2 5 23/2 15/2 5 23/2 15/2 5 23/2 11/2 5 19/2 11/2 5 19/2 11/2 5 19/2 11/2 5 19/2 11/2 5 19/2 11/2 5 19/2 7/2 5 15/2 7/2 5 15/2 7/2 5 15/2 7/2 5 15/2 7/2 5 15/2 7/2 5 15/2 3/2 5 11/2 3/2 5 11/2 3/2 5 11/2 3/2 5 11/2 3/2 5 11/2 3/2 5 11/2 - 1073741824 k k0 Sqrt[2 Pi] x 1073741824 k k0 Sqrt[2 Pi] x 1073741824 k k0 Sqrt[2 Pi] x 536870912 k k0 Sqrt[2 Pi] x 536870912 k k0 Sqrt[2 Pi] x 1073741824 k k0 Sqrt[2 Pi] x 2097152 k k0 Sqrt[2 Pi] x 2097152 k k0 Sqrt[2 Pi] x 2097152 k k0 Sqrt[2 Pi] x 1048576 k k0 Sqrt[2 Pi] x 1048576 k k0 Sqrt[2 Pi] x 2097152 k k0 Sqrt[2 Pi] x 16384 k k0 Sqrt[2 Pi] x 16384 k k0 Sqrt[2 Pi] x 16384 k k0 Sqrt[2 Pi] x 8192 k k0 Sqrt[2 Pi] x 8192 k k0 Sqrt[2 Pi] x 16384 k k0 Sqrt[2 Pi] x 64 k k0 Sqrt[2 Pi] x 64 k k0 Sqrt[2 Pi] x 64 k k0 Sqrt[2 Pi] x 32 k k0 Sqrt[2 Pi] x 32 k k0 Sqrt[2 Pi] x 64 k k0 Sqrt[2 Pi] x Sqrt[k] k0 x Sqrt[k] k0 x Sqrt[k] k0 x Sqrt[k] k0 x Sqrt[k] k0 x Sqrt[k] k0 x 8589934592 k k0 Sqrt[2 Pi] x 8589934592 k k0 Sqrt[2 Pi] x 8589934592 k k0 Sqrt[2 Pi] x 4294967296 k k0 Sqrt[2 Pi] x 4294967296 k k0 Sqrt[2 Pi] x 8589934592 k k0 Sqrt[2 Pi] x 16777216 k k0 Sqrt[2 Pi] x 16777216 k k0 Sqrt[2 Pi] x 16777216 k k0 Sqrt[2 Pi] x 8388608 k k0 Sqrt[2 Pi] x 8388608 k k0 Sqrt[2 Pi] x 16777216 k k0 Sqrt[2 Pi] x 131072 k k0 Sqrt[2 Pi] x 131072 k k0 Sqrt[2 Pi] x 131072 k k0 Sqrt[2 Pi] x 65536 k k0 Sqrt[2 Pi] x 65536 k k0 Sqrt[2 Pi] x 131072 k k0 Sqrt[2 Pi] x 512 k k0 Sqrt[2 Pi] x 512 k k0 Sqrt[2 Pi] x 512 k k0 Sqrt[2 Pi] x 256 k k0 Sqrt[2 Pi] x 256 k k0 Sqrt[2 Pi] x 512 k k0 Sqrt[2 Pi] x 4 k k0 Sqrt[2 Pi] x 4 k k0 Sqrt[2 Pi] x 4 k k0 Sqrt[2 Pi] x 2 k k0 Sqrt[2 Pi] x 2 k k0 Sqrt[2 Pi] x 4 k k0 Sqrt[2 Pi] x -Series[Integrate[(E^(I*k0*x)*(1 - E^(-(c*x)))^5*BesselJ[0, k*x])/(k0^5*x^4), {x, 0, Infinity}, Assumptions -> n == 0 && q == 5 && κ == 5 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0 && k < k0], {k, Infinity, 10}] - -Simplify::time: Time spent on a transformation exceeded 300. seconds, and the transformation was aborted. Increasing the value of TimeConstraint option may improve the result of simplification. -Integrate[(E^(I*k0*x)*(1 - E^(-(c*x)))^5*BesselJ[0, k*x])/(k0^5*x^4), {x, 0, Infinity}, Assumptions -> n == 0 && q == 5 && κ == 5] diff --git a/besseltransforms/ksmall/5-5-1 b/besseltransforms/ksmall/5-5-1 deleted file mode 100644 index f952c67..0000000 --- a/besseltransforms/ksmall/5-5-1 +++ /dev/null @@ -1,13 +0,0 @@ -Integrate[(E^(I*k0*x)*(1 - E^(-(c*x)))^5*BesselJ[1, k*x])/(k0^5*x^4), {x, 0, Infinity}, Assumptions -> n == 1 && q == 5 && κ == 5 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0 && k < k0] -Integrate((Power(E,I*k0*x)*Power(1 - Power(E,-(c*x)),5)*BesselJ(1,k*x))/(Power(k0,5)*Power(x,4)),List(x,0,DirectedInfinity(1)),Rule(Assumptions,n == 1 && q == 5 && κ == 5 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0 && k < k0)) - - I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi I k0 x 2 Pi -5 c x + I k0 x 2 Pi -4 c x + I k0 x 2 Pi -3 c x + I k0 x 2 Pi -2 c x + I k0 x 2 Pi -(c x) + I k0 x 2 Pi I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi - 14783093325 E Cos[-- + k x] 14783093325 E Cos[-- + k x] 73915466625 E Cos[-- + k x] 73915466625 E Cos[-- + k x] 73915466625 E Cos[-- + k x] 73915466625 E Cos[-- + k x] 2837835 E Cos[-- + k x] 2837835 E Cos[-- + k x] 14189175 E Cos[-- + k x] 14189175 E Cos[-- + k x] 14189175 E Cos[-- + k x] 14189175 E Cos[-- + k x] 4725 E Cos[-- + k x] 4725 E Cos[-- + k x] 23625 E Cos[-- + k x] 23625 E Cos[-- + k x] 23625 E Cos[-- + k x] 23625 E Cos[-- + k x] 15 E Cos[-- + k x] 15 E Cos[-- + k x] 75 E Cos[-- + k x] 75 E Cos[-- + k x] 75 E Cos[-- + k x] 75 E Cos[-- + k x] E Sqrt[--] Cos[-- + k x] E Sqrt[--] Cos[-- + k x] 5 E Sqrt[--] Cos[-- + k x] 10 E Sqrt[--] Cos[-- + k x] 10 E Sqrt[--] Cos[-- + k x] 5 E Sqrt[--] Cos[-- + k x] 468131288625 E Sin[-- + k x] 468131288625 E Sin[-- + k x] 2340656443125 E Sin[-- + k x] 2340656443125 E Sin[-- + k x] 2340656443125 E Sin[-- + k x] 2340656443125 E Sin[-- + k x] 66891825 E Sin[-- + k x] 66891825 E Sin[-- + k x] 334459125 E Sin[-- + k x] 334459125 E Sin[-- + k x] 334459125 E Sin[-- + k x] 334459125 E Sin[-- + k x] 72765 E Sin[-- + k x] 72765 E Sin[-- + k x] 363825 E Sin[-- + k x] 363825 E Sin[-- + k x] 363825 E Sin[-- + k x] 363825 E Sin[-- + k x] 105 E Sin[-- + k x] 105 E Sin[-- + k x] 525 E Sin[-- + k x] 525 E Sin[-- + k x] 525 E Sin[-- + k x] 525 E Sin[-- + k x] 3 E Sin[-- + k x] 3 E Sin[-- + k x] 15 E Sin[-- + k x] 15 E Sin[-- + k x] 15 E Sin[-- + k x] 15 E Sin[-- + k x] - 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 Pi 4 Pi 4 Pi 4 Pi 4 Pi 4 Pi 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 -Integrate::idiv: Integral of ------------------------------------- - ------------------------------------------ + ------------------------------------------ - ------------------------------------------ + ------------------------------------------ - ------------------------------------------ - ---------------------------------- + -------------------------------------- - --------------------------------------- + --------------------------------------- - --------------------------------------- + --------------------------------------- + ------------------------------- - ----------------------------------- + ------------------------------------ - ------------------------------------ + ------------------------------------ - ------------------------------------ - ---------------------------- + --------------------------------- - --------------------------------- + --------------------------------- - --------------------------------- + --------------------------------- - ------------------------------ + --------------------------------------- - ----------------------------------------- + ------------------------------------------ - ------------------------------------------ + ----------------------------------------- + ------------------------------------- - ------------------------------------------- + -------------------------------------------- - -------------------------------------------- + -------------------------------------------- - -------------------------------------------- - ----------------------------------- + --------------------------------------- - ---------------------------------------- + ---------------------------------------- - ---------------------------------------- + ---------------------------------------- + --------------------------------- - ------------------------------------ + ------------------------------------- - ------------------------------------- + ------------------------------------- - ------------------------------------- - ----------------------------- + ---------------------------------- - ---------------------------------- + ---------------------------------- - ---------------------------------- + ---------------------------------- + --------------------------- - -------------------------------- + --------------------------------- - --------------------------------- + --------------------------------- - --------------------------------- does not converge on {0, Infinity}. - 17/2 5 25/2 17/2 5 25/2 17/2 5 25/2 17/2 5 25/2 17/2 5 25/2 17/2 5 25/2 13/2 5 21/2 13/2 5 21/2 13/2 5 21/2 13/2 5 21/2 13/2 5 21/2 13/2 5 21/2 9/2 5 17/2 9/2 5 17/2 9/2 5 17/2 9/2 5 17/2 9/2 5 17/2 9/2 5 17/2 5/2 5 13/2 5/2 5 13/2 5/2 5 13/2 5/2 5 13/2 5/2 5 13/2 5/2 5 13/2 5 9/2 5 9/2 5 9/2 5 9/2 5 9/2 5 9/2 19/2 5 27/2 19/2 5 27/2 19/2 5 27/2 19/2 5 27/2 19/2 5 27/2 19/2 5 27/2 15/2 5 23/2 15/2 5 23/2 15/2 5 23/2 15/2 5 23/2 15/2 5 23/2 15/2 5 23/2 11/2 5 19/2 11/2 5 19/2 11/2 5 19/2 11/2 5 19/2 11/2 5 19/2 11/2 5 19/2 7/2 5 15/2 7/2 5 15/2 7/2 5 15/2 7/2 5 15/2 7/2 5 15/2 7/2 5 15/2 3/2 5 11/2 3/2 5 11/2 3/2 5 11/2 3/2 5 11/2 3/2 5 11/2 3/2 5 11/2 - 1073741824 k k0 Sqrt[2 Pi] x 1073741824 k k0 Sqrt[2 Pi] x 1073741824 k k0 Sqrt[2 Pi] x 536870912 k k0 Sqrt[2 Pi] x 536870912 k k0 Sqrt[2 Pi] x 1073741824 k k0 Sqrt[2 Pi] x 2097152 k k0 Sqrt[2 Pi] x 2097152 k k0 Sqrt[2 Pi] x 2097152 k k0 Sqrt[2 Pi] x 1048576 k k0 Sqrt[2 Pi] x 1048576 k k0 Sqrt[2 Pi] x 2097152 k k0 Sqrt[2 Pi] x 16384 k k0 Sqrt[2 Pi] x 16384 k k0 Sqrt[2 Pi] x 16384 k k0 Sqrt[2 Pi] x 8192 k k0 Sqrt[2 Pi] x 8192 k k0 Sqrt[2 Pi] x 16384 k k0 Sqrt[2 Pi] x 64 k k0 Sqrt[2 Pi] x 64 k k0 Sqrt[2 Pi] x 64 k k0 Sqrt[2 Pi] x 32 k k0 Sqrt[2 Pi] x 32 k k0 Sqrt[2 Pi] x 64 k k0 Sqrt[2 Pi] x Sqrt[k] k0 x Sqrt[k] k0 x Sqrt[k] k0 x Sqrt[k] k0 x Sqrt[k] k0 x Sqrt[k] k0 x 8589934592 k k0 Sqrt[2 Pi] x 8589934592 k k0 Sqrt[2 Pi] x 8589934592 k k0 Sqrt[2 Pi] x 4294967296 k k0 Sqrt[2 Pi] x 4294967296 k k0 Sqrt[2 Pi] x 8589934592 k k0 Sqrt[2 Pi] x 16777216 k k0 Sqrt[2 Pi] x 16777216 k k0 Sqrt[2 Pi] x 16777216 k k0 Sqrt[2 Pi] x 8388608 k k0 Sqrt[2 Pi] x 8388608 k k0 Sqrt[2 Pi] x 16777216 k k0 Sqrt[2 Pi] x 131072 k k0 Sqrt[2 Pi] x 131072 k k0 Sqrt[2 Pi] x 131072 k k0 Sqrt[2 Pi] x 65536 k k0 Sqrt[2 Pi] x 65536 k k0 Sqrt[2 Pi] x 131072 k k0 Sqrt[2 Pi] x 512 k k0 Sqrt[2 Pi] x 512 k k0 Sqrt[2 Pi] x 512 k k0 Sqrt[2 Pi] x 256 k k0 Sqrt[2 Pi] x 256 k k0 Sqrt[2 Pi] x 512 k k0 Sqrt[2 Pi] x 4 k k0 Sqrt[2 Pi] x 4 k k0 Sqrt[2 Pi] x 4 k k0 Sqrt[2 Pi] x 2 k k0 Sqrt[2 Pi] x 2 k k0 Sqrt[2 Pi] x 4 k k0 Sqrt[2 Pi] x -Series[Integrate[(E^(I*k0*x)*(1 - E^(-(c*x)))^5*BesselJ[1, k*x])/(k0^5*x^4), {x, 0, Infinity}, Assumptions -> n == 1 && q == 5 && κ == 5 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0 && k < k0], {k, Infinity, 10}] - -Simplify::time: Time spent on a transformation exceeded 300. seconds, and the transformation was aborted. Increasing the value of TimeConstraint option may improve the result of simplification. -Integrate[(E^(I*k0*x)*(1 - E^(-(c*x)))^5*BesselJ[1, k*x])/(k0^5*x^4), {x, 0, Infinity}, Assumptions -> n == 1 && q == 5 && κ == 5] diff --git a/besseltransforms/ksmall/5-5-2 b/besseltransforms/ksmall/5-5-2 deleted file mode 100644 index a56d134..0000000 --- a/besseltransforms/ksmall/5-5-2 +++ /dev/null @@ -1,11 +0,0 @@ -Integrate[(E^(I*k0*x)*(1 - E^(-(c*x)))^5*BesselJ[2, k*x])/(k0^5*x^4), {x, 0, Infinity}, Assumptions -> n == 2 && q == 5 && κ == 5 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0 && k < k0] -Integrate((Power(E,I*k0*x)*Power(1 - Power(E,-(c*x)),5)*BesselJ(2,k*x))/(Power(k0,5)*Power(x,4)),List(x,0,DirectedInfinity(1)),Rule(Assumptions,n == 2 && q == 5 && κ == 5 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0 && k < k0)) - - I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi I k0 x 2 Pi -5 c x + I k0 x 2 Pi -4 c x + I k0 x 2 Pi -3 c x + I k0 x 2 Pi -2 c x + I k0 x 2 Pi -(c x) + I k0 x 2 Pi I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi - -21606059475 E Cos[-- - k x] 21606059475 E Cos[-- - k x] 108030297375 E Cos[-- - k x] 108030297375 E Cos[-- - k x] 108030297375 E Cos[-- - k x] 108030297375 E Cos[-- - k x] 4729725 E Cos[-- - k x] 4729725 E Cos[-- - k x] 23648625 E Cos[-- - k x] 23648625 E Cos[-- - k x] 23648625 E Cos[-- - k x] 23648625 E Cos[-- - k x] 10395 E Cos[-- - k x] 10395 E Cos[-- - k x] 51975 E Cos[-- - k x] 51975 E Cos[-- - k x] 51975 E Cos[-- - k x] 51975 E Cos[-- - k x] 105 E Cos[-- - k x] 105 E Cos[-- - k x] 525 E Cos[-- - k x] 525 E Cos[-- - k x] 525 E Cos[-- - k x] 525 E Cos[-- - k x] E Sqrt[--] Cos[-- - k x] E Sqrt[--] Cos[-- - k x] 5 E Sqrt[--] Cos[-- - k x] 10 E Sqrt[--] Cos[-- - k x] 10 E Sqrt[--] Cos[-- - k x] 5 E Sqrt[--] Cos[-- - k x] 655383804075 E Sin[-- - k x] 655383804075 E Sin[-- - k x] 3276919020375 E Sin[-- - k x] 3276919020375 E Sin[-- - k x] 3276919020375 E Sin[-- - k x] 3276919020375 E Sin[-- - k x] 103378275 E Sin[-- - k x] 103378275 E Sin[-- - k x] 516891375 E Sin[-- - k x] 516891375 E Sin[-- - k x] 516891375 E Sin[-- - k x] 516891375 E Sin[-- - k x] 135135 E Sin[-- - k x] 135135 E Sin[-- - k x] 675675 E Sin[-- - k x] 675675 E Sin[-- - k x] 675675 E Sin[-- - k x] 675675 E Sin[-- - k x] 315 E Sin[-- - k x] 315 E Sin[-- - k x] 1575 E Sin[-- - k x] 1575 E Sin[-- - k x] 1575 E Sin[-- - k x] 1575 E Sin[-- - k x] 15 E Sin[-- - k x] 15 E Sin[-- - k x] 75 E Sin[-- - k x] 75 E Sin[-- - k x] 75 E Sin[-- - k x] 75 E Sin[-- - k x] - 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 Pi 4 Pi 4 Pi 4 Pi 4 Pi 4 Pi 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 -Integrate::idiv: Integral of ------------------------------------- + ------------------------------------------ - ------------------------------------------- + ------------------------------------------- - ------------------------------------------- + ------------------------------------------- + ---------------------------------- - -------------------------------------- + --------------------------------------- - --------------------------------------- + --------------------------------------- - --------------------------------------- - ------------------------------- + ------------------------------------ - ------------------------------------ + ------------------------------------ - ------------------------------------ + ------------------------------------ + ---------------------------- - ---------------------------------- + ---------------------------------- - ---------------------------------- + ---------------------------------- - ---------------------------------- - ------------------------------ + --------------------------------------- - ----------------------------------------- + ------------------------------------------ - ------------------------------------------ + ----------------------------------------- + ------------------------------------- - ------------------------------------------- + -------------------------------------------- - -------------------------------------------- + -------------------------------------------- - -------------------------------------------- - ----------------------------------- + ---------------------------------------- - ---------------------------------------- + ---------------------------------------- - ---------------------------------------- + ---------------------------------------- + --------------------------------- - ------------------------------------- + ------------------------------------- - ------------------------------------- + ------------------------------------- - ------------------------------------- - ----------------------------- + ---------------------------------- - ----------------------------------- + ----------------------------------- - ----------------------------------- + ----------------------------------- - --------------------------- + --------------------------------- - --------------------------------- + --------------------------------- - --------------------------------- + --------------------------------- does not converge on {0, Infinity}. - 17/2 5 25/2 17/2 5 25/2 17/2 5 25/2 17/2 5 25/2 17/2 5 25/2 17/2 5 25/2 13/2 5 21/2 13/2 5 21/2 13/2 5 21/2 13/2 5 21/2 13/2 5 21/2 13/2 5 21/2 9/2 5 17/2 9/2 5 17/2 9/2 5 17/2 9/2 5 17/2 9/2 5 17/2 9/2 5 17/2 5/2 5 13/2 5/2 5 13/2 5/2 5 13/2 5/2 5 13/2 5/2 5 13/2 5/2 5 13/2 5 9/2 5 9/2 5 9/2 5 9/2 5 9/2 5 9/2 19/2 5 27/2 19/2 5 27/2 19/2 5 27/2 19/2 5 27/2 19/2 5 27/2 19/2 5 27/2 15/2 5 23/2 15/2 5 23/2 15/2 5 23/2 15/2 5 23/2 15/2 5 23/2 15/2 5 23/2 11/2 5 19/2 11/2 5 19/2 11/2 5 19/2 11/2 5 19/2 11/2 5 19/2 11/2 5 19/2 7/2 5 15/2 7/2 5 15/2 7/2 5 15/2 7/2 5 15/2 7/2 5 15/2 7/2 5 15/2 3/2 5 11/2 3/2 5 11/2 3/2 5 11/2 3/2 5 11/2 3/2 5 11/2 3/2 5 11/2 - 1073741824 k k0 Sqrt[2 Pi] x 1073741824 k k0 Sqrt[2 Pi] x 1073741824 k k0 Sqrt[2 Pi] x 536870912 k k0 Sqrt[2 Pi] x 536870912 k k0 Sqrt[2 Pi] x 1073741824 k k0 Sqrt[2 Pi] x 2097152 k k0 Sqrt[2 Pi] x 2097152 k k0 Sqrt[2 Pi] x 2097152 k k0 Sqrt[2 Pi] x 1048576 k k0 Sqrt[2 Pi] x 1048576 k k0 Sqrt[2 Pi] x 2097152 k k0 Sqrt[2 Pi] x 16384 k k0 Sqrt[2 Pi] x 16384 k k0 Sqrt[2 Pi] x 16384 k k0 Sqrt[2 Pi] x 8192 k k0 Sqrt[2 Pi] x 8192 k k0 Sqrt[2 Pi] x 16384 k k0 Sqrt[2 Pi] x 64 k k0 Sqrt[2 Pi] x 64 k k0 Sqrt[2 Pi] x 64 k k0 Sqrt[2 Pi] x 32 k k0 Sqrt[2 Pi] x 32 k k0 Sqrt[2 Pi] x 64 k k0 Sqrt[2 Pi] x Sqrt[k] k0 x Sqrt[k] k0 x Sqrt[k] k0 x Sqrt[k] k0 x Sqrt[k] k0 x Sqrt[k] k0 x 8589934592 k k0 Sqrt[2 Pi] x 8589934592 k k0 Sqrt[2 Pi] x 8589934592 k k0 Sqrt[2 Pi] x 4294967296 k k0 Sqrt[2 Pi] x 4294967296 k k0 Sqrt[2 Pi] x 8589934592 k k0 Sqrt[2 Pi] x 16777216 k k0 Sqrt[2 Pi] x 16777216 k k0 Sqrt[2 Pi] x 16777216 k k0 Sqrt[2 Pi] x 8388608 k k0 Sqrt[2 Pi] x 8388608 k k0 Sqrt[2 Pi] x 16777216 k k0 Sqrt[2 Pi] x 131072 k k0 Sqrt[2 Pi] x 131072 k k0 Sqrt[2 Pi] x 131072 k k0 Sqrt[2 Pi] x 65536 k k0 Sqrt[2 Pi] x 65536 k k0 Sqrt[2 Pi] x 131072 k k0 Sqrt[2 Pi] x 512 k k0 Sqrt[2 Pi] x 512 k k0 Sqrt[2 Pi] x 512 k k0 Sqrt[2 Pi] x 256 k k0 Sqrt[2 Pi] x 256 k k0 Sqrt[2 Pi] x 512 k k0 Sqrt[2 Pi] x 4 k k0 Sqrt[2 Pi] x 4 k k0 Sqrt[2 Pi] x 4 k k0 Sqrt[2 Pi] x 2 k k0 Sqrt[2 Pi] x 2 k k0 Sqrt[2 Pi] x 4 k k0 Sqrt[2 Pi] x -Series[Integrate[(E^(I*k0*x)*(1 - E^(-(c*x)))^5*BesselJ[2, k*x])/(k0^5*x^4), {x, 0, Infinity}, Assumptions -> n == 2 && q == 5 && κ == 5 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0 && k < k0], {k, Infinity, 10}] -Integrate[(E^(I*k0*x)*(1 - E^(-(c*x)))^5*BesselJ[2, k*x])/(k0^5*x^4), {x, 0, Infinity}, Assumptions -> n == 2 && q == 5 && κ == 5] diff --git a/besseltransforms/ksmall/5-5-3 b/besseltransforms/ksmall/5-5-3 deleted file mode 100644 index d5216b8..0000000 --- a/besseltransforms/ksmall/5-5-3 +++ /dev/null @@ -1,13 +0,0 @@ -Integrate[(E^(I*k0*x)*(1 - E^(-(c*x)))^5*BesselJ[3, k*x])/(k0^5*x^4), {x, 0, Infinity}, Assumptions -> n == 3 && q == 5 && κ == 5 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0 && k < k0] -Integrate((Power(E,I*k0*x)*Power(1 - Power(E,-(c*x)),5)*BesselJ(3,k*x))/(Power(k0,5)*Power(x,4)),List(x,0,DirectedInfinity(1)),Rule(Assumptions,n == 3 && q == 5 && κ == 5 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0 && k < k0)) - - I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi I k0 x 2 Pi -5 c x + I k0 x 2 Pi -4 c x + I k0 x 2 Pi -3 c x + I k0 x 2 Pi -2 c x + I k0 x 2 Pi -(c x) + I k0 x 2 Pi I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi - -41247931725 E Cos[-- + k x] 41247931725 E Cos[-- + k x] 206239658625 E Cos[-- + k x] 206239658625 E Cos[-- + k x] 206239658625 E Cos[-- + k x] 206239658625 E Cos[-- + k x] 11486475 E Cos[-- + k x] 11486475 E Cos[-- + k x] 57432375 E Cos[-- + k x] 57432375 E Cos[-- + k x] 57432375 E Cos[-- + k x] 57432375 E Cos[-- + k x] 45045 E Cos[-- + k x] 45045 E Cos[-- + k x] 225225 E Cos[-- + k x] 225225 E Cos[-- + k x] 225225 E Cos[-- + k x] 225225 E Cos[-- + k x] 945 E Cos[-- + k x] 945 E Cos[-- + k x] 4725 E Cos[-- + k x] 4725 E Cos[-- + k x] 4725 E Cos[-- + k x] 4725 E Cos[-- + k x] E Sqrt[--] Cos[-- + k x] E Sqrt[--] Cos[-- + k x] 5 E Sqrt[--] Cos[-- + k x] 10 E Sqrt[--] Cos[-- + k x] 10 E Sqrt[--] Cos[-- + k x] 5 E Sqrt[--] Cos[-- + k x] 1159525191825 E Sin[-- + k x] 1159525191825 E Sin[-- + k x] 5797625959125 E Sin[-- + k x] 5797625959125 E Sin[-- + k x] 5797625959125 E Sin[-- + k x] 5797625959125 E Sin[-- + k x] 218243025 E Sin[-- + k x] 218243025 E Sin[-- + k x] 1091215125 E Sin[-- + k x] 1091215125 E Sin[-- + k x] 1091215125 E Sin[-- + k x] 1091215125 E Sin[-- + k x] 405405 E Sin[-- + k x] 405405 E Sin[-- + k x] 2027025 E Sin[-- + k x] 2027025 E Sin[-- + k x] 2027025 E Sin[-- + k x] 2027025 E Sin[-- + k x] 3465 E Sin[-- + k x] 3465 E Sin[-- + k x] 17325 E Sin[-- + k x] 17325 E Sin[-- + k x] 17325 E Sin[-- + k x] 17325 E Sin[-- + k x] 35 E Sin[-- + k x] 35 E Sin[-- + k x] 175 E Sin[-- + k x] 175 E Sin[-- + k x] 175 E Sin[-- + k x] 175 E Sin[-- + k x] - 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 Pi 4 Pi 4 Pi 4 Pi 4 Pi 4 Pi 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 -Integrate::idiv: Integral of ------------------------------------- + ------------------------------------------ - ------------------------------------------- + ------------------------------------------- - ------------------------------------------- + ------------------------------------------- + ---------------------------------- - --------------------------------------- + --------------------------------------- - --------------------------------------- + --------------------------------------- - --------------------------------------- - ------------------------------- + ------------------------------------ - ------------------------------------- + ------------------------------------- - ------------------------------------- + ------------------------------------- - ---------------------------- + ---------------------------------- - ----------------------------------- + ----------------------------------- - ----------------------------------- + ----------------------------------- + ------------------------------ - --------------------------------------- + ----------------------------------------- - ------------------------------------------ + ------------------------------------------ - ----------------------------------------- - ------------------------------------- + -------------------------------------------- - -------------------------------------------- + -------------------------------------------- - -------------------------------------------- + -------------------------------------------- + ----------------------------------- - ---------------------------------------- + ----------------------------------------- - ----------------------------------------- + ----------------------------------------- - ----------------------------------------- - --------------------------------- + ------------------------------------- - -------------------------------------- + -------------------------------------- - -------------------------------------- + -------------------------------------- + ----------------------------- - ----------------------------------- + ------------------------------------ - ------------------------------------ + ------------------------------------ - ------------------------------------ - --------------------------- + --------------------------------- - ---------------------------------- + ---------------------------------- - ---------------------------------- + ---------------------------------- does not converge on {0, Infinity}. - 17/2 5 25/2 17/2 5 25/2 17/2 5 25/2 17/2 5 25/2 17/2 5 25/2 17/2 5 25/2 13/2 5 21/2 13/2 5 21/2 13/2 5 21/2 13/2 5 21/2 13/2 5 21/2 13/2 5 21/2 9/2 5 17/2 9/2 5 17/2 9/2 5 17/2 9/2 5 17/2 9/2 5 17/2 9/2 5 17/2 5/2 5 13/2 5/2 5 13/2 5/2 5 13/2 5/2 5 13/2 5/2 5 13/2 5/2 5 13/2 5 9/2 5 9/2 5 9/2 5 9/2 5 9/2 5 9/2 19/2 5 27/2 19/2 5 27/2 19/2 5 27/2 19/2 5 27/2 19/2 5 27/2 19/2 5 27/2 15/2 5 23/2 15/2 5 23/2 15/2 5 23/2 15/2 5 23/2 15/2 5 23/2 15/2 5 23/2 11/2 5 19/2 11/2 5 19/2 11/2 5 19/2 11/2 5 19/2 11/2 5 19/2 11/2 5 19/2 7/2 5 15/2 7/2 5 15/2 7/2 5 15/2 7/2 5 15/2 7/2 5 15/2 7/2 5 15/2 3/2 5 11/2 3/2 5 11/2 3/2 5 11/2 3/2 5 11/2 3/2 5 11/2 3/2 5 11/2 - 1073741824 k k0 Sqrt[2 Pi] x 1073741824 k k0 Sqrt[2 Pi] x 1073741824 k k0 Sqrt[2 Pi] x 536870912 k k0 Sqrt[2 Pi] x 536870912 k k0 Sqrt[2 Pi] x 1073741824 k k0 Sqrt[2 Pi] x 2097152 k k0 Sqrt[2 Pi] x 2097152 k k0 Sqrt[2 Pi] x 2097152 k k0 Sqrt[2 Pi] x 1048576 k k0 Sqrt[2 Pi] x 1048576 k k0 Sqrt[2 Pi] x 2097152 k k0 Sqrt[2 Pi] x 16384 k k0 Sqrt[2 Pi] x 16384 k k0 Sqrt[2 Pi] x 16384 k k0 Sqrt[2 Pi] x 8192 k k0 Sqrt[2 Pi] x 8192 k k0 Sqrt[2 Pi] x 16384 k k0 Sqrt[2 Pi] x 64 k k0 Sqrt[2 Pi] x 64 k k0 Sqrt[2 Pi] x 64 k k0 Sqrt[2 Pi] x 32 k k0 Sqrt[2 Pi] x 32 k k0 Sqrt[2 Pi] x 64 k k0 Sqrt[2 Pi] x Sqrt[k] k0 x Sqrt[k] k0 x Sqrt[k] k0 x Sqrt[k] k0 x Sqrt[k] k0 x Sqrt[k] k0 x 8589934592 k k0 Sqrt[2 Pi] x 8589934592 k k0 Sqrt[2 Pi] x 8589934592 k k0 Sqrt[2 Pi] x 4294967296 k k0 Sqrt[2 Pi] x 4294967296 k k0 Sqrt[2 Pi] x 8589934592 k k0 Sqrt[2 Pi] x 16777216 k k0 Sqrt[2 Pi] x 16777216 k k0 Sqrt[2 Pi] x 16777216 k k0 Sqrt[2 Pi] x 8388608 k k0 Sqrt[2 Pi] x 8388608 k k0 Sqrt[2 Pi] x 16777216 k k0 Sqrt[2 Pi] x 131072 k k0 Sqrt[2 Pi] x 131072 k k0 Sqrt[2 Pi] x 131072 k k0 Sqrt[2 Pi] x 65536 k k0 Sqrt[2 Pi] x 65536 k k0 Sqrt[2 Pi] x 131072 k k0 Sqrt[2 Pi] x 512 k k0 Sqrt[2 Pi] x 512 k k0 Sqrt[2 Pi] x 512 k k0 Sqrt[2 Pi] x 256 k k0 Sqrt[2 Pi] x 256 k k0 Sqrt[2 Pi] x 512 k k0 Sqrt[2 Pi] x 4 k k0 Sqrt[2 Pi] x 4 k k0 Sqrt[2 Pi] x 4 k k0 Sqrt[2 Pi] x 2 k k0 Sqrt[2 Pi] x 2 k k0 Sqrt[2 Pi] x 4 k k0 Sqrt[2 Pi] x -Series[Integrate[(E^(I*k0*x)*(1 - E^(-(c*x)))^5*BesselJ[3, k*x])/(k0^5*x^4), {x, 0, Infinity}, Assumptions -> n == 3 && q == 5 && κ == 5 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0 && k < k0], {k, Infinity, 10}] - -Simplify::time: Time spent on a transformation exceeded 300. seconds, and the transformation was aborted. Increasing the value of TimeConstraint option may improve the result of simplification. -Integrate[(E^(I*k0*x)*(1 - E^(-(c*x)))^5*BesselJ[3, k*x])/(k0^5*x^4), {x, 0, Infinity}, Assumptions -> n == 3 && q == 5 && κ == 5] diff --git a/besseltransforms/ksmall/5-5-4 b/besseltransforms/ksmall/5-5-4 deleted file mode 100644 index dcba466..0000000 --- a/besseltransforms/ksmall/5-5-4 +++ /dev/null @@ -1,4 +0,0 @@ -(-(k^6*(-35 + 16*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0) + 2*k^4*(-35 + 24*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^3 + 8*k^2*(-7 + 6*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^5 + 16*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^7)/(336*k^4) + (k^6*(-35 + 16*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0) + 2*k^4*(-35 + 24*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^3 + 8*k^2*(-7 + 6*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^5 + 16*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^7)/(168*k^4) - (k^6*(-35 + 16*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0) + 2*k^4*(-35 + 24*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^3 + 8*k^2*(-7 + 6*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^5 + 16*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^7)/(168*k^4) + (k^6*(-35 + 16*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0) + 2*k^4*(-35 + 24*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^3 + 8*k^2*(-7 + 6*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^5 + 16*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^7)/(336*k^4) - (k^6*(-35 + 16*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0) + 2*k^4*(-35 + 24*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^3 + 8*k^2*(-7 + 6*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^5 + 16*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^7)/(1680*k^4) + (I/1680*(k^6*(35*k0 - 16*Sqrt[-k^2 + k0^2]) + 16*k0^6*(-k0 + Sqrt[-k^2 + k0^2]) - 8*k^2*k0^4*(-7*k0 + 6*Sqrt[-k^2 + k0^2]) + 2*k^4*k0^2*(-35*k0 + 24*Sqrt[-k^2 + k0^2])))/k^4)/k0^5 -(-(Power(k,6)*(-35 + 16*Sqrt(1 + Power(k,2)/Power(c - Complex(0,1)*k0,2)))*(c - Complex(0,1)*k0) + 2*Power(k,4)*(-35 + 24*Sqrt(1 + Power(k,2)/Power(c - Complex(0,1)*k0,2)))*Power(c - Complex(0,1)*k0,3) + 8*Power(k,2)*(-7 + 6*Sqrt(1 + Power(k,2)/Power(c - Complex(0,1)*k0,2)))*Power(c - Complex(0,1)*k0,5) + 16*(-1 + Sqrt(1 + Power(k,2)/Power(c - Complex(0,1)*k0,2)))*Power(c - Complex(0,1)*k0,7))/(336.*Power(k,4)) + (Power(k,6)*(-35 + 16*Sqrt(1 + Power(k,2)/Power(2*c - Complex(0,1)*k0,2)))*(2*c - Complex(0,1)*k0) + 2*Power(k,4)*(-35 + 24*Sqrt(1 + Power(k,2)/Power(2*c - Complex(0,1)*k0,2)))*Power(2*c - Complex(0,1)*k0,3) + 8*Power(k,2)*(-7 + 6*Sqrt(1 + Power(k,2)/Power(2*c - Complex(0,1)*k0,2)))*Power(2*c - Complex(0,1)*k0,5) + 16*(-1 + Sqrt(1 + Power(k,2)/Power(2*c - Complex(0,1)*k0,2)))*Power(2*c - Complex(0,1)*k0,7))/(168.*Power(k,4)) - (Power(k,6)*(-35 + 16*Sqrt(1 + Power(k,2)/Power(3*c - Complex(0,1)*k0,2)))*(3*c - Complex(0,1)*k0) + 2*Power(k,4)*(-35 + 24*Sqrt(1 + Power(k,2)/Power(3*c - Complex(0,1)*k0,2)))*Power(3*c - Complex(0,1)*k0,3) + 8*Power(k,2)*(-7 + 6*Sqrt(1 + Power(k,2)/Power(3*c - Complex(0,1)*k0,2)))*Power(3*c - Complex(0,1)*k0,5) + 16*(-1 + Sqrt(1 + Power(k,2)/Power(3*c - Complex(0,1)*k0,2)))*Power(3*c - Complex(0,1)*k0,7))/(168.*Power(k,4)) + (Power(k,6)*(-35 + 16*Sqrt(1 + Power(k,2)/Power(4*c - Complex(0,1)*k0,2)))*(4*c - Complex(0,1)*k0) + 2*Power(k,4)*(-35 + 24*Sqrt(1 + Power(k,2)/Power(4*c - Complex(0,1)*k0,2)))*Power(4*c - Complex(0,1)*k0,3) + 8*Power(k,2)*(-7 + 6*Sqrt(1 + Power(k,2)/Power(4*c - Complex(0,1)*k0,2)))*Power(4*c - Complex(0,1)*k0,5) + 16*(-1 + Sqrt(1 + Power(k,2)/Power(4*c - Complex(0,1)*k0,2)))*Power(4*c - Complex(0,1)*k0,7))/(336.*Power(k,4)) - (Power(k,6)*(-35 + 16*Sqrt(1 + Power(k,2)/Power(5*c - Complex(0,1)*k0,2)))*(5*c - Complex(0,1)*k0) + 2*Power(k,4)*(-35 + 24*Sqrt(1 + Power(k,2)/Power(5*c - Complex(0,1)*k0,2)))*Power(5*c - Complex(0,1)*k0,3) + 8*Power(k,2)*(-7 + 6*Sqrt(1 + Power(k,2)/Power(5*c - Complex(0,1)*k0,2)))*Power(5*c - Complex(0,1)*k0,5) + 16*(-1 + Sqrt(1 + Power(k,2)/Power(5*c - Complex(0,1)*k0,2)))*Power(5*c - Complex(0,1)*k0,7))/(1680.*Power(k,4)) + (Complex(0,0.0005952380952380953)*(Power(k,6)*(35*k0 - 16*Sqrt(-Power(k,2) + Power(k0,2))) + 16*Power(k0,6)*(-k0 + Sqrt(-Power(k,2) + Power(k0,2))) - 8*Power(k,2)*Power(k0,4)*(-7*k0 + 6*Sqrt(-Power(k,2) + Power(k0,2))) + 2*Power(k,4)*Power(k0,2)*(-35*k0 + 24*Sqrt(-Power(k,2) + Power(k0,2)))))/Power(k,4))/Power(k0,5) -SeriesData[k, Infinity, {(4*c^5)/k0^5, (-75*c^6)/(2*k0^5) + ((15*I)*c^5)/k0^4, (160*c^7)/k0^5 - ((120*I)*c^6)/k0^4 - (24*c^5)/k0^3, (-35*(75*c^8 - (80*I)*c^7*k0 - 30*c^6*k0^2 + (4*I)*c^5*k0^3))/(8*k0^5), 0, (21*(2025*c^10 - (3310*I)*c^9*k0 - 2250*c^8*k0^2 + (800*I)*c^7*k0^3 + 150*c^6*k0^4 - (12*I)*c^5*k0^5))/(32*k0^5), 0, (-33*(20900*c^12 - (44860*I)*c^11*k0 - 42525*c^10*k0^2 + (23170*I)*c^9*k0^3 + 7875*c^8*k0^4 - (1680*I)*c^7*k0^5 - 210*c^6*k0^6 + (12*I)*c^5*k0^7))/(64*k0^5)}, 2, 11, 1] --(5*(k^6*(-35 + 16*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0) + 2*k^4*(-35 + 24*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^3 + 8*k^2*(-7 + 6*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^5 + 16*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^7) - 10*(k^6*(-35 + 16*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0) + 2*k^4*(-35 + 24*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^3 + 8*k^2*(-7 + 6*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^5 + 16*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^7) + 10*(k^6*(-35 + 16*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0) + 2*k^4*(-35 + 24*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^3 + 8*k^2*(-7 + 6*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^5 + 16*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^7) - 5*(k^6*(-35 + 16*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0) + 2*k^4*(-35 + 24*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^3 + 8*k^2*(-7 + 6*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^5 + 16*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^7) + k^6*(-35 + 16*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0) + 2*k^4*(-35 + 24*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^3 + 8*k^2*(-7 + 6*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^5 + 16*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^7 - I*(k^6*(35*k0 - 16*Sqrt[-k^2 + k0^2]) + 16*k0^6*(-k0 + Sqrt[-k^2 + k0^2]) - 8*k^2*k0^4*(-7*k0 + 6*Sqrt[-k^2 + k0^2]) + 2*k^4*k0^2*(-35*k0 + 24*Sqrt[-k^2 + k0^2])))/(1680*k^4*k0^5) diff --git a/besseltransforms/ksmall/5-5-5 b/besseltransforms/ksmall/5-5-5 deleted file mode 100644 index 979dc9e..0000000 --- a/besseltransforms/ksmall/5-5-5 +++ /dev/null @@ -1,4 +0,0 @@ -(-(35*k^8 + 8*k^6*(35 - 16*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^2 + 16*k^4*(35 - 24*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^4 + 64*k^2*(7 - 6*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^6 - 128*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^8)/(2688*k^5) + (35*k^8 + 8*k^6*(35 - 16*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^2 + 16*k^4*(35 - 24*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^4 + 64*k^2*(7 - 6*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^6 - 128*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^8)/(1344*k^5) - (35*k^8 + 8*k^6*(35 - 16*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^2 + 16*k^4*(35 - 24*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^4 + 64*k^2*(7 - 6*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^6 - 128*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^8)/(1344*k^5) + (35*k^8 + 8*k^6*(35 - 16*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^2 + 16*k^4*(35 - 24*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^4 + 64*k^2*(7 - 6*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^6 - 128*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^8)/(2688*k^5) - (35*k^8 + 8*k^6*(35 - 16*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^2 + 16*k^4*(35 - 24*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^4 + 64*k^2*(7 - 6*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^6 - 128*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^8)/(13440*k^5) + (35*k^8 + 16*k^4*k0^3*(35*k0 - 24*Sqrt[-k^2 + k0^2]) + 128*k0^7*(k0 - Sqrt[-k^2 + k0^2]) + 64*k^2*k0^5*(-7*k0 + 6*Sqrt[-k^2 + k0^2]) + 8*k^6*k0*(-35*k0 + 16*Sqrt[-k^2 + k0^2]))/(13440*k^5))/k0^5 -(-(35*Power(k,8) + 8*Power(k,6)*(35 - 16*Sqrt(1 + Power(k,2)/Power(c - Complex(0,1)*k0,2)))*Power(c - Complex(0,1)*k0,2) + 16*Power(k,4)*(35 - 24*Sqrt(1 + Power(k,2)/Power(c - Complex(0,1)*k0,2)))*Power(c - Complex(0,1)*k0,4) + 64*Power(k,2)*(7 - 6*Sqrt(1 + Power(k,2)/Power(c - Complex(0,1)*k0,2)))*Power(c - Complex(0,1)*k0,6) - 128*(-1 + Sqrt(1 + Power(k,2)/Power(c - Complex(0,1)*k0,2)))*Power(c - Complex(0,1)*k0,8))/(2688.*Power(k,5)) + (35*Power(k,8) + 8*Power(k,6)*(35 - 16*Sqrt(1 + Power(k,2)/Power(2*c - Complex(0,1)*k0,2)))*Power(2*c - Complex(0,1)*k0,2) + 16*Power(k,4)*(35 - 24*Sqrt(1 + Power(k,2)/Power(2*c - Complex(0,1)*k0,2)))*Power(2*c - Complex(0,1)*k0,4) + 64*Power(k,2)*(7 - 6*Sqrt(1 + Power(k,2)/Power(2*c - Complex(0,1)*k0,2)))*Power(2*c - Complex(0,1)*k0,6) - 128*(-1 + Sqrt(1 + Power(k,2)/Power(2*c - Complex(0,1)*k0,2)))*Power(2*c - Complex(0,1)*k0,8))/(1344.*Power(k,5)) - (35*Power(k,8) + 8*Power(k,6)*(35 - 16*Sqrt(1 + Power(k,2)/Power(3*c - Complex(0,1)*k0,2)))*Power(3*c - Complex(0,1)*k0,2) + 16*Power(k,4)*(35 - 24*Sqrt(1 + Power(k,2)/Power(3*c - Complex(0,1)*k0,2)))*Power(3*c - Complex(0,1)*k0,4) + 64*Power(k,2)*(7 - 6*Sqrt(1 + Power(k,2)/Power(3*c - Complex(0,1)*k0,2)))*Power(3*c - Complex(0,1)*k0,6) - 128*(-1 + Sqrt(1 + Power(k,2)/Power(3*c - Complex(0,1)*k0,2)))*Power(3*c - Complex(0,1)*k0,8))/(1344.*Power(k,5)) + (35*Power(k,8) + 8*Power(k,6)*(35 - 16*Sqrt(1 + Power(k,2)/Power(4*c - Complex(0,1)*k0,2)))*Power(4*c - Complex(0,1)*k0,2) + 16*Power(k,4)*(35 - 24*Sqrt(1 + Power(k,2)/Power(4*c - Complex(0,1)*k0,2)))*Power(4*c - Complex(0,1)*k0,4) + 64*Power(k,2)*(7 - 6*Sqrt(1 + Power(k,2)/Power(4*c - Complex(0,1)*k0,2)))*Power(4*c - Complex(0,1)*k0,6) - 128*(-1 + Sqrt(1 + Power(k,2)/Power(4*c - Complex(0,1)*k0,2)))*Power(4*c - Complex(0,1)*k0,8))/(2688.*Power(k,5)) - (35*Power(k,8) + 8*Power(k,6)*(35 - 16*Sqrt(1 + Power(k,2)/Power(5*c - Complex(0,1)*k0,2)))*Power(5*c - Complex(0,1)*k0,2) + 16*Power(k,4)*(35 - 24*Sqrt(1 + Power(k,2)/Power(5*c - Complex(0,1)*k0,2)))*Power(5*c - Complex(0,1)*k0,4) + 64*Power(k,2)*(7 - 6*Sqrt(1 + Power(k,2)/Power(5*c - Complex(0,1)*k0,2)))*Power(5*c - Complex(0,1)*k0,6) - 128*(-1 + Sqrt(1 + Power(k,2)/Power(5*c - Complex(0,1)*k0,2)))*Power(5*c - Complex(0,1)*k0,8))/(13440.*Power(k,5)) + (35*Power(k,8) + 16*Power(k,4)*Power(k0,3)*(35*k0 - 24*Sqrt(-Power(k,2) + Power(k0,2))) + 128*Power(k0,7)*(k0 - Sqrt(-Power(k,2) + Power(k0,2))) + 64*Power(k,2)*Power(k0,5)*(-7*k0 + 6*Sqrt(-Power(k,2) + Power(k0,2))) + 8*Power(k,6)*k0*(-35*k0 + 16*Sqrt(-Power(k,2) + Power(k0,2))))/(13440.*Power(k,5)))/Power(k0,5) -SeriesData[k, Infinity, {(5*c^5)/k0^5, (-60*c^6)/k0^5 + ((24*I)*c^5)/k0^4, (35*(20*c^7 - (15*I)*c^6*k0 - 3*c^5*k0^2))/(2*k0^5), (-1200*c^8)/k0^5 + ((1280*I)*c^7)/k0^4 + (480*c^6)/k0^3 - ((64*I)*c^5)/k0^2, (105*(331*c^9 - (450*I)*c^8*k0 - 240*c^7*k0^2 + (60*I)*c^6*k0^3 + 6*c^5*k0^4))/(16*k0^5), 0, (-11*(22430*c^11 - (42525*I)*c^10*k0 - 34755*c^9*k0^2 + (15750*I)*c^8*k0^3 + 4200*c^7*k0^4 - (630*I)*c^6*k0^5 - 42*c^5*k0^6))/(32*k0^5), 0, (143*(52507*c^13 - (125400*I)*c^12*k0 - 134580*c^11*k0^2 + (85050*I)*c^10*k0^3 + 34755*c^9*k0^4 - (9450*I)*c^8*k0^5 - 1680*c^7*k0^6 + (180*I)*c^6*k0^7 + 9*c^5*k0^8))/(128*k0^5)}, 2, 11, 1] -(5*k^6*(-35 + 16*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^2 + 10*k^4*(-35 + 24*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^4 + 40*k^2*(-7 + 6*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^6 + 80*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^8 + 10*k^6*(35 - 16*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^2 + 20*k^4*(35 - 24*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^4 + 80*k^2*(7 - 6*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^6 - 160*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^8 + 10*k^6*(-35 + 16*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^2 + 20*k^4*(-35 + 24*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^4 + 80*k^2*(-7 + 6*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^6 + 160*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^8 + 5*k^6*(35 - 16*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^2 + 10*k^4*(35 - 24*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^4 + 40*k^2*(7 - 6*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^6 - 80*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^8 + k^6*(-35 + 16*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^2 + 2*k^4*(-35 + 24*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^4 + 8*k^2*(-7 + 6*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^6 + 16*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^8 + 2*k^4*k0^3*(35*k0 - 24*Sqrt[-k^2 + k0^2]) + 16*k0^7*(k0 - Sqrt[-k^2 + k0^2]) + 8*k^2*k0^5*(-7*k0 + 6*Sqrt[-k^2 + k0^2]) + k^6*k0*(-35*k0 + 16*Sqrt[-k^2 + k0^2]))/(1680*k^5*k0^5) diff --git a/besseltransforms/ksmall/runit.sh b/besseltransforms/ksmall/runit.sh deleted file mode 100755 index d277388..0000000 --- a/besseltransforms/ksmall/runit.sh +++ /dev/null @@ -1,11 +0,0 @@ -#!/bin/bash -K=$1 -Q=$2 -N=$3 -module load mathematica -cat - vzor.m <<<" -kk=$K; -qq=$Q; -nn=$N; -" | math -noprompt > "${K}-${Q}-${N}" - diff --git a/besseltransforms/ksmall/vzor.m b/besseltransforms/ksmall/vzor.m deleted file mode 100644 index 0146350..0000000 --- a/besseltransforms/ksmall/vzor.m +++ /dev/null @@ -1,8 +0,0 @@ -$Assumptions = k >= 0 && k < k0 && k0 >= 0 && c >= 0 && n >= 0 ; -f = Refine[Integrate[(1 - Exp[-c x])^\[Kappa] (k0 x)^(-q) Exp[ - I k0 x] x BesselJ[n, k x], {x, - 0, \[Infinity]}], {\[Kappa] == kk, q == qq, n == nn}] -CForm[f] -Series[f, {k, \[Infinity], 10}] -Simplify[f] -Quit[ ] diff --git a/besseltransforms/runit.sh b/besseltransforms/runit.sh deleted file mode 100755 index d277388..0000000 --- a/besseltransforms/runit.sh +++ /dev/null @@ -1,11 +0,0 @@ -#!/bin/bash -K=$1 -Q=$2 -N=$3 -module load mathematica -cat - vzor.m <<<" -kk=$K; -qq=$Q; -nn=$N; -" | math -noprompt > "${K}-${Q}-${N}" - diff --git a/besseltransforms/vzor.m b/besseltransforms/vzor.m deleted file mode 100644 index 0c1706e..0000000 --- a/besseltransforms/vzor.m +++ /dev/null @@ -1,6 +0,0 @@ -$Assumptions = k >= 0 && k0 >= 0 && c >= 0 && n >= 0 ; -Simplify[Refine[Integrate[(1 - Exp[-c x])^\[Kappa] (k0 x)^(-q) Exp[ - I k0 x] x BesselJ[n, k x], {x, - 0, \[Infinity]}], {\[Kappa] == kk, q == qq, n == nn}]] -Series[%, {k, \[Infinity], 10}] -Quit[ ]