qpms/besseltransforms/2-1-1

(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
Mathematica bessel transforms Former-commit-id: eb38775c75d1c2d5d7a5015bd4a9936108a28d00 2018-03-28 11:52:50 +03:00			`(k^(-1) - (2(1 - 1/Sqrt[1 + k^2/(c - Ik0)^2]))/k - 1/(kSqrt[1 + k^2/(2c - Ik0)^2]) + Sqrt[Pi]((IPiecewise[{{k0/(Sqrt[k^2 - k0^2]Sqrt[Pi]), k0^2/k^2 < 1}}, 0])/k + Piecewise[{{(k0(1 - k0/Sqrt[-k^2 + k0^2]))/(kSqrt[Pi]), k^2/k0^2 < 1}, {k0/(k*Sqrt[Pi]), k^2/k0^2 > 1}}, 0]/k0))/k0`
			Piecewise[{{SeriesData[k, Infinity, {(3c^2(c - Ik0))/(k^2k0), 0, (15(-3c^5 + (7I)c^4k0 + 6c^3k0^2 - (2I)c^2k0^3))/(4k^2k0), 0, (35(9c^7 - (31I)c^6k0 - 45c^5k0^2 + (35I)c^4k0^3 + 15c^3k0^4 - (3I)c^2k0^5))/(8k^2k0), 0, (105(-85c^9 + (381I)c^8k0 + 756c^7k0^2 - (868I)c^6k0^3 - 630c^5k0^4 + (294I)c^4k0^5 + 84c^3k0^6 - (12I)c^2k0^7))/(64k^2k0), 0, (693(93c^11 - (511I)c^10k0 - 1275c^9k0^2 + (1905I)c^8k0^3 + 1890c^7k0^4 - (1302I)c^6k0^5 - 630c^5k0^6 + (210I)c^4k0^7 + 45c^3k0^8 - (5I)c^2k0^9))/(128k^2k0)}, 2, 11, 1], (k0 <= 0 && k^2/k0^2 > 1) \|\| k0 > 0}}, SeriesData[k, Infinity, {I/k^2, 0, (I/2((-6I)c^3 - 6c^2k0 + k0^3))/(k^2k0), 0, ((I/2(6c^3 - Ic^2k0 + 6ck0^2 - (3I)k0^3)((-I/2(c - Ik0)(2c - Ik0)k0^2)/k^2 - I(-((c - Ik0)^3(2c - Ik0))/(2k^2) - ((c - Ik0)(2c - Ik0)^3)/(2k^2) + ((c - Ik0)(2c - Ik0)k0^2)/(2k^2))))/((c - Ik0)(2c - Ik0)) - (k0(((-3I)/8(c - Ik0)(2c - Ik0)k0^4)/k^2 - I/2k0^2(-((c - Ik0)^3(2c - Ik0))/(2k^2) - ((c - Ik0)(2c - Ik0)^3)/(2k^2) + ((c - Ik0)(2c - Ik0)k0^2)/(2k^2)) - I(((c - Ik0)^3(2c - Ik0)^3)/(4k^2) + ((-((c - Ik0)^3(2c - Ik0))/(2k^2) - ((c - Ik0)(2c - Ik0)^3)/(2k^2))k0^2)/2 + (3(c - Ik0)(2c - Ik0)k0^4)/(8k^2) + (3(c - Ik0)^4(2c - Ik0)(c/k - (Ik0)/k))/(8k) + (3(c - Ik0)(2c - Ik0)^4((2c)/k - (Ik0)/k))/(8k))))/((c - Ik0)(2c - Ik0)) + (I(c - Ik0)(2c - Ik0)((-I/8k0^4)/(c - Ik0) - I/2k0^2((c - Ik0)/2 - k0^2/(2(c - Ik0))) + I(-(c - Ik0)^3/8 - ((c - Ik0)k0^2)/4 - k0^4/(8(c - Ik0))) + k0(-(c - Ik0)^3/(8(2c - Ik0)) + ((c - Ik0)(2c - Ik0))/4 - (2c - Ik0)^3/(8(c - Ik0)) - (((c - Ik0)/(2(2c - Ik0)) + (2c - Ik0)/(2(c - Ik0)))k0^2)/2 - k0^4/(8(c - Ik0)(2c - Ik0))) - Ik0(I(-(c - Ik0)^3/(8(2c - Ik0)) + ((c - Ik0)(2c - Ik0))/4 - (2c - Ik0)^3/(8(c - Ik0))) - I/2((c - Ik0)/(2(2c - Ik0)) + (2c - Ik0)/(2(c - Ik0)))k0^2 - (I/8k0^4)/((c - Ik0)(2c - Ik0))) - 2((-I/8k0^4)/(2c - Ik0) - I/2k0^2((2c - Ik0)/2 - k0^2/(2(2c - Ik0))) + I(-(2c - Ik0)^3/8 - ((2c - Ik0)k0^2)/4 - k0^4/(8(2c - Ik0))))))/k^2)/k0, 0, ((I/2(6c^3 - Ic^2k0 + 6ck0^2 - (3I)k0^3)(((-3I)/8(c - Ik0)(2c - Ik0)k0^4)/k^2 - I/2k0^2(-((c - Ik0)^3(2c - Ik0))/(2k^2) - ((c - Ik0)(2c - Ik0)^3)/(2k^2) + ((c - Ik0)(2c - Ik0)k0^2)/(2k^2)) - I(((c - Ik0)^3(2c - Ik0)^3)/(4k^2) + ((-((c - Ik0)^3(2c - Ik0))/(2k^2) - ((c - Ik0)(2c - Ik0)^3)/(2k^2))k0^2)/2 + (3(c - Ik0)(2c - Ik0)k0^4)/(8k^2) + (3(c - Ik0)^4(2c - Ik0)(c/k - (Ik0)/k))/(8k) + (3(c - Ik0)(2c - Ik0)^4((2c)/k - (Ik0)/k))/(8k))))/((c - Ik0)(2c - Ik0)) - ((-I/2(c - Ik0)(2c - Ik0)k0^2)/k^2 - I(-((c - Ik0)^3(2c - Ik0))/(2k^2) - ((c - Ik0)(2c - Ik0)^3)/(2k^2) + ((c - Ik0)(2c - Ik0)k0^2)/(2k^2)))((-I/8k0^4)/(c - Ik0) - I/2k0^2((c - Ik0)/2 - k0^2/(2(c - Ik0))) + I(-(c - Ik0)^3/8 - ((c - Ik0)k0^2)/4 - k0^4/(8(c - Ik0))) + k0(-(c - Ik0)^3/(8(2c - Ik0)) + ((c - Ik0)(2c - Ik0))/4 - (2c - Ik0)^3/(8(c - Ik0)) - (((c - Ik0)/(2(2c - Ik0)) + (2c - Ik0)/(2(c - Ik0)))k0^2)/2 - k0^4/(8(c - Ik0)(2c - Ik0))) - Ik0(I(-(c - Ik0)^3/(8(2c - Ik0)) + ((c - Ik0)(2c - Ik0))/4 - (2c - Ik0)^3/(8(c - Ik0))) - I/2((c - Ik0)/(2(2c - Ik0)) + (2c - Ik0)/(2(c - Ik0)))k0^2 - (I/8k0^4)/((c - Ik0)(2c - Ik0))) - 2((-I/8k0^4)/(2c - Ik0) - I/2k0^2((2c - Ik0)/2 - k0^2/(2(2c - Ik0))) + I(-(2c - Ik0)^3/8 - ((2c - Ik0)k0^2)/4 - k0^4/(8(2c - Ik0))))) + (I(c - Ik0)(2c - Ik0)((-I/16k0^6)/(c - Ik0) - I/8k0^4((c - Ik0)/2 - k0^2/(2(c - Ik0))) - I/2k0^2(-(c - Ik0)^3/8 - ((c - Ik0)k0^2)/4 - k0^4/(8(c - Ik0))) + I((c - Ik0)^5/16 + ((c - Ik0)^3k0^2)/16 - ((c - Ik0)k0^4)/16 - k0^6/(16(c - Ik0))) + k0((c - Ik0)^5/(16(2c - Ik0)) - ((c - Ik0)^3(2c - Ik0))/16 - ((c - Ik0)(2c - Ik0)^3)/16 + (2c - Ik0)^5/(16(c - Ik0)) - ((-(c - Ik0)^3/(8(2c - Ik0)) + ((c - Ik0)(2c