qpms/besseltransforms/3-1-1

(-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)/
Mathematica bessel transforms Former-commit-id: eb38775c75d1c2d5d7a5015bd4a9936108a28d00 2018-03-28 11:52:50 +03:00			`(-k^(-1) - (3(1 - 1/Sqrt[1 + k^2/(c - Ik0)^2]))/k + (3(1 - 1/Sqrt[1 + k^2/(2c - Ik0)^2]))/k + 1/(kSqrt[1 + k^2/(3c - 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/(kSqrt[Pi]), k^2/k0^2 > 1}}, 0]/k0))/k0`
			Piecewise[{{SeriesData[k, Infinity, {(-3c^3)/(k^3k0), 0, (-45(-5c^5 + (6I)c^4k0 + 2c^3k0^2))/(4k^3k0), 0, (-105(43c^7 - (90I)c^6k0 - 75c^5k0^2 + (30I)c^4k0^3 + 5c^3k0^4))/(8k^3k0), 0, ((((-((c - Ik0)^3(2c - Ik0))/(2k^2) - ((c - Ik0)(2c - Ik0)^3)/(2k^2))(3c - Ik0))/k - ((c - Ik0)(2c - Ik0)(3c - Ik0)^3)/(2k^3) + ((c - Ik0)(2c - Ik0)(3c - Ik0)k0^2)/(2k^3))((c - Ik0)^5/(16(2c - Ik0)) - ((c - Ik0)^3(2c - Ik0))/16 - ((c - Ik0)(2c - Ik0)^3)/16 + (2c - Ik0)^5/(16(c - Ik0)) + I(((c - Ik0)^5/(16(2c - Ik0)) - ((c - Ik0)^3(2c - Ik0))/16 - ((c - Ik0)(2c - Ik0)^3)/16 + (2c - Ik0)^5/(16(c - Ik0)))/(3c - Ik0) + ((-(c - Ik0)^3/(8(2c - Ik0)) + ((c - Ik0)(2c - Ik0))/4 - (2c - Ik0)^3/(8(c - Ik0)))(3c - Ik0))/2 - (((c - Ik0)/(2(2c - Ik0)) + (2c - Ik0)/(2(c - Ik0)))(3c - Ik0)^3)/8 + (3c - Ik0)^5/(16(c - Ik0)(2c - Ik0)))k0 - ((-(c - Ik0)^3/(8(2c - Ik0)) + ((c - Ik0)(2c - Ik0))/4 - (2c - Ik0)^3/(8(c - Ik0)))k0^2)/2 - (((c - Ik0)/(2(2c - Ik0)) + (2c - Ik0)/(2(c - Ik0)))k0^4)/8 - k0^6/(16(c - Ik0)(2c - Ik0)) - 3((c - Ik0)^5/(16(3c - Ik0)) - ((c - Ik0)^3(3c - Ik0))/16 - ((c - Ik0)(3c - Ik0)^3)/16 + (3c - Ik0)^5/(16(c - Ik0)) - ((-(c - Ik0)^3/(8(3c - Ik0)) + ((c - Ik0)(3c - Ik0))/4 - (3c - Ik0)^3/(8(c - Ik0)))k0^2)/2 - (((c - Ik0)/(2(3c - Ik0)) + (3c - Ik0)/(2(c - Ik0)))k0^4)/8 - k0^6/(16(c - Ik0)(3c - Ik0))) + 3((2c - Ik0)^5/(16(3c - Ik0)) - ((2c - Ik0)^3(3c - Ik0))/16 - ((2c - Ik0)(3c - Ik0)^3)/16 + (3c - Ik0)^5/(16(2c - Ik0)) - ((-(2c - Ik0)^3/(8(3c - Ik0)) + ((2c - Ik0)(3c - Ik0))/4 - (3c - Ik0)^3/(8(2c - Ik0)))k0^2)/2 - (((2c - Ik0)/(2(3c - Ik0)) + (3c - Ik0)/(2(2c - Ik0)))k0^4)/8 - k0^6/(16(2c - Ik0)(3c - Ik0)))) + ((c - Ik0)(2c - Ik0)(3c - Ik0)((-5(c - Ik0)^7)/(128(2c - Ik0)) + ((c - Ik0)^5(2c - Ik0))/32 + ((c - Ik0)^3(2c - Ik0)^3)/64 + ((c - Ik0)(2c - Ik0)^5)/32 - (5(2c - Ik0)^7)/(128(c - Ik0)) + I(((-5(c - Ik0)^7)/(128(2c - Ik0)) + ((c - Ik0)^5(2c - Ik0))/32 + ((c - Ik0)^3(2c - Ik0)^3)/64 + ((c - Ik0)(2c - Ik0)^5)/32 - (5(2c - Ik0)^7)/(128(c - Ik0)))/(3c - Ik0) + (((c - Ik0)^5/(16(2c - Ik0)) - ((c - Ik0)^3(2c - Ik0))/16 - ((c - Ik0)(2c - Ik0)^3)/16 + (2c - Ik0)^5/(16(c - Ik0)))(3c - Ik0))/2 - ((-(c - Ik0)^3/(8(2c - Ik0)) + ((c - Ik0)(2c - Ik0))/4 - (2c - Ik0)^3/(8(c - Ik0)))(3c - Ik0)^3)/8 + (((c - Ik0)/(2(2c - Ik0)) + (2c - Ik0)/(2(c - Ik0)))(3c - Ik0)^5)/16 - (5(3c - Ik0)^7)/(128(c - Ik0)(2c - 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)))k0^2)/2 - ((-(c - Ik0)^3/(8(2c - Ik0)) + ((c - Ik0)(2c - Ik0))/4 - (2c - Ik0)^3/(8(c - Ik0)))k0^4)/8 - (((c - Ik0)/(2(2c - Ik0)) + (2c - Ik0)/(2(c - Ik0)))k0^6)/16 - (5k0^8)/(128(c - Ik0)(2c - Ik0)) - 3((-5(c - Ik0)^7)/(128(3c - Ik0)) + ((c - Ik0)^5(3c - Ik0))/32 + ((c - Ik0)^3(3c - Ik0)^3)/64 + ((c - Ik0)(3c - Ik0)^5)/32 - (5(3c - Ik0)^7)/(128(c - Ik0)) - (((c - Ik0)^5/(16(3c - Ik0)) - ((c - Ik0)^3(3c - Ik0))/16 - ((c - Ik0)(3c - Ik0)^3)/16 + (3c - Ik0)^5/(16(c - Ik0)))k0^2)/2 - ((-(c - Ik0)^3/(8(3c - Ik0)) + ((c - Ik0)(3c - Ik0))/4 - (3c - Ik0)^3/(8(c - Ik0)))k0^4)/8 - (((c - Ik0)/(2(3c - Ik0)) + (3c - Ik0)/(2(c - Ik0)))k0^6)/16 - (5k0^8)/(128(c - Ik0)(3c - Ik0))) + 3((-5(2c - Ik0)^7)/(128(3c - Ik0)) + ((2c - Ik0)^5(3c - Ik0))/32 + ((2c - Ik0)^3(3c - Ik0)^3)/64 + ((2c - Ik0)(3c - Ik0)^5)/32 - (5(3c - Ik0)^7)/(128(2c - Ik0)) - (((2c - Ik0)^5/(16(3c - Ik0)) - ((2c - Ik0)^3(3c - Ik0))/16 - ((2c - Ik0)(3c - Ik0)^3)/16 + (3c - Ik0)^5/(16(2c - Ik0)))k0^2)/2 - ((-(2c - Ik0)^3/(8(3c - Ik0)) + ((2c - Ik0)(3c - Ik0))/4 - (3c - Ik0)^3/(8(2c - Ik0)))k0^4)/8 - (((2c - Ik0)/(2(3c - Ik0)) + (3c - Ik0)/