qpms/besseltransforms/3-1-0

(-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
Mathematica bessel transforms Former-commit-id: eb38775c75d1c2d5d7a5015bd4a9936108a28d00 2018-03-28 11:52:50 +03:00			`(-3/(Sqrt[1 + k^2/(c - Ik0)^2](c - Ik0)) + 3/(Sqrt[1 + k^2/(2c - Ik0)^2](2c - Ik0)) - 1/(Sqrt[1 + k^2/(3c - Ik0)^2](3c - Ik0)) + (Sqrt[Pi](IPiecewise[{{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(3c^4 - (2I)c^3k0))/(2k^3k0), 0, ((-9(3c^4 - (2I)c^3k0)(((-((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)))/2 + ((c - Ik0)(2c - Ik0)(3c - Ik0)(6c^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)))/(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))) - (11I)c^2(((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 - 6c(((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)))k0^2 + 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)))k0^3 - 2c^2((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 - 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))) + (3I)ck0((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 - 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))) + k0^2((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 - 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))) + 9c^2((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))) - (12I)ck0((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))) - 3k0^2((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))) - 18c^2((2c - Ik0)^5/(16(3