qpms/besseltransforms/3-2-1

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((-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0) - 3*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0) + 3*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0) - (-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0))/(k*k0^2)
SeriesData[k, Infinity, {(15*c^4)/(2*k0^2) - ((3*I)*c^3)/k0, 0, (-15*(35*c^6 - (39*I)*c^5*k0 - 15*c^4*k0^2 + (2*I)*c^3*k0^3))/(4*k0^2), 0, (105*(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*k0^2), 0, (-105*(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*k0^2)}, 4, 11, 1]