((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]