qpms/besseltransforms/7-5-6

((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)/(8640*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)/(2880*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)/(1728*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)/(1728*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)/(2880*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)/(8640*k^6) - (k^8*(-315 + 64*Sqrt[1 + k^2/(8*c - I*k0)^2])*(8*c - I*k0) + 16*k^6*(-105 + 52*Sqrt[1 + k^2/(8*c - I*k0)^2])*(8*c - I*k0)^3 + 48*k^4*(-63 + 44*Sqrt[1 + k^2/(8*c - I*k0)^2])*(8*c - I*k0)^5 + 64*k^2*(-36 + 31*Sqrt[1 + k^2/(8*c - I*k0)^2])*(8*c - I*k0)^7 + 640*(-1 + Sqrt[1 + k^2/(8*c - I*k0)^2])*(8*c - I*k0)^9)/(60480*k^6))/k0^5
SeriesData[k, Infinity, {(192*c^7)/k0^5, (-8505*c^8)/(2*k0^5) + ((945*I)*c^7)/k0^4, (40000*c^9)/k0^5 - ((17280*I)*c^8)/k0^4 - (1920*c^7)/k0^3, (-3465*(198*c^10 - (125*I)*c^9*k0 - 27*c^8*k0^2 + (2*I)*c^7*k0^3))/(4*k0^5), 0, (3003*(14391*c^12 - (14457*I)*c^11*k0 - 5940*c^10*k0^2 + (1250*I)*c^9*k0^3 + 135*c^8*k0^4 - (6*I)*c^7*k0^5))/(16*k0^5)}, 4, 11, 1]
Bessel transform mathematica results etc. Former-commit-id: 3dca9d0ccbfefa4c5f3867ce4ba31229646ca2d9 2018-01-15 15:14:15 +02:00			((k^8(-315 + 64Sqrt[1 + k^2/(c - Ik0)^2])(c - Ik0) + 16k^6(-105 + 52Sqrt[1 + k^2/(c - Ik0)^2])(c - Ik0)^3 + 48k^4(-63 + 44Sqrt[1 + k^2/(c - Ik0)^2])(c - Ik0)^5 + 64k^2(-36 + 31Sqrt[1 + k^2/(c - Ik0)^2])(c - Ik0)^7 + 640(-1 + Sqrt[1 + k^2/(c - Ik0)^2])(c - Ik0)^9)/(60480k^6) - (k^8(-315 + 64Sqrt[1 + k^2/(2c - Ik0)^2])(2c - Ik0) + 16k^6(-105 + 52Sqrt[1 + k^2/(2c - Ik0)^2])(2c - Ik0)^3 + 48k^4(-63 + 44Sqrt[1 + k^2/(2c - Ik0)^2])(2c - Ik0)^5 + 64k^2(-36 + 31Sqrt[1 + k^2/(2c - Ik0)^2])(2c - Ik0)^7 + 640(-1 + Sqrt[1 + k^2/(2c - Ik0)^2])(2c - Ik0)^9)/(8640k^6) + (k^8(-315 + 64Sqrt[1 + k^2/(3c - Ik0)^2])(3c - Ik0) + 16k^6(-105 + 52Sqrt[1 + k^2/(3c - Ik0)^2])(3c - Ik0)^3 + 48k^4(-63 + 44Sqrt[1 + k^2/(3c - Ik0)^2])(3c - Ik0)^5 + 64k^2(-36 + 31Sqrt[1 + k^2/(3c - Ik0)^2])(3c - Ik0)^7 + 640(-1 + Sqrt[1 + k^2/(3c - Ik0)^2])(3c - Ik0)^9)/(2880k^6) - (k^8(-315 + 64Sqrt[1 + k^2/(4c - Ik0)^2])(4c - Ik0) + 16k^6(-105 + 52Sqrt[1 + k^2/(4c - Ik0)^2])(4c - Ik0)^3 + 48k^4(-63 + 44Sqrt[1 + k^2/(4c - Ik0)^2])(4c - Ik0)^5 + 64k^2(-36 + 31Sqrt[1 + k^2/(4c - Ik0)^2])(4c - Ik0)^7 + 640(-1 + Sqrt[1 + k^2/(4c - Ik0)^2])(4c - Ik0)^9)/(1728k^6) + (k^8(-315 + 64Sqrt[1 + k^2/(5c - Ik0)^2])(5c - Ik0) + 16k^6(-105 + 52Sqrt[1 + k^2/(5c - Ik0)^2])(5c - Ik0)^3 + 48k^4(-63 + 44Sqrt[1 + k^2/(5c - Ik0)^2])(5c - Ik0)^5 + 64k^2(-36 + 31Sqrt[1 + k^2/(5c - Ik0)^2])(5c - Ik0)^7 + 640(-1 + Sqrt[1 + k^2/(5c - Ik0)^2])(5c - Ik0)^9)/(1728k^6) - (k^8(-315 + 64Sqrt[1 + k^2/(6c - Ik0)^2])(6c - Ik0) + 16k^6(-105 + 52Sqrt[1 + k^2/(6c - Ik0)^2])(6c - Ik0)^3 + 48k^4(-63 + 44Sqrt[1 + k^2/(6c - Ik0)^2])(6c - Ik0)^5 + 64k^2(-36 + 31Sqrt[1 + k^2/(6c - Ik0)^2])(6c - Ik0)^7 + 640(-1 + Sqrt[1 + k^2/(6c - Ik0)^2])(6c - Ik0)^9)/(2880k^6) + (k^8(-315 + 64Sqrt[1 + k^2/(7c - Ik0)^2])(7c - Ik0) + 16k^6(-105 + 52Sqrt[1 + k^2/(7c - Ik0)^2])(7c - Ik0)^3 + 48k^4(-63 + 44Sqrt[1 + k^2/(7c - Ik0)^2])(7c - Ik0)^5 + 64k^2(-36 + 31Sqrt[1 + k^2/(7c - Ik0)^2])(7c - Ik0)^7 + 640(-1 + Sqrt[1 + k^2/(7c - Ik0)^2])(7c - Ik0)^9)/(8640k^6) - (k^8(-315 + 64Sqrt[1 + k^2/(8c - Ik0)^2])(8c - Ik0) + 16k^6(-105 + 52Sqrt[1 + k^2/(8c - Ik0)^2])(8c - Ik0)^3 + 48k^4(-63 + 44Sqrt[1 + k^2/(8c - Ik0)^2])(8c - Ik0)^5 + 64k^2(-36 + 31Sqrt[1 + k^2/(8c - Ik0)^2])(8c - Ik0)^7 + 640(-1 + Sqrt[1 + k^2/(8c - Ik0)^2])(8c - Ik0)^9)/(60480k^6))/k0^5
			`SeriesData[k, Infinity, {(192c^7)/k0^5, (-8505c^8)/(2k0^5) + ((945I)c^7)/k0^4, (40000c^9)/k0^5 - ((17280I)c^8)/k0^4 - (1920c^7)/k0^3, (-3465(198c^10 - (125I)c^9k0 - 27c^8k0^2 + (2I)c^7k0^3))/(4k0^5), 0, (3003(14391c^12 - (14457I)c^11k0 - 5940c^10k0^2 + (1250I)c^9k0^3 + 135c^8k0^4 - (6I)c^7k0^5))/(16k0^5)}, 4, 11, 1]`