qpms/besseltransforms/7-6-7

((k^10*(-693 + 128*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0) + 4*k^8*(-1155 + 512*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^3 + 144*k^6*(-77 + 48*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^5 + 128*k^4*(-99 + 76*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^7 + 128*k^2*(-55 + 49*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^9 + 1536*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^11)/(1330560*k^7) - (k^10*(-693 + 128*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0) + 4*k^8*(-1155 + 512*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^3 + 144*k^6*(-77 + 48*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^5 + 128*k^4*(-99 + 76*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^7 + 128*k^2*(-55 + 49*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^9 + 1536*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^11)/(190080*k^7) + (k^10*(-693 + 128*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0) + 4*k^8*(-1155 + 512*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^3 + 144*k^6*(-77 + 48*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^5 + 128*k^4*(-99 + 76*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^7 + 128*k^2*(-55 + 49*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^9 + 1536*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^11)/(63360*k^7) - (k^10*(-693 + 128*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0) + 4*k^8*(-1155 + 512*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^3 + 144*k^6*(-77 + 48*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^5 + 128*k^4*(-99 + 76*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^7 + 128*k^2*(-55 + 49*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^9 + 1536*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^11)/(38016*k^7) + (k^10*(-693 + 128*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0) + 4*k^8*(-1155 + 512*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^3 + 144*k^6*(-77 + 48*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^5 + 128*k^4*(-99 + 76*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^7 + 128*k^2*(-55 + 49*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^9 + 1536*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^11)/(38016*k^7) - (k^10*(-693 + 128*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0) + 4*k^8*(-1155 + 512*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^3 + 144*k^6*(-77 + 48*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^5 + 128*k^4*(-99 + 76*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^7 + 128*k^2*(-55 + 49*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^9 + 1536*(-1 + Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^11)/(63360*k^7) + (k^10*(-693 + 128*Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0) + 4*k^8*(-1155 + 512*Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^3 + 144*k^6*(-77 + 48*Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^5 + 128*k^4*(-99 + 76*Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^7 + 128*k^2*(-55 + 49*Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^9 + 1536*(-1 + Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^11)/(190080*k^7) - (k^10*(-693 + 128*Sqrt[1 + k^2/(8*c - I*k0)^2])*(8*c - I*k0) + 4*k^8*(-1155 + 512*Sqrt[1 + k^2/(8*c - I*k0)^2])*(8*c - I*k0)^3 + 144*k^6*(-77 + 48*Sqrt[1 + k^2/(8*c - I*k0)^2])*(8*c - I*k0)^5 + 128*k^4*(-99 + 76*Sqrt[1 + k^2/(8*c - I*k0)^2])*(8*c - I*k0)^7 + 128*k^2*(-55 + 49*Sqrt[1 + k^2/(8*c - I*k0)^2])*(8*c - I*k0)^9 + 1536*(-1 + Sqrt[1 + k^2/(8*c - I*k0)^2])*(8*c - I*k0)^11)/(1330560*k^7))/k0^6
SeriesData[k, Infinity, {(48*c^7)/k0^6, (-2835*c^8)/(2*k0^6) + ((315*I)*c^7)/k0^5, (20000*c^9)/k0^6 - ((8640*I)*c^8)/k0^5 - (960*c^7)/k0^4, (-3465*(198*c^10 - (125*I)*c^9*k0 - 27*c^8*k0^2 + (2*I)*c^7*k0^3))/(4*k0^6), (925248*c^11)/k0^6 - ((760320*I)*c^10)/k0^5 - (240000*c^9)/k0^4 + ((34560*I)*c^8)/k0^3 + (1920*c^7)/k0^2, (-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*k0^6), 0, (2145*(378720*c^14 - (511840*I)*c^13*k0 - 302211*c^12*k0^2 + (101199*I)*c^11*k0^3 + 20790*c^10*k0^4 - (2625*I)*c^9*k0^5 - 189*c^8*k0^6 + (6*I)*c^7*k0^7))/(32*k0^6)}, 3, 11, 1]
Bessel transform mathematica results etc. Former-commit-id: 3dca9d0ccbfefa4c5f3867ce4ba31229646ca2d9 2018-01-15 15:14:15 +02:00			((k^10(-693 + 128Sqrt[1 + k^2/(c - Ik0)^2])(c - Ik0) + 4k^8(-1155 + 512Sqrt[1 + k^2/(c - Ik0)^2])(c - Ik0)^3 + 144k^6(-77 + 48Sqrt[1 + k^2/(c - Ik0)^2])(c - Ik0)^5 + 128k^4(-99 + 76Sqrt[1 + k^2/(c - Ik0)^2])(c - Ik0)^7 + 128k^2(-55 + 49Sqrt[1 + k^2/(c - Ik0)^2])(c - Ik0)^9 + 1536(-1 + Sqrt[1 + k^2/(c - Ik0)^2])(c - Ik0)^11)/(1330560k^7) - (k^10(-693 + 128Sqrt[1 + k^2/(2c - Ik0)^2])(2c - Ik0) + 4k^8(-1155 + 512Sqrt[1 + k^2/(2c - Ik0)^2])(2c - Ik0)^3 + 144k^6(-77 + 48Sqrt[1 + k^2/(2c - Ik0)^2])(2c - Ik0)^5 + 128k^4(-99 + 76Sqrt[1 + k^2/(2c - Ik0)^2])(2c - Ik0)^7 + 128k^2(-55 + 49Sqrt[1 + k^2/(2c - Ik0)^2])(2c - Ik0)^9 + 1536(-1 + Sqrt[1 + k^2/(2c - Ik0)^2])(2c - Ik0)^11)/(190080k^7) + (k^10(-693 + 128Sqrt[1 + k^2/(3c - Ik0)^2])(3c - Ik0) + 4k^8(-1155 + 512Sqrt[1 + k^2/(3c - Ik0)^2])(3c - Ik0)^3 + 144k^6(-77 + 48Sqrt[1 + k^2/(3c - Ik0)^2])(3c - Ik0)^5 + 128k^4(-99 + 76Sqrt[1 + k^2/(3c - Ik0)^2])(3c - Ik0)^7 + 128k^2(-55 + 49Sqrt[1 + k^2/(3c - Ik0)^2])(3c - Ik0)^9 + 1536(-1 + Sqrt[1 + k^2/(3c - Ik0)^2])(3c - Ik0)^11)/(63360k^7) - (k^10(-693 + 128Sqrt[1 + k^2/(4c - Ik0)^2])(4c - Ik0) + 4k^8(-1155 + 512Sqrt[1 + k^2/(4c - Ik0)^2])(4c - Ik0)^3 + 144k^6(-77 + 48Sqrt[1 + k^2/(4c - Ik0)^2])(4c - Ik0)^5 + 128k^4(-99 + 76Sqrt[1 + k^2/(4c - Ik0)^2])(4c - Ik0)^7 + 128k^2(-55 + 49Sqrt[1 + k^2/(4c - Ik0)^2])(4c - Ik0)^9 + 1536(-1 + Sqrt[1 + k^2/(4c - Ik0)^2])(4c - Ik0)^11)/(38016k^7) + (k^10(-693 + 128Sqrt[1 + k^2/(5c - Ik0)^2])(5c - Ik0) + 4k^8(-1155 + 512Sqrt[1 + k^2/(5c - Ik0)^2])(5c - Ik0)^3 + 144k^6(-77 + 48Sqrt[1 + k^2/(5c - Ik0)^2])(5c - Ik0)^5 + 128k^4(-99 + 76Sqrt[1 + k^2/(5c - Ik0)^2])(5c - Ik0)^7 + 128k^2(-55 + 49Sqrt[1 + k^2/(5c - Ik0)^2])(5c - Ik0)^9 + 1536(-1 + Sqrt[1 + k^2/(5c - Ik0)^2])(5c - Ik0)^11)/(38016k^7) - (k^10(-693 + 128Sqrt[1 + k^2/(6c - Ik0)^2])(6c - Ik0) + 4k^8(-1155 + 512Sqrt[1 + k^2/(6c - Ik0)^2])(6c - Ik0)^3 + 144k^6(-77 + 48Sqrt[1 + k^2/(6c - Ik0)^2])(6c - Ik0)^5 + 128k^4(-99 + 76Sqrt[1 + k^2/(6c - Ik0)^2])(6c - Ik0)^7 + 128k^2(-55 + 49Sqrt[1 + k^2/(6c - Ik0)^2])(6c - Ik0)^9 + 1536(-1 + Sqrt[1 + k^2/(6c - Ik0)^2])(6c - Ik0)^11)/(63360k^7) + (k^10(-693 + 128Sqrt[1 + k^2/(7c - Ik0)^2])(7c - Ik0) + 4k^8(-1155 + 512Sqrt[1 + k^2/(7c - Ik0)^2])(7c - Ik0)^3 + 144k^6(-77 + 48Sqrt[1 + k^2/(7c - Ik0)^2])(7c - Ik0)^5 + 128k^4(-99 + 76Sqrt[1 + k^2/(7c - Ik0)^2])(7c - Ik0)^7 + 128k^2(-55 + 49Sqrt[1 + k^2/(7c - Ik0)^2])(7c - Ik0)^9 + 1536(-1 + Sqrt[1 + k^2/(7c - Ik0)^2])(7c - Ik0)^11)/(190080k^7) - (k^10(-693 + 128Sqrt[1 + k^2/(8c - Ik0)^2])(8c - Ik0) + 4k^8(-1155 + 512Sqrt[1 + k^2/(8c - Ik0)^2])(8c - Ik0)^3 + 144k^6(-77 + 48Sqrt[1 + k^2/(8c - Ik0)^2])(8c - Ik0)^5 + 128k^4(-99 + 76Sqrt[1 + k^2/(8c - Ik0)^2])(8c - Ik0)^7 + 128k^2(-55 + 49Sqrt[1 + k^2/(8c - Ik0)^2])(8c - Ik0)^9 + 1536(-1 + Sqrt[1 + k^2/(8c - Ik0)^2])(8c - Ik0)^11)/(1330560k^7))/k0^6
			SeriesData[k, Infinity, {(48c^7)/k0^6, (-2835c^8)/(2k0^6) + ((315I)c^7)/k0^5, (20000c^9)/k0^6 - ((8640I)c^8)/k0^5 - (960c^7)/k0^4, (-3465(198c^10 - (125I)c^9k0 - 27c^8k0^2 + (2I)c^7k0^3))/(4k0^6), (925248c^11)/k0^6 - ((760320I)c^10)/k0^5 - (240000c^9)/k0^4 + ((34560I)c^8)/k0^3 + (1920c^7)/k0^2, (-3003(14391c^12 - (14457I)c^11k0 - 5940c^10k0^2 + (1250I)c^9k0^3 + 135c^8k0^4 - (6I)c^7k0^5))/(16k0^6), 0, (2145(378720c^14 - (511840I)c^13k0 - 302211c^12k0^2 + (101199I)c^11k0^3 + 20790c^10k0^4 - (2625I)c^9k0^5 - 189c^8k0^6 + (6I)c^7k0^7))/(32k0^6)}, 3, 11, 1]