qpms/besseltransforms/klarge/5-3-5

(-(5*k^6 + 12*k^4*(5 - 2*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^2 + 8*k^2*(15 - 11*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^4 - 64*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^6)/(24*k^5) + (5*k^6 + 12*k^4*(5 - 2*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^2 + 8*k^2*(15 - 11*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^4 - 64*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^6)/(12*k^5) - (5*k^6 + 12*k^4*(5 - 2*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^2 + 8*k^2*(15 - 11*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^4 - 64*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^6)/(12*k^5) + (5*k^6 + 12*k^4*(5 - 2*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^2 + 8*k^2*(15 - 11*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^4 - 64*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^6)/(24*k^5) - (5*k^6 + 12*k^4*(5 - 2*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^2 + 8*k^2*(15 - 11*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^4 - 64*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^6)/(120*k^5) + (5*k^6 + 12*k^4*k0*(-5*k0 + (2*I)*Sqrt[k^2 - k0^2]) + 8*k^2*k0^3*(15*k0 - (11*I)*Sqrt[k^2 - k0^2]) + (64*I)*k0^5*(I*k0 + Sqrt[k^2 - k0^2]))/(120*k^5))/k0^3
(-(5*Power(k,6) + 12*Power(k,4)*(5 - 2*Sqrt(1 + Power(k,2)/Power(c - Complex(0,1)*k0,2)))*Power(c - Complex(0,1)*k0,2) + 8*Power(k,2)*(15 - 11*Sqrt(1 + Power(k,2)/Power(c - Complex(0,1)*k0,2)))*Power(c - Complex(0,1)*k0,4) - 64*(-1 + Sqrt(1 + Power(k,2)/Power(c - Complex(0,1)*k0,2)))*Power(c - Complex(0,1)*k0,6))/(24.*Power(k,5)) + (5*Power(k,6) + 12*Power(k,4)*(5 - 2*Sqrt(1 + Power(k,2)/Power(2*c - Complex(0,1)*k0,2)))*Power(2*c - Complex(0,1)*k0,2) + 8*Power(k,2)*(15 - 11*Sqrt(1 + Power(k,2)/Power(2*c - Complex(0,1)*k0,2)))*Power(2*c - Complex(0,1)*k0,4) - 64*(-1 + Sqrt(1 + Power(k,2)/Power(2*c - Complex(0,1)*k0,2)))*Power(2*c - Complex(0,1)*k0,6))/(12.*Power(k,5)) - (5*Power(k,6) + 12*Power(k,4)*(5 - 2*Sqrt(1 + Power(k,2)/Power(3*c - Complex(0,1)*k0,2)))*Power(3*c - Complex(0,1)*k0,2) + 8*Power(k,2)*(15 - 11*Sqrt(1 + Power(k,2)/Power(3*c - Complex(0,1)*k0,2)))*Power(3*c - Complex(0,1)*k0,4) - 64*(-1 + Sqrt(1 + Power(k,2)/Power(3*c - Complex(0,1)*k0,2)))*Power(3*c - Complex(0,1)*k0,6))/(12.*Power(k,5)) + (5*Power(k,6) + 12*Power(k,4)*(5 - 2*Sqrt(1 + Power(k,2)/Power(4*c - Complex(0,1)*k0,2)))*Power(4*c - Complex(0,1)*k0,2) + 8*Power(k,2)*(15 - 11*Sqrt(1 + Power(k,2)/Power(4*c - Complex(0,1)*k0,2)))*Power(4*c - Complex(0,1)*k0,4) - 64*(-1 + Sqrt(1 + Power(k,2)/Power(4*c - Complex(0,1)*k0,2)))*Power(4*c - Complex(0,1)*k0,6))/(24.*Power(k,5)) - (5*Power(k,6) + 12*Power(k,4)*(5 - 2*Sqrt(1 + Power(k,2)/Power(5*c - Complex(0,1)*k0,2)))*Power(5*c - Complex(0,1)*k0,2) + 8*Power(k,2)*(15 - 11*Sqrt(1 + Power(k,2)/Power(5*c - Complex(0,1)*k0,2)))*Power(5*c - Complex(0,1)*k0,4) - 64*(-1 + Sqrt(1 + Power(k,2)/Power(5*c - Complex(0,1)*k0,2)))*Power(5*c - Complex(0,1)*k0,6))/(120.*Power(k,5)) + (5*Power(k,6) + 12*Power(k,4)*k0*(-5*k0 + Complex(0,2)*Sqrt(Power(k,2) - Power(k0,2))) + 8*Power(k,2)*Power(k0,3)*(15*k0 - Complex(0,11)*Sqrt(Power(k,2) - Power(k0,2))) + Complex(0,64)*Power(k0,5)*(Complex(0,1)*k0 + Sqrt(Power(k,2) - Power(k0,2))))/(120.*Power(k,5)))/Power(k0,3)
SeriesData[k, Infinity, {(105*c^5)/k0^3, (-960*c^6)/k0^3 + ((384*I)*c^5)/k0^2, (315*(20*c^7 - (15*I)*c^6*k0 - 3*c^5*k0^2))/(2*k0^3), 0, (-1155*(331*c^9 - (450*I)*c^8*k0 - 240*c^7*k0^2 + (60*I)*c^6*k0^3 + 6*c^5*k0^4))/(16*k0^3), 0, (429*(22430*c^11 - (42525*I)*c^10*k0 - 34755*c^9*k0^2 + (15750*I)*c^8*k0^3 + 4200*c^7*k0^4 - (630*I)*c^6*k0^5 - 42*c^5*k0^6))/(32*k0^3)}, 4, 11, 1]
(15*k^4*(-5 + 2*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^2 + 10*k^2*(-15 + 11*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^4 + 80*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^6 + 30*k^4*(5 - 2*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^2 + 20*k^2*(15 - 11*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^4 - 160*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^6 + 30*k^4*(-5 + 2*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^2 + 20*k^2*(-15 + 11*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^4 + 160*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^6 + 15*k^4*(5 - 2*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^2 + 10*k^2*(15 - 11*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^4 - 80*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^6 + 3*k^4*(-5 + 2*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^2 + 2*k^2*(-15 + 11*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^4 + 16*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^6 + 3*k^4*k0*(-5*k0 + (2*I)*Sqrt[k^2 - k0^2]) + 2*k^2*k0^3*(15*k0 - (11*I)*Sqrt[k^2 - k0^2]) + (16*I)*k0^5*(I*k0 + Sqrt[k^2 - k0^2]))/(30*k^5*k0^3)
Další Hankelovy transformace pro kappa=5 Former-commit-id: cc20e7f5dbf8651a81543f84ac066d011e84082b 2018-01-23 00:52:10 +02:00			(-(5k^6 + 12k^4(5 - 2Sqrt[1 + k^2/(c - Ik0)^2])(c - Ik0)^2 + 8k^2(15 - 11Sqrt[1 + k^2/(c - Ik0)^2])(c - Ik0)^4 - 64(-1 + Sqrt[1 + k^2/(c - Ik0)^2])(c - Ik0)^6)/(24k^5) + (5k^6 + 12k^4(5 - 2Sqrt[1 + k^2/(2c - Ik0)^2])(2c - Ik0)^2 + 8k^2(15 - 11Sqrt[1 + k^2/(2c - Ik0)^2])(2c - Ik0)^4 - 64(-1 + Sqrt[1 + k^2/(2c - Ik0)^2])(2c - Ik0)^6)/(12k^5) - (5k^6 + 12k^4(5 - 2Sqrt[1 + k^2/(3c - Ik0)^2])(3c - Ik0)^2 + 8k^2(15 - 11Sqrt[1 + k^2/(3c - Ik0)^2])(3c - Ik0)^4 - 64(-1 + Sqrt[1 + k^2/(3c - Ik0)^2])(3c - Ik0)^6)/(12k^5) + (5k^6 + 12k^4(5 - 2Sqrt[1 + k^2/(4c - Ik0)^2])(4c - Ik0)^2 + 8k^2(15 - 11Sqrt[1 + k^2/(4c - Ik0)^2])(4c - Ik0)^4 - 64(-1 + Sqrt[1 + k^2/(4c - Ik0)^2])(4c - Ik0)^6)/(24k^5) - (5k^6 + 12k^4(5 - 2Sqrt[1 + k^2/(5c - Ik0)^2])(5c - Ik0)^2 + 8k^2(15 - 11Sqrt[1 + k^2/(5c - Ik0)^2])(5c - Ik0)^4 - 64(-1 + Sqrt[1 + k^2/(5c - Ik0)^2])(5c - Ik0)^6)/(120k^5) + (5k^6 + 12k^4k0(-5k0 + (2I)Sqrt[k^2 - k0^2]) + 8k^2k0^3(15k0 - (11I)Sqrt[k^2 - k0^2]) + (64I)k0^5(Ik0 + Sqrt[k^2 - k0^2]))/(120k^5))/k0^3
			(-(5Power(k,6) + 12Power(k,4)(5 - 2Sqrt(1 + Power(k,2)/Power(c - Complex(0,1)k0,2)))Power(c - Complex(0,1)k0,2) + 8Power(k,2)(15 - 11Sqrt(1 + Power(k,2)/Power(c - Complex(0,1)k0,2)))Power(c - Complex(0,1)k0,4) - 64(-1 + Sqrt(1 + Power(k,2)/Power(c - Complex(0,1)k0,2)))Power(c - Complex(0,1)k0,6))/(24.Power(k,5)) + (5Power(k,6) + 12Power(k,4)(5 - 2Sqrt(1 + Power(k,2)/Power(2c - Complex(0,1)k0,2)))Power(2c - Complex(0,1)k0,2) + 8Power(k,2)(15 - 11Sqrt(1 + Power(k,2)/Power(2c - Complex(0,1)k0,2)))Power(2c - Complex(0,1)k0,4) - 64(-1 + Sqrt(1 + Power(k,2)/Power(2c - Complex(0,1)k0,2)))Power(2c - Complex(0,1)k0,6))/(12.Power(k,5)) - (5Power(k,6) + 12Power(k,4)(5 - 2Sqrt(1 + Power(k,2)/Power(3c - Complex(0,1)k0,2)))Power(3c - Complex(0,1)k0,2) + 8Power(k,2)(15 - 11Sqrt(1 + Power(k,2)/Power(3c - Complex(0,1)k0,2)))Power(3c - Complex(0,1)k0,4) - 64(-1 + Sqrt(1 + Power(k,2)/Power(3c - Complex(0,1)k0,2)))Power(3c - Complex(0,1)k0,6))/(12.Power(k,5)) + (5Power(k,6) + 12Power(k,4)(5 - 2Sqrt(1 + Power(k,2)/Power(4c - Complex(0,1)k0,2)))Power(4c - Complex(0,1)k0,2) + 8Power(k,2)(15 - 11Sqrt(1 + Power(k,2)/Power(4c - Complex(0,1)k0,2)))Power(4c - Complex(0,1)k0,4) - 64(-1 + Sqrt(1 + Power(k,2)/Power(4c - Complex(0,1)k0,2)))Power(4c - Complex(0,1)k0,6))/(24.Power(k,5)) - (5Power(k,6) + 12Power(k,4)(5 - 2Sqrt(1 + Power(k,2)/Power(5c - Complex(0,1)k0,2)))Power(5c - Complex(0,1)k0,2) + 8Power(k,2)(15 - 11Sqrt(1 + Power(k,2)/Power(5c - Complex(0,1)k0,2)))Power(5c - Complex(0,1)k0,4) - 64(-1 + Sqrt(1 + Power(k,2)/Power(5c - Complex(0,1)k0,2)))Power(5c - Complex(0,1)k0,6))/(120.Power(k,5)) + (5Power(k,6) + 12Power(k,4)k0(-5k0 + Complex(0,2)Sqrt(Power(k,2) - Power(k0,2))) + 8Power(k,2)Power(k0,3)(15k0 - Complex(0,11)Sqrt(Power(k,2) - Power(k0,2))) + Complex(0,64)Power(k0,5)(Complex(0,1)k0 + Sqrt(Power(k,2) - Power(k0,2))))/(120.*Power(k,5)))/Power(k0,3)
			`SeriesData[k, Infinity, {(105c^5)/k0^3, (-960c^6)/k0^3 + ((384I)c^5)/k0^2, (315(20c^7 - (15I)c^6k0 - 3c^5k0^2))/(2k0^3), 0, (-1155(331c^9 - (450I)c^8k0 - 240c^7k0^2 + (60I)c^6k0^3 + 6c^5k0^4))/(16k0^3), 0, (429(22430c^11 - (42525I)c^10k0 - 34755c^9k0^2 + (15750I)c^8k0^3 + 4200c^7k0^4 - (630I)c^6k0^5 - 42c^5k0^6))/(32*k0^3)}, 4, 11, 1]`
			(15k^4(-5 + 2Sqrt[1 + k^2/(c - Ik0)^2])(c - Ik0)^2 + 10k^2(-15 + 11Sqrt[1 + k^2/(c - Ik0)^2])(c - Ik0)^4 + 80(-1 + Sqrt[1 + k^2/(c - Ik0)^2])(c - Ik0)^6 + 30k^4(5 - 2Sqrt[1 + k^2/(2c - Ik0)^2])(2c - Ik0)^2 + 20k^2(15 - 11Sqrt[1 + k^2/(2c - Ik0)^2])(2c - Ik0)^4 - 160(-1 + Sqrt[1 + k^2/(2c - Ik0)^2])(2c - Ik0)^6 + 30k^4(-5 + 2Sqrt[1 + k^2/(3c - Ik0)^2])(3c - Ik0)^2 + 20k^2(-15 + 11Sqrt[1 + k^2/(3c - Ik0)^2])(3c - Ik0)^4 + 160(-1 + Sqrt[1 + k^2/(3c - Ik0)^2])(3c - Ik0)^6 + 15k^4(5 - 2Sqrt[1 + k^2/(4c - Ik0)^2])(4c - Ik0)^2 + 10k^2(15 - 11Sqrt[1 + k^2/(4c - Ik0)^2])(4c - Ik0)^4 - 80(-1 + Sqrt[1 + k^2/(4c - Ik0)^2])(4c - Ik0)^6 + 3k^4(-5 + 2Sqrt[1 + k^2/(5c - Ik0)^2])(5c - Ik0)^2 + 2k^2(-15 + 11Sqrt[1 + k^2/(5c - Ik0)^2])(5c - Ik0)^4 + 16(-1 + Sqrt[1 + k^2/(5c - Ik0)^2])(5c - Ik0)^6 + 3k^4k0(-5k0 + (2I)Sqrt[k^2 - k0^2]) + 2k^2k0^3(15k0 - (11I)Sqrt[k^2 - k0^2]) + (16I)k0^5(Ik0 + Sqrt[k^2 - k0^2]))/(30k^5k0^3)