qpms/besseltransforms/klarge/5-4-3

(-(k^4*(-15 + 8*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0) + 4*k^2*(-5 + 4*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^3 + 8*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^5)/(24*k^3) + (k^4*(-15 + 8*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0) + 4*k^2*(-5 + 4*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^3 + 8*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^5)/(12*k^3) - (k^4*(-15 + 8*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0) + 4*k^2*(-5 + 4*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^3 + 8*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^5)/(12*k^3) + (k^4*(-15 + 8*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0) + 4*k^2*(-5 + 4*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^3 + 8*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^5)/(24*k^3) - (k^4*(-15 + 8*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0) + 4*k^2*(-5 + 4*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^3 + 8*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^5)/(120*k^3) + (8*(k^2 - k0^2)^(5/2) + I*(15*k^4*k0 - 20*k^2*k0^3 + 8*k0^5))/(120*k^3))/k0^4
(-(Power(k,4)*(-15 + 8*Sqrt(1 + Power(k,2)/Power(c - Complex(0,1)*k0,2)))*(c - Complex(0,1)*k0) + 4*Power(k,2)*(-5 + 4*Sqrt(1 + Power(k,2)/Power(c - Complex(0,1)*k0,2)))*Power(c - Complex(0,1)*k0,3) + 8*(-1 + Sqrt(1 + Power(k,2)/Power(c - Complex(0,1)*k0,2)))*Power(c - Complex(0,1)*k0,5))/(24.*Power(k,3)) + (Power(k,4)*(-15 + 8*Sqrt(1 + Power(k,2)/Power(2*c - Complex(0,1)*k0,2)))*(2*c - Complex(0,1)*k0) + 4*Power(k,2)*(-5 + 4*Sqrt(1 + Power(k,2)/Power(2*c - Complex(0,1)*k0,2)))*Power(2*c - Complex(0,1)*k0,3) + 8*(-1 + Sqrt(1 + Power(k,2)/Power(2*c - Complex(0,1)*k0,2)))*Power(2*c - Complex(0,1)*k0,5))/(12.*Power(k,3)) - (Power(k,4)*(-15 + 8*Sqrt(1 + Power(k,2)/Power(3*c - Complex(0,1)*k0,2)))*(3*c - Complex(0,1)*k0) + 4*Power(k,2)*(-5 + 4*Sqrt(1 + Power(k,2)/Power(3*c - Complex(0,1)*k0,2)))*Power(3*c - Complex(0,1)*k0,3) + 8*(-1 + Sqrt(1 + Power(k,2)/Power(3*c - Complex(0,1)*k0,2)))*Power(3*c - Complex(0,1)*k0,5))/(12.*Power(k,3)) + (Power(k,4)*(-15 + 8*Sqrt(1 + Power(k,2)/Power(4*c - Complex(0,1)*k0,2)))*(4*c - Complex(0,1)*k0) + 4*Power(k,2)*(-5 + 4*Sqrt(1 + Power(k,2)/Power(4*c - Complex(0,1)*k0,2)))*Power(4*c - Complex(0,1)*k0,3) + 8*(-1 + Sqrt(1 + Power(k,2)/Power(4*c - Complex(0,1)*k0,2)))*Power(4*c - Complex(0,1)*k0,5))/(24.*Power(k,3)) - (Power(k,4)*(-15 + 8*Sqrt(1 + Power(k,2)/Power(5*c - Complex(0,1)*k0,2)))*(5*c - Complex(0,1)*k0) + 4*Power(k,2)*(-5 + 4*Sqrt(1 + Power(k,2)/Power(5*c - Complex(0,1)*k0,2)))*Power(5*c - Complex(0,1)*k0,3) + 8*(-1 + Sqrt(1 + Power(k,2)/Power(5*c - Complex(0,1)*k0,2)))*Power(5*c - Complex(0,1)*k0,5))/(120.*Power(k,3)) + (8*Power(Power(k,2) - Power(k0,2),2.5) + Complex(0,1)*(15*Power(k,4)*k0 - 20*Power(k,2)*Power(k0,3) + 8*Power(k0,5)))/(120.*Power(k,3)))/Power(k0,4)
SeriesData[k, Infinity, {(8*c^5)/k0^4, (-75*c^6)/(2*k0^4) + ((15*I)*c^5)/k0^3, 0, (35*(75*c^8 - (80*I)*c^7*k0 - 30*c^6*k0^2 + (4*I)*c^5*k0^3))/(8*k0^4), 0, (-63*(2025*c^10 - (3310*I)*c^9*k0 - 2250*c^8*k0^2 + (800*I)*c^7*k0^3 + 150*c^6*k0^4 - (12*I)*c^5*k0^5))/(32*k0^4), 0, (165*(20900*c^12 - (44860*I)*c^11*k0 - 42525*c^10*k0^2 + (23170*I)*c^9*k0^3 + 7875*c^8*k0^4 - (1680*I)*c^7*k0^5 - 210*c^6*k0^6 + (12*I)*c^5*k0^7))/(64*k0^4)}, 3, 11, 1]
-(5*(k^4*(-15 + 8*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0) + 4*k^2*(-5 + 4*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^3 + 8*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^5) - 10*(k^4*(-15 + 8*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0) + 4*k^2*(-5 + 4*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^3 + 8*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^5) + 10*(k^4*(-15 + 8*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0) + 4*k^2*(-5 + 4*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^3 + 8*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^5) - 5*(k^4*(-15 + 8*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0) + 4*k^2*(-5 + 4*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^3 + 8*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^5) + k^4*(-15 + 8*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0) + 4*k^2*(-5 + 4*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^3 + 8*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^5 - 8*(k^2 - k0^2)^(5/2) - I*(15*k^4*k0 - 20*k^2*k0^3 + 8*k0^5))/(120*k^3*k0^4)
Další Hankelovy transformace pro kappa=5 Former-commit-id: cc20e7f5dbf8651a81543f84ac066d011e84082b 2018-01-23 00:52:10 +02:00			(-(k^4(-15 + 8Sqrt[1 + k^2/(c - Ik0)^2])(c - Ik0) + 4k^2(-5 + 4Sqrt[1 + k^2/(c - Ik0)^2])(c - Ik0)^3 + 8(-1 + Sqrt[1 + k^2/(c - Ik0)^2])(c - Ik0)^5)/(24k^3) + (k^4(-15 + 8Sqrt[1 + k^2/(2c - Ik0)^2])(2c - Ik0) + 4k^2(-5 + 4Sqrt[1 + k^2/(2c - Ik0)^2])(2c - Ik0)^3 + 8(-1 + Sqrt[1 + k^2/(2c - Ik0)^2])(2c - Ik0)^5)/(12k^3) - (k^4(-15 + 8Sqrt[1 + k^2/(3c - Ik0)^2])(3c - Ik0) + 4k^2(-5 + 4Sqrt[1 + k^2/(3c - Ik0)^2])(3c - Ik0)^3 + 8(-1 + Sqrt[1 + k^2/(3c - Ik0)^2])(3c - Ik0)^5)/(12k^3) + (k^4(-15 + 8Sqrt[1 + k^2/(4c - Ik0)^2])(4c - Ik0) + 4k^2(-5 + 4Sqrt[1 + k^2/(4c - Ik0)^2])(4c - Ik0)^3 + 8(-1 + Sqrt[1 + k^2/(4c - Ik0)^2])(4c - Ik0)^5)/(24k^3) - (k^4(-15 + 8Sqrt[1 + k^2/(5c - Ik0)^2])(5c - Ik0) + 4k^2(-5 + 4Sqrt[1 + k^2/(5c - Ik0)^2])(5c - Ik0)^3 + 8(-1 + Sqrt[1 + k^2/(5c - Ik0)^2])(5c - Ik0)^5)/(120k^3) + (8(k^2 - k0^2)^(5/2) + I(15k^4k0 - 20k^2k0^3 + 8k0^5))/(120k^3))/k0^4
			(-(Power(k,4)(-15 + 8Sqrt(1 + Power(k,2)/Power(c - Complex(0,1)k0,2)))(c - Complex(0,1)k0) + 4Power(k,2)(-5 + 4Sqrt(1 + Power(k,2)/Power(c - Complex(0,1)k0,2)))Power(c - Complex(0,1)k0,3) + 8(-1 + Sqrt(1 + Power(k,2)/Power(c - Complex(0,1)k0,2)))Power(c - Complex(0,1)k0,5))/(24.Power(k,3)) + (Power(k,4)(-15 + 8Sqrt(1 + Power(k,2)/Power(2c - Complex(0,1)k0,2)))(2c - Complex(0,1)k0) + 4Power(k,2)(-5 + 4Sqrt(1 + Power(k,2)/Power(2c - Complex(0,1)k0,2)))Power(2c - Complex(0,1)k0,3) + 8(-1 + Sqrt(1 + Power(k,2)/Power(2c - Complex(0,1)k0,2)))Power(2c - Complex(0,1)k0,5))/(12.Power(k,3)) - (Power(k,4)(-15 + 8Sqrt(1 + Power(k,2)/Power(3c - Complex(0,1)k0,2)))(3c - Complex(0,1)k0) + 4Power(k,2)(-5 + 4Sqrt(1 + Power(k,2)/Power(3c - Complex(0,1)k0,2)))Power(3c - Complex(0,1)k0,3) + 8(-1 + Sqrt(1 + Power(k,2)/Power(3c - Complex(0,1)k0,2)))Power(3c - Complex(0,1)k0,5))/(12.Power(k,3)) + (Power(k,4)(-15 + 8Sqrt(1 + Power(k,2)/Power(4c - Complex(0,1)k0,2)))(4c - Complex(0,1)k0) + 4Power(k,2)(-5 + 4Sqrt(1 + Power(k,2)/Power(4c - Complex(0,1)k0,2)))Power(4c - Complex(0,1)k0,3) + 8(-1 + Sqrt(1 + Power(k,2)/Power(4c - Complex(0,1)k0,2)))Power(4c - Complex(0,1)k0,5))/(24.Power(k,3)) - (Power(k,4)(-15 + 8Sqrt(1 + Power(k,2)/Power(5c - Complex(0,1)k0,2)))(5c - Complex(0,1)k0) + 4Power(k,2)(-5 + 4Sqrt(1 + Power(k,2)/Power(5c - Complex(0,1)k0,2)))Power(5c - Complex(0,1)k0,3) + 8(-1 + Sqrt(1 + Power(k,2)/Power(5c - Complex(0,1)k0,2)))Power(5c - Complex(0,1)k0,5))/(120.Power(k,3)) + (8Power(Power(k,2) - Power(k0,2),2.5) + Complex(0,1)(15Power(k,4)k0 - 20Power(k,2)Power(k0,3) + 8Power(k0,5)))/(120.Power(k,3)))/Power(k0,4)
			`SeriesData[k, Infinity, {(8c^5)/k0^4, (-75c^6)/(2k0^4) + ((15I)c^5)/k0^3, 0, (35(75c^8 - (80I)c^7k0 - 30c^6k0^2 + (4I)c^5k0^3))/(8k0^4), 0, (-63(2025c^10 - (3310I)c^9k0 - 2250c^8k0^2 + (800I)c^7k0^3 + 150c^6k0^4 - (12I)c^5k0^5))/(32k0^4), 0, (165(20900c^12 - (44860I)c^11k0 - 42525c^10k0^2 + (23170I)c^9k0^3 + 7875c^8k0^4 - (1680I)c^7k0^5 - 210c^6k0^6 + (12I)c^5k0^7))/(64*k0^4)}, 3, 11, 1]`
			-(5(k^4(-15 + 8Sqrt[1 + k^2/(c - Ik0)^2])(c - Ik0) + 4k^2(-5 + 4Sqrt[1 + k^2/(c - Ik0)^2])(c - Ik0)^3 + 8(-1 + Sqrt[1 + k^2/(c - Ik0)^2])(c - Ik0)^5) - 10(k^4(-15 + 8Sqrt[1 + k^2/(2c - Ik0)^2])(2c - Ik0) + 4k^2(-5 + 4Sqrt[1 + k^2/(2c - Ik0)^2])(2c - Ik0)^3 + 8(-1 + Sqrt[1 + k^2/(2c - Ik0)^2])(2c - Ik0)^5) + 10(k^4(-15 + 8Sqrt[1 + k^2/(3c - Ik0)^2])(3c - Ik0) + 4k^2(-5 + 4Sqrt[1 + k^2/(3c - Ik0)^2])(3c - Ik0)^3 + 8(-1 + Sqrt[1 + k^2/(3c - Ik0)^2])(3c - Ik0)^5) - 5(k^4(-15 + 8Sqrt[1 + k^2/(4c - Ik0)^2])(4c - Ik0) + 4k^2(-5 + 4Sqrt[1 + k^2/(4c - Ik0)^2])(4c - Ik0)^3 + 8(-1 + Sqrt[1 + k^2/(4c - Ik0)^2])(4c - Ik0)^5) + k^4(-15 + 8Sqrt[1 + k^2/(5c - Ik0)^2])(5c - Ik0) + 4k^2(-5 + 4Sqrt[1 + k^2/(5c - Ik0)^2])(5c - Ik0)^3 + 8(-1 + Sqrt[1 + k^2/(5c - Ik0)^2])(5c - Ik0)^5 - 8(k^2 - k0^2)^(5/2) - I(15k^4k0 - 20k^2k0^3 + 8k0^5))/(120k^3k0^4)