qpms/besseltransforms/ksmall/5-4-4

(-(5*k^6 + 2*k^4*(15 - 8*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^2 + 8*k^2*(5 - 4*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^4 - 16*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^6)/(48*k^4) + (5*k^6 + 2*k^4*(15 - 8*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^2 + 8*k^2*(5 - 4*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^4 - 16*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^6)/(24*k^4) - (5*k^6 + 2*k^4*(15 - 8*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^2 + 8*k^2*(5 - 4*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^4 - 16*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^6)/(24*k^4) + (5*k^6 + 2*k^4*(15 - 8*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^2 + 8*k^2*(5 - 4*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^4 - 16*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^6)/(48*k^4) - (5*k^6 + 2*k^4*(15 - 8*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^2 + 8*k^2*(5 - 4*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)/(240*k^4) + (5*k^6 + 16*k0^5*(-k0 + Sqrt[-k^2 + k0^2]) - 8*k^2*k0^3*(-5*k0 + 4*Sqrt[-k^2 + k0^2]) + 2*k^4*k0*(-15*k0 + 8*Sqrt[-k^2 + k0^2]))/(240*k^4))/k0^4
(-(5*Power(k,6) + 2*Power(k,4)*(15 - 8*Sqrt(1 + Power(k,2)/Power(c - Complex(0,1)*k0,2)))*Power(c - Complex(0,1)*k0,2) + 8*Power(k,2)*(5 - 4*Sqrt(1 + Power(k,2)/Power(c - Complex(0,1)*k0,2)))*Power(c - Complex(0,1)*k0,4) - 16*(-1 + Sqrt(1 + Power(k,2)/Power(c - Complex(0,1)*k0,2)))*Power(c - Complex(0,1)*k0,6))/(48.*Power(k,4)) + (5*Power(k,6) + 2*Power(k,4)*(15 - 8*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)*(5 - 4*Sqrt(1 + Power(k,2)/Power(2*c - Complex(0,1)*k0,2)))*Power(2*c - Complex(0,1)*k0,4) - 16*(-1 + Sqrt(1 + Power(k,2)/Power(2*c - Complex(0,1)*k0,2)))*Power(2*c - Complex(0,1)*k0,6))/(24.*Power(k,4)) - (5*Power(k,6) + 2*Power(k,4)*(15 - 8*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)*(5 - 4*Sqrt(1 + Power(k,2)/Power(3*c - Complex(0,1)*k0,2)))*Power(3*c - Complex(0,1)*k0,4) - 16*(-1 + Sqrt(1 + Power(k,2)/Power(3*c - Complex(0,1)*k0,2)))*Power(3*c - Complex(0,1)*k0,6))/(24.*Power(k,4)) + (5*Power(k,6) + 2*Power(k,4)*(15 - 8*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)*(5 - 4*Sqrt(1 + Power(k,2)/Power(4*c - Complex(0,1)*k0,2)))*Power(4*c - Complex(0,1)*k0,4) - 16*(-1 + Sqrt(1 + Power(k,2)/Power(4*c - Complex(0,1)*k0,2)))*Power(4*c - Complex(0,1)*k0,6))/(48.*Power(k,4)) - (5*Power(k,6) + 2*Power(k,4)*(15 - 8*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)*(5 - 4*Sqrt(1 + Power(k,2)/Power(5*c - Complex(0,1)*k0,2)))*Power(5*c - Complex(0,1)*k0,4) - 16*(-1 + Sqrt(1 + Power(k,2)/Power(5*c - Complex(0,1)*k0,2)))*Power(5*c - Complex(0,1)*k0,6))/(240.*Power(k,4)) + (5*Power(k,6) + 16*Power(k0,5)*(-k0 + Sqrt(-Power(k,2) + Power(k0,2))) - 8*Power(k,2)*Power(k0,3)*(-5*k0 + 4*Sqrt(-Power(k,2) + Power(k0,2))) + 2*Power(k,4)*k0*(-15*k0 + 8*Sqrt(-Power(k,2) + Power(k0,2))))/(240.*Power(k,4)))/Power(k0,4)
SeriesData[k, Infinity, {(15*c^5)/k0^4, (-120*c^6)/k0^4 + ((48*I)*c^5)/k0^3, (35*(20*c^7 - (15*I)*c^6*k0 - 3*c^5*k0^2))/(2*k0^4), 0, (-105*(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*k0^4), 0, (33*(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*k0^4)}, 3, 11, 1]
(5*k^4*(-15 + 8*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^2 + 20*k^2*(-5 + 4*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^4 + 40*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^6 + 10*k^4*(15 - 8*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^2 + 40*k^2*(5 - 4*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^4 - 80*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^6 + 10*k^4*(-15 + 8*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^2 + 40*k^2*(-5 + 4*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^4 + 80*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^6 + 5*k^4*(15 - 8*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^2 + 20*k^2*(5 - 4*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^4 - 40*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^6 + k^4*(-15 + 8*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^2 + 4*k^2*(-5 + 4*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^4 + 8*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^6 + 8*k0^5*(-k0 + Sqrt[-k^2 + k0^2]) - 4*k^2*k0^3*(-5*k0 + 4*Sqrt[-k^2 + k0^2]) + k^4*k0*(-15*k0 + 8*Sqrt[-k^2 + k0^2]))/(120*k^4*k0^4)
Další Hankelovy transformace pro kappa=5 Former-commit-id: cc20e7f5dbf8651a81543f84ac066d011e84082b 2018-01-23 00:52:10 +02:00			(-(5k^6 + 2k^4(15 - 8Sqrt[1 + k^2/(c - Ik0)^2])(c - Ik0)^2 + 8k^2(5 - 4Sqrt[1 + k^2/(c - Ik0)^2])(c - Ik0)^4 - 16(-1 + Sqrt[1 + k^2/(c - Ik0)^2])(c - Ik0)^6)/(48k^4) + (5k^6 + 2k^4(15 - 8Sqrt[1 + k^2/(2c - Ik0)^2])(2c - Ik0)^2 + 8k^2(5 - 4Sqrt[1 + k^2/(2c - Ik0)^2])(2c - Ik0)^4 - 16(-1 + Sqrt[1 + k^2/(2c - Ik0)^2])(2c - Ik0)^6)/(24k^4) - (5k^6 + 2k^4(15 - 8Sqrt[1 + k^2/(3c - Ik0)^2])(3c - Ik0)^2 + 8k^2(5 - 4Sqrt[1 + k^2/(3c - Ik0)^2])(3c - Ik0)^4 - 16(-1 + Sqrt[1 + k^2/(3c - Ik0)^2])(3c - Ik0)^6)/(24k^4) + (5k^6 + 2k^4(15 - 8Sqrt[1 + k^2/(4c - Ik0)^2])(4c - Ik0)^2 + 8k^2(5 - 4Sqrt[1 + k^2/(4c - Ik0)^2])(4c - Ik0)^4 - 16(-1 + Sqrt[1 + k^2/(4c - Ik0)^2])(4c - Ik0)^6)/(48k^4) - (5k^6 + 2k^4(15 - 8Sqrt[1 + k^2/(5c - Ik0)^2])(5c - Ik0)^2 + 8k^2(5 - 4Sqrt[1 + k^2/(5c - Ik0)^2])(5c - Ik0)^4 - 16(-1 + Sqrt[1 + k^2/(5c - Ik0)^2])(5c - Ik0)^6)/(240k^4) + (5k^6 + 16k0^5(-k0 + Sqrt[-k^2 + k0^2]) - 8k^2k0^3(-5k0 + 4Sqrt[-k^2 + k0^2]) + 2k^4k0(-15k0 + 8Sqrt[-k^2 + k0^2]))/(240k^4))/k0^4
			(-(5Power(k,6) + 2Power(k,4)(15 - 8Sqrt(1 + Power(k,2)/Power(c - Complex(0,1)k0,2)))Power(c - Complex(0,1)k0,2) + 8Power(k,2)(5 - 4Sqrt(1 + Power(k,2)/Power(c - Complex(0,1)k0,2)))Power(c - Complex(0,1)k0,4) - 16(-1 + Sqrt(1 + Power(k,2)/Power(c - Complex(0,1)k0,2)))Power(c - Complex(0,1)k0,6))/(48.Power(k,4)) + (5Power(k,6) + 2Power(k,4)(15 - 8Sqrt(1 + Power(k,2)/Power(2c - Complex(0,1)k0,2)))Power(2c - Complex(0,1)k0,2) + 8Power(k,2)(5 - 4Sqrt(1 + Power(k,2)/Power(2c - Complex(0,1)k0,2)))Power(2c - Complex(0,1)k0,4) - 16(-1 + Sqrt(1 + Power(k,2)/Power(2c - Complex(0,1)k0,2)))Power(2c - Complex(0,1)k0,6))/(24.Power(k,4)) - (5Power(k,6) + 2Power(k,4)(15 - 8Sqrt(1 + Power(k,2)/Power(3c - Complex(0,1)k0,2)))Power(3c - Complex(0,1)k0,2) + 8Power(k,2)(5 - 4Sqrt(1 + Power(k,2)/Power(3c - Complex(0,1)k0,2)))Power(3c - Complex(0,1)k0,4) - 16(-1 + Sqrt(1 + Power(k,2)/Power(3c - Complex(0,1)k0,2)))Power(3c - Complex(0,1)k0,6))/(24.Power(k,4)) + (5Power(k,6) + 2Power(k,4)(15 - 8Sqrt(1 + Power(k,2)/Power(4c - Complex(0,1)k0,2)))Power(4c - Complex(0,1)k0,2) + 8Power(k,2)(5 - 4Sqrt(1 + Power(k,2)/Power(4c - Complex(0,1)k0,2)))Power(4c - Complex(0,1)k0,4) - 16(-1 + Sqrt(1 + Power(k,2)/Power(4c - Complex(0,1)k0,2)))Power(4c - Complex(0,1)k0,6))/(48.Power(k,4)) - (5Power(k,6) + 2Power(k,4)(15 - 8Sqrt(1 + Power(k,2)/Power(5c - Complex(0,1)k0,2)))Power(5c - Complex(0,1)k0,2) + 8Power(k,2)(5 - 4Sqrt(1 + Power(k,2)/Power(5c - Complex(0,1)k0,2)))Power(5c - Complex(0,1)k0,4) - 16(-1 + Sqrt(1 + Power(k,2)/Power(5c - Complex(0,1)k0,2)))Power(5c - Complex(0,1)k0,6))/(240.Power(k,4)) + (5Power(k,6) + 16Power(k0,5)(-k0 + Sqrt(-Power(k,2) + Power(k0,2))) - 8Power(k,2)Power(k0,3)(-5k0 + 4Sqrt(-Power(k,2) + Power(k0,2))) + 2Power(k,4)k0(-15k0 + 8Sqrt(-Power(k,2) + Power(k0,2))))/(240.Power(k,4)))/Power(k0,4)
			`SeriesData[k, Infinity, {(15c^5)/k0^4, (-120c^6)/k0^4 + ((48I)c^5)/k0^3, (35(20c^7 - (15I)c^6k0 - 3c^5k0^2))/(2k0^4), 0, (-105(331c^9 - (450I)c^8k0 - 240c^7k0^2 + (60I)c^6k0^3 + 6c^5k0^4))/(16k0^4), 0, (33(22430c^11 - (42525I)c^10k0 - 34755c^9k0^2 + (15750I)c^8k0^3 + 4200c^7k0^4 - (630I)c^6k0^5 - 42c^5k0^6))/(32*k0^4)}, 3, 11, 1]`
			(5k^4(-15 + 8Sqrt[1 + k^2/(c - Ik0)^2])(c - Ik0)^2 + 20k^2(-5 + 4Sqrt[1 + k^2/(c - Ik0)^2])(c - Ik0)^4 + 40(-1 + Sqrt[1 + k^2/(c - Ik0)^2])(c - Ik0)^6 + 10k^4(15 - 8Sqrt[1 + k^2/(2c - Ik0)^2])(2c - Ik0)^2 + 40k^2(5 - 4Sqrt[1 + k^2/(2c - Ik0)^2])(2c - Ik0)^4 - 80(-1 + Sqrt[1 + k^2/(2c - Ik0)^2])(2c - Ik0)^6 + 10k^4(-15 + 8Sqrt[1 + k^2/(3c - Ik0)^2])(3c - Ik0)^2 + 40k^2(-5 + 4Sqrt[1 + k^2/(3c - Ik0)^2])(3c - Ik0)^4 + 80(-1 + Sqrt[1 + k^2/(3c - Ik0)^2])(3c - Ik0)^6 + 5k^4(15 - 8Sqrt[1 + k^2/(4c - Ik0)^2])(4c - Ik0)^2 + 20k^2(5 - 4Sqrt[1 + k^2/(4c - Ik0)^2])(4c - Ik0)^4 - 40(-1 + Sqrt[1 + k^2/(4c - Ik0)^2])(4c - Ik0)^6 + k^4(-15 + 8Sqrt[1 + k^2/(5c - Ik0)^2])(5c - Ik0)^2 + 4k^2(-5 + 4Sqrt[1 + k^2/(5c - Ik0)^2])(5c - Ik0)^4 + 8(-1 + Sqrt[1 + k^2/(5c - Ik0)^2])(5c - Ik0)^6 + 8k0^5(-k0 + Sqrt[-k^2 + k0^2]) - 4k^2k0^3(-5k0 + 4Sqrt[-k^2 + k0^2]) + k^4k0(-15k0 + 8Sqrt[-k^2 + k0^2]))/(120k^4k0^4)