qpms/besseltransforms/klarge/5-2-5

(-((k^4*(-5 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0) + 4*k^2*(-5 + 3*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^3 + 16*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^5)/k^5) + (2*(k^4*(-5 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0) + 4*k^2*(-5 + 3*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^3 + 16*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^5))/k^5 - (2*(k^4*(-5 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0) + 4*k^2*(-5 + 3*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^3 + 16*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^5))/k^5 + (k^4*(-5 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0) + 4*k^2*(-5 + 3*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^3 + 16*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^5)/k^5 - (k^4*(-5 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0) + 4*k^2*(-5 + 3*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^3 + 16*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^5)/(5*k^5) + (16*k0^4*(I*k0 + Sqrt[k^2 - k0^2]) + k^4*((5*I)*k0 + Sqrt[k^2 - k0^2]) - 4*k^2*k0^2*((5*I)*k0 + 3*Sqrt[k^2 - k0^2]))/(5*k^5))/k0^2
(-((Power(k,4)*(-5 + Sqrt(1 + Power(k,2)/Power(c - Complex(0,1)*k0,2)))*(c - Complex(0,1)*k0) + 4*Power(k,2)*(-5 + 3*Sqrt(1 + Power(k,2)/Power(c - Complex(0,1)*k0,2)))*Power(c - Complex(0,1)*k0,3) + 16*(-1 + Sqrt(1 + Power(k,2)/Power(c - Complex(0,1)*k0,2)))*Power(c - Complex(0,1)*k0,5))/Power(k,5)) + (2*(Power(k,4)*(-5 + Sqrt(1 + Power(k,2)/Power(2*c - Complex(0,1)*k0,2)))*(2*c - Complex(0,1)*k0) + 4*Power(k,2)*(-5 + 3*Sqrt(1 + Power(k,2)/Power(2*c - Complex(0,1)*k0,2)))*Power(2*c - Complex(0,1)*k0,3) + 16*(-1 + Sqrt(1 + Power(k,2)/Power(2*c - Complex(0,1)*k0,2)))*Power(2*c - Complex(0,1)*k0,5)))/Power(k,5) - (2*(Power(k,4)*(-5 + Sqrt(1 + Power(k,2)/Power(3*c - Complex(0,1)*k0,2)))*(3*c - Complex(0,1)*k0) + 4*Power(k,2)*(-5 + 3*Sqrt(1 + Power(k,2)/Power(3*c - Complex(0,1)*k0,2)))*Power(3*c - Complex(0,1)*k0,3) + 16*(-1 + Sqrt(1 + Power(k,2)/Power(3*c - Complex(0,1)*k0,2)))*Power(3*c - Complex(0,1)*k0,5)))/Power(k,5) + (Power(k,4)*(-5 + Sqrt(1 + Power(k,2)/Power(4*c - Complex(0,1)*k0,2)))*(4*c - Complex(0,1)*k0) + 4*Power(k,2)*(-5 + 3*Sqrt(1 + Power(k,2)/Power(4*c - Complex(0,1)*k0,2)))*Power(4*c - Complex(0,1)*k0,3) + 16*(-1 + Sqrt(1 + Power(k,2)/Power(4*c - Complex(0,1)*k0,2)))*Power(4*c - Complex(0,1)*k0,5))/Power(k,5) - (Power(k,4)*(-5 + Sqrt(1 + Power(k,2)/Power(5*c - Complex(0,1)*k0,2)))*(5*c - Complex(0,1)*k0) + 4*Power(k,2)*(-5 + 3*Sqrt(1 + Power(k,2)/Power(5*c - Complex(0,1)*k0,2)))*Power(5*c - Complex(0,1)*k0,3) + 16*(-1 + Sqrt(1 + Power(k,2)/Power(5*c - Complex(0,1)*k0,2)))*Power(5*c - Complex(0,1)*k0,5))/(5.*Power(k,5)) + (16*Power(k0,4)*(Complex(0,1)*k0 + Sqrt(Power(k,2) - Power(k0,2))) + Power(k,4)*(Complex(0,5)*k0 + Sqrt(Power(k,2) - Power(k0,2))) - 4*Power(k,2)*Power(k0,2)*(Complex(0,5)*k0 + 3*Sqrt(Power(k,2) - Power(k0,2))))/(5.*Power(k,5)))/Power(k0,2)
SeriesData[k, Infinity, {(384*c^5)/k0^2, (-4725*c^6)/(2*k0^2) + ((945*I)*c^5)/k0, 0, (-51975*c^6)/4 + (259875*c^8)/(8*k0^2) - ((34650*I)*c^7)/k0 + (3465*I)/2*c^5*k0, 0, (-9009*(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*k0^2)}, 5, 11, 1]
-(5*(k^4*(-5 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0) + 4*k^2*(-5 + 3*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^3 + 16*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^5) - 10*(k^4*(-5 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0) + 4*k^2*(-5 + 3*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^3 + 16*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^5) + 10*(k^4*(-5 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0) + 4*k^2*(-5 + 3*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^3 + 16*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^5) - 5*(k^4*(-5 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0) + 4*k^2*(-5 + 3*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^3 + 16*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^5) + k^4*(-5 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0) + 4*k^2*(-5 + 3*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^3 + 16*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^5 - 16*k0^4*(I*k0 + Sqrt[k^2 - k0^2]) - k^4*((5*I)*k0 + Sqrt[k^2 - k0^2]) + 4*k^2*k0^2*((5*I)*k0 + 3*Sqrt[k^2 - k0^2]))/(5*k^5*k0^2)
Další Hankelovy transformace pro kappa=5 Former-commit-id: cc20e7f5dbf8651a81543f84ac066d011e84082b 2018-01-23 00:52:10 +02:00			(-((k^4(-5 + Sqrt[1 + k^2/(c - Ik0)^2])(c - Ik0) + 4k^2(-5 + 3Sqrt[1 + k^2/(c - Ik0)^2])(c - Ik0)^3 + 16(-1 + Sqrt[1 + k^2/(c - Ik0)^2])(c - Ik0)^5)/k^5) + (2(k^4(-5 + Sqrt[1 + k^2/(2c - Ik0)^2])(2c - Ik0) + 4k^2(-5 + 3Sqrt[1 + k^2/(2c - Ik0)^2])(2c - Ik0)^3 + 16(-1 + Sqrt[1 + k^2/(2c - Ik0)^2])(2c - Ik0)^5))/k^5 - (2(k^4(-5 + Sqrt[1 + k^2/(3c - Ik0)^2])(3c - Ik0) + 4k^2(-5 + 3Sqrt[1 + k^2/(3c - Ik0)^2])(3c - Ik0)^3 + 16(-1 + Sqrt[1 + k^2/(3c - Ik0)^2])(3c - Ik0)^5))/k^5 + (k^4(-5 + Sqrt[1 + k^2/(4c - Ik0)^2])(4c - Ik0) + 4k^2(-5 + 3Sqrt[1 + k^2/(4c - Ik0)^2])(4c - Ik0)^3 + 16(-1 + Sqrt[1 + k^2/(4c - Ik0)^2])(4c - Ik0)^5)/k^5 - (k^4(-5 + Sqrt[1 + k^2/(5c - Ik0)^2])(5c - Ik0) + 4k^2(-5 + 3Sqrt[1 + k^2/(5c - Ik0)^2])(5c - Ik0)^3 + 16(-1 + Sqrt[1 + k^2/(5c - Ik0)^2])(5c - Ik0)^5)/(5k^5) + (16k0^4(Ik0 + Sqrt[k^2 - k0^2]) + k^4((5I)k0 + Sqrt[k^2 - k0^2]) - 4k^2k0^2((5I)k0 + 3Sqrt[k^2 - k0^2]))/(5k^5))/k0^2
			(-((Power(k,4)(-5 + Sqrt(1 + Power(k,2)/Power(c - Complex(0,1)k0,2)))(c - Complex(0,1)k0) + 4Power(k,2)(-5 + 3Sqrt(1 + Power(k,2)/Power(c - Complex(0,1)k0,2)))Power(c - Complex(0,1)k0,3) + 16(-1 + Sqrt(1 + Power(k,2)/Power(c - Complex(0,1)k0,2)))Power(c - Complex(0,1)k0,5))/Power(k,5)) + (2(Power(k,4)(-5 + Sqrt(1 + Power(k,2)/Power(2c - Complex(0,1)k0,2)))(2c - Complex(0,1)k0) + 4Power(k,2)(-5 + 3Sqrt(1 + Power(k,2)/Power(2c - Complex(0,1)k0,2)))Power(2c - Complex(0,1)k0,3) + 16(-1 + Sqrt(1 + Power(k,2)/Power(2c - Complex(0,1)k0,2)))Power(2c - Complex(0,1)k0,5)))/Power(k,5) - (2(Power(k,4)(-5 + Sqrt(1 + Power(k,2)/Power(3c - Complex(0,1)k0,2)))(3c - Complex(0,1)k0) + 4Power(k,2)(-5 + 3Sqrt(1 + Power(k,2)/Power(3c - Complex(0,1)k0,2)))Power(3c - Complex(0,1)k0,3) + 16(-1 + Sqrt(1 + Power(k,2)/Power(3c - Complex(0,1)k0,2)))Power(3c - Complex(0,1)k0,5)))/Power(k,5) + (Power(k,4)(-5 + Sqrt(1 + Power(k,2)/Power(4c - Complex(0,1)k0,2)))(4c - Complex(0,1)k0) + 4Power(k,2)(-5 + 3Sqrt(1 + Power(k,2)/Power(4c - Complex(0,1)k0,2)))Power(4c - Complex(0,1)k0,3) + 16(-1 + Sqrt(1 + Power(k,2)/Power(4c - Complex(0,1)k0,2)))Power(4c - Complex(0,1)k0,5))/Power(k,5) - (Power(k,4)(-5 + Sqrt(1 + Power(k,2)/Power(5c - Complex(0,1)k0,2)))(5c - Complex(0,1)k0) + 4Power(k,2)(-5 + 3Sqrt(1 + Power(k,2)/Power(5c - Complex(0,1)k0,2)))Power(5c - Complex(0,1)k0,3) + 16(-1 + Sqrt(1 + Power(k,2)/Power(5c - Complex(0,1)k0,2)))Power(5c - Complex(0,1)k0,5))/(5.Power(k,5)) + (16Power(k0,4)(Complex(0,1)k0 + Sqrt(Power(k,2) - Power(k0,2))) + Power(k,4)(Complex(0,5)k0 + Sqrt(Power(k,2) - Power(k0,2))) - 4Power(k,2)Power(k0,2)(Complex(0,5)k0 + 3Sqrt(Power(k,2) - Power(k0,2))))/(5.Power(k,5)))/Power(k0,2)
			`SeriesData[k, Infinity, {(384c^5)/k0^2, (-4725c^6)/(2k0^2) + ((945I)c^5)/k0, 0, (-51975c^6)/4 + (259875c^8)/(8k0^2) - ((34650I)c^7)/k0 + (3465I)/2c^5k0, 0, (-9009(2025c^10 - (3310I)c^9k0 - 2250c^8k0^2 + (800I)c^7k0^3 + 150c^6k0^4 - (12I)c^5k0^5))/(32*k0^2)}, 5, 11, 1]`
			-(5(k^4(-5 + Sqrt[1 + k^2/(c - Ik0)^2])(c - Ik0) + 4k^2(-5 + 3Sqrt[1 + k^2/(c - Ik0)^2])(c - Ik0)^3 + 16(-1 + Sqrt[1 + k^2/(c - Ik0)^2])(c - Ik0)^5) - 10(k^4(-5 + Sqrt[1 + k^2/(2c - Ik0)^2])(2c - Ik0) + 4k^2(-5 + 3Sqrt[1 + k^2/(2c - Ik0)^2])(2c - Ik0)^3 + 16(-1 + Sqrt[1 + k^2/(2c - Ik0)^2])(2c - Ik0)^5) + 10(k^4(-5 + Sqrt[1 + k^2/(3c - Ik0)^2])(3c - Ik0) + 4k^2(-5 + 3Sqrt[1 + k^2/(3c - Ik0)^2])(3c - Ik0)^3 + 16(-1 + Sqrt[1 + k^2/(3c - Ik0)^2])(3c - Ik0)^5) - 5(k^4(-5 + Sqrt[1 + k^2/(4c - Ik0)^2])(4c - Ik0) + 4k^2(-5 + 3Sqrt[1 + k^2/(4c - Ik0)^2])(4c - Ik0)^3 + 16(-1 + Sqrt[1 + k^2/(4c - Ik0)^2])(4c - Ik0)^5) + k^4(-5 + Sqrt[1 + k^2/(5c - Ik0)^2])(5c - Ik0) + 4k^2(-5 + 3Sqrt[1 + k^2/(5c - Ik0)^2])(5c - Ik0)^3 + 16(-1 + Sqrt[1 + k^2/(5c - Ik0)^2])(5c - Ik0)^5 - 16k0^4(Ik0 + Sqrt[k^2 - k0^2]) - k^4((5I)k0 + Sqrt[k^2 - k0^2]) + 4k^2k0^2((5I)k0 + 3Sqrt[k^2 - k0^2]))/(5k^5k0^2)