qpms/besseltransforms/klarge/5-3-2

(-5*(((-3 + 2*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0))/6 + ((-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^3)/(3*k^2)) + 10*(((-3 + 2*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0))/6 + ((-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^3)/(3*k^2)) - 10*(((-3 + 2*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0))/6 + ((-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^3)/(3*k^2)) + 5*(((-3 + 2*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0))/6 + ((-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^3)/(3*k^2)) - ((-3 + 2*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0))/6 - ((-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^3)/(3*k^2) + ((3*I)*k0 + 2*Sqrt[k^2 - k0^2] - (2*k0^2*(I*k0 + Sqrt[k^2 - k0^2]))/k^2)/6)/k0^3
(-5*(((-3 + 2*Sqrt(1 + Power(k,2)/Power(c - Complex(0,1)*k0,2)))*(c - Complex(0,1)*k0))/6. + ((-1 + Sqrt(1 + Power(k,2)/Power(c - Complex(0,1)*k0,2)))*Power(c - Complex(0,1)*k0,3))/(3.*Power(k,2))) + 10*(((-3 + 2*Sqrt(1 + Power(k,2)/Power(2*c - Complex(0,1)*k0,2)))*(2*c - Complex(0,1)*k0))/6. + ((-1 + Sqrt(1 + Power(k,2)/Power(2*c - Complex(0,1)*k0,2)))*Power(2*c - Complex(0,1)*k0,3))/(3.*Power(k,2))) - 10*(((-3 + 2*Sqrt(1 + Power(k,2)/Power(3*c - Complex(0,1)*k0,2)))*(3*c - Complex(0,1)*k0))/6. + ((-1 + Sqrt(1 + Power(k,2)/Power(3*c - Complex(0,1)*k0,2)))*Power(3*c - Complex(0,1)*k0,3))/(3.*Power(k,2))) + 5*(((-3 + 2*Sqrt(1 + Power(k,2)/Power(4*c - Complex(0,1)*k0,2)))*(4*c - Complex(0,1)*k0))/6. + ((-1 + Sqrt(1 + Power(k,2)/Power(4*c - Complex(0,1)*k0,2)))*Power(4*c - Complex(0,1)*k0,3))/(3.*Power(k,2))) - ((-3 + 2*Sqrt(1 + Power(k,2)/Power(5*c - Complex(0,1)*k0,2)))*(5*c - Complex(0,1)*k0))/6. - ((-1 + Sqrt(1 + Power(k,2)/Power(5*c - Complex(0,1)*k0,2)))*Power(5*c - Complex(0,1)*k0,3))/(3.*Power(k,2)) + (Complex(0,3)*k0 + 2*Sqrt(Power(k,2) - Power(k0,2)) - (2*Power(k0,2)*(Complex(0,1)*k0 + Sqrt(Power(k,2) - Power(k0,2))))/Power(k,2))/6.)/Power(k0,3)
SeriesData[k, Infinity, {(75*c^6)/(2*k0^3) - ((15*I)*c^5)/k0^2, 0, (-105*(75*c^8 - (80*I)*c^7*k0 - 30*c^6*k0^2 + (4*I)*c^5*k0^3))/(8*k0^3), 0, (315*(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*k0^3)}, 5, 11, 1]
(5*(3 - 2*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0) - (10*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^3)/k^2 + 10*(-3 + 2*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0) + (20*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^3)/k^2 + 10*(3 - 2*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0) - (20*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^3)/k^2 + 5*(-3 + 2*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0) + (10*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^3)/k^2 + (3 - 2*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0) - (2*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^3)/k^2 + (3*I)*k0 + 2*Sqrt[k^2 - k0^2] - (2*k0^2*(I*k0 + Sqrt[k^2 - k0^2]))/k^2)/(6*k0^3)
Další Hankelovy transformace pro kappa=5 Former-commit-id: cc20e7f5dbf8651a81543f84ac066d011e84082b 2018-01-23 00:52:10 +02:00			(-5(((-3 + 2Sqrt[1 + k^2/(c - Ik0)^2])(c - Ik0))/6 + ((-1 + Sqrt[1 + k^2/(c - Ik0)^2])(c - Ik0)^3)/(3k^2)) + 10(((-3 + 2Sqrt[1 + k^2/(2c - Ik0)^2])(2c - Ik0))/6 + ((-1 + Sqrt[1 + k^2/(2c - Ik0)^2])(2c - Ik0)^3)/(3k^2)) - 10(((-3 + 2Sqrt[1 + k^2/(3c - Ik0)^2])(3c - Ik0))/6 + ((-1 + Sqrt[1 + k^2/(3c - Ik0)^2])(3c - Ik0)^3)/(3k^2)) + 5(((-3 + 2Sqrt[1 + k^2/(4c - Ik0)^2])(4c - Ik0))/6 + ((-1 + Sqrt[1 + k^2/(4c - Ik0)^2])(4c - Ik0)^3)/(3k^2)) - ((-3 + 2Sqrt[1 + k^2/(5c - Ik0)^2])(5c - Ik0))/6 - ((-1 + Sqrt[1 + k^2/(5c - Ik0)^2])(5c - Ik0)^3)/(3k^2) + ((3I)k0 + 2Sqrt[k^2 - k0^2] - (2k0^2(Ik0 + Sqrt[k^2 - k0^2]))/k^2)/6)/k0^3
			(-5(((-3 + 2Sqrt(1 + Power(k,2)/Power(c - Complex(0,1)k0,2)))(c - Complex(0,1)k0))/6. + ((-1 + Sqrt(1 + Power(k,2)/Power(c - Complex(0,1)k0,2)))Power(c - Complex(0,1)k0,3))/(3.Power(k,2))) + 10(((-3 + 2Sqrt(1 + Power(k,2)/Power(2c - Complex(0,1)k0,2)))(2c - Complex(0,1)k0))/6. + ((-1 + Sqrt(1 + Power(k,2)/Power(2c - Complex(0,1)k0,2)))Power(2c - Complex(0,1)k0,3))/(3.Power(k,2))) - 10(((-3 + 2Sqrt(1 + Power(k,2)/Power(3c - Complex(0,1)k0,2)))(3c - Complex(0,1)k0))/6. + ((-1 + Sqrt(1 + Power(k,2)/Power(3c - Complex(0,1)k0,2)))Power(3c - Complex(0,1)k0,3))/(3.Power(k,2))) + 5(((-3 + 2Sqrt(1 + Power(k,2)/Power(4c - Complex(0,1)k0,2)))(4c - Complex(0,1)k0))/6. + ((-1 + Sqrt(1 + Power(k,2)/Power(4c - Complex(0,1)k0,2)))Power(4c - Complex(0,1)k0,3))/(3.Power(k,2))) - ((-3 + 2Sqrt(1 + Power(k,2)/Power(5c - Complex(0,1)k0,2)))(5c - Complex(0,1)k0))/6. - ((-1 + Sqrt(1 + Power(k,2)/Power(5c - Complex(0,1)k0,2)))Power(5c - Complex(0,1)k0,3))/(3.Power(k,2)) + (Complex(0,3)k0 + 2Sqrt(Power(k,2) - Power(k0,2)) - (2Power(k0,2)(Complex(0,1)*k0 + Sqrt(Power(k,2) - Power(k0,2))))/Power(k,2))/6.)/Power(k0,3)
			`SeriesData[k, Infinity, {(75c^6)/(2k0^3) - ((15I)c^5)/k0^2, 0, (-105(75c^8 - (80I)c^7k0 - 30c^6k0^2 + (4I)c^5k0^3))/(8k0^3), 0, (315(2025c^10 - (3310I)c^9k0 - 2250c^8k0^2 + (800I)c^7k0^3 + 150c^6k0^4 - (12I)c^5k0^5))/(32*k0^3)}, 5, 11, 1]`
			(5(3 - 2Sqrt[1 + k^2/(c - Ik0)^2])(c - Ik0) - (10(-1 + Sqrt[1 + k^2/(c - Ik0)^2])(c - Ik0)^3)/k^2 + 10(-3 + 2Sqrt[1 + k^2/(2c - Ik0)^2])(2c - Ik0) + (20(-1 + Sqrt[1 + k^2/(2c - Ik0)^2])(2c - Ik0)^3)/k^2 + 10(3 - 2Sqrt[1 + k^2/(3c - Ik0)^2])(3c - Ik0) - (20(-1 + Sqrt[1 + k^2/(3c - Ik0)^2])(3c - Ik0)^3)/k^2 + 5(-3 + 2Sqrt[1 + k^2/(4c - Ik0)^2])(4c - Ik0) + (10(-1 + Sqrt[1 + k^2/(4c - Ik0)^2])(4c - Ik0)^3)/k^2 + (3 - 2Sqrt[1 + k^2/(5c - Ik0)^2])(5c - Ik0) - (2(-1 + Sqrt[1 + k^2/(5c - Ik0)^2])(5c - Ik0)^3)/k^2 + (3I)k0 + 2Sqrt[k^2 - k0^2] - (2k0^2(Ik0 + Sqrt[k^2 - k0^2]))/k^2)/(6*k0^3)