qpms/besseltransforms/ksmall/5-4-5

(-(k^6*(-35 + 8*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0) + 20*k^4*(-7 + 4*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^3 + 8*k^2*(-21 + 17*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^5 + 64*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^7)/(168*k^5) + (k^6*(-35 + 8*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0) + 20*k^4*(-7 + 4*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^3 + 8*k^2*(-21 + 17*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^5 + 64*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^7)/(84*k^5) - (k^6*(-35 + 8*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0) + 20*k^4*(-7 + 4*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^3 + 8*k^2*(-21 + 17*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^5 + 64*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^7)/(84*k^5) + (k^6*(-35 + 8*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0) + 20*k^4*(-7 + 4*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^3 + 8*k^2*(-21 + 17*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^5 + 64*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^7)/(168*k^5) - (k^6*(-35 + 8*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0) + 20*k^4*(-7 + 4*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^3 + 8*k^2*(-21 + 17*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^5 + 64*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^7)/(840*k^5) + (I/840*(k^6*(35*k0 - 8*Sqrt[-k^2 + k0^2]) + 64*k0^6*(-k0 + Sqrt[-k^2 + k0^2]) + 20*k^4*k0^2*(-7*k0 + 4*Sqrt[-k^2 + k0^2]) - 8*k^2*k0^4*(-21*k0 + 17*Sqrt[-k^2 + k0^2])))/k^5)/k0^4
(-(Power(k,6)*(-35 + 8*Sqrt(1 + Power(k,2)/Power(c - Complex(0,1)*k0,2)))*(c - Complex(0,1)*k0) + 20*Power(k,4)*(-7 + 4*Sqrt(1 + Power(k,2)/Power(c - Complex(0,1)*k0,2)))*Power(c - Complex(0,1)*k0,3) + 8*Power(k,2)*(-21 + 17*Sqrt(1 + Power(k,2)/Power(c - Complex(0,1)*k0,2)))*Power(c - Complex(0,1)*k0,5) + 64*(-1 + Sqrt(1 + Power(k,2)/Power(c - Complex(0,1)*k0,2)))*Power(c - Complex(0,1)*k0,7))/(168.*Power(k,5)) + (Power(k,6)*(-35 + 8*Sqrt(1 + Power(k,2)/Power(2*c - Complex(0,1)*k0,2)))*(2*c - Complex(0,1)*k0) + 20*Power(k,4)*(-7 + 4*Sqrt(1 + Power(k,2)/Power(2*c - Complex(0,1)*k0,2)))*Power(2*c - Complex(0,1)*k0,3) + 8*Power(k,2)*(-21 + 17*Sqrt(1 + Power(k,2)/Power(2*c - Complex(0,1)*k0,2)))*Power(2*c - Complex(0,1)*k0,5) + 64*(-1 + Sqrt(1 + Power(k,2)/Power(2*c - Complex(0,1)*k0,2)))*Power(2*c - Complex(0,1)*k0,7))/(84.*Power(k,5)) - (Power(k,6)*(-35 + 8*Sqrt(1 + Power(k,2)/Power(3*c - Complex(0,1)*k0,2)))*(3*c - Complex(0,1)*k0) + 20*Power(k,4)*(-7 + 4*Sqrt(1 + Power(k,2)/Power(3*c - Complex(0,1)*k0,2)))*Power(3*c - Complex(0,1)*k0,3) + 8*Power(k,2)*(-21 + 17*Sqrt(1 + Power(k,2)/Power(3*c - Complex(0,1)*k0,2)))*Power(3*c - Complex(0,1)*k0,5) + 64*(-1 + Sqrt(1 + Power(k,2)/Power(3*c - Complex(0,1)*k0,2)))*Power(3*c - Complex(0,1)*k0,7))/(84.*Power(k,5)) + (Power(k,6)*(-35 + 8*Sqrt(1 + Power(k,2)/Power(4*c - Complex(0,1)*k0,2)))*(4*c - Complex(0,1)*k0) + 20*Power(k,4)*(-7 + 4*Sqrt(1 + Power(k,2)/Power(4*c - Complex(0,1)*k0,2)))*Power(4*c - Complex(0,1)*k0,3) + 8*Power(k,2)*(-21 + 17*Sqrt(1 + Power(k,2)/Power(4*c - Complex(0,1)*k0,2)))*Power(4*c - Complex(0,1)*k0,5) + 64*(-1 + Sqrt(1 + Power(k,2)/Power(4*c - Complex(0,1)*k0,2)))*Power(4*c - Complex(0,1)*k0,7))/(168.*Power(k,5)) - (Power(k,6)*(-35 + 8*Sqrt(1 + Power(k,2)/Power(5*c - Complex(0,1)*k0,2)))*(5*c - Complex(0,1)*k0) + 20*Power(k,4)*(-7 + 4*Sqrt(1 + Power(k,2)/Power(5*c - Complex(0,1)*k0,2)))*Power(5*c - Complex(0,1)*k0,3) + 8*Power(k,2)*(-21 + 17*Sqrt(1 + Power(k,2)/Power(5*c - Complex(0,1)*k0,2)))*Power(5*c - Complex(0,1)*k0,5) + 64*(-1 + Sqrt(1 + Power(k,2)/Power(5*c - Complex(0,1)*k0,2)))*Power(5*c - Complex(0,1)*k0,7))/(840.*Power(k,5)) + (Complex(0,0.0011904761904761906)*(Power(k,6)*(35*k0 - 8*Sqrt(-Power(k,2) + Power(k0,2))) + 64*Power(k0,6)*(-k0 + Sqrt(-Power(k,2) + Power(k0,2))) + 20*Power(k,4)*Power(k0,2)*(-7*k0 + 4*Sqrt(-Power(k,2) + Power(k0,2))) - 8*Power(k,2)*Power(k0,4)*(-21*k0 + 17*Sqrt(-Power(k,2) + Power(k0,2)))))/Power(k,5))/Power(k0,4)
SeriesData[k, Infinity, {(24*c^5)/k0^4, (-525*c^6)/(2*k0^4) + ((105*I)*c^5)/k0^3, (1280*c^7)/k0^4 - ((960*I)*c^6)/k0^3 - (192*c^5)/k0^2, (-315*(75*c^8 - (80*I)*c^7*k0 - 30*c^6*k0^2 + (4*I)*c^5*k0^3))/(8*k0^4), 0, (231*(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, (-429*(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^6*(-35 + 8*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0) + 20*k^4*(-7 + 4*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^3 + 8*k^2*(-21 + 17*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^5 + 64*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^7) - 10*(k^6*(-35 + 8*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0) + 20*k^4*(-7 + 4*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^3 + 8*k^2*(-21 + 17*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^5 + 64*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^7) + 10*(k^6*(-35 + 8*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0) + 20*k^4*(-7 + 4*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^3 + 8*k^2*(-21 + 17*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^5 + 64*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^7) - 5*(k^6*(-35 + 8*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0) + 20*k^4*(-7 + 4*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^3 + 8*k^2*(-21 + 17*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^5 + 64*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^7) + k^6*(-35 + 8*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0) + 20*k^4*(-7 + 4*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^3 + 8*k^2*(-21 + 17*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^5 + 64*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^7 - I*(k^6*(35*k0 - 8*Sqrt[-k^2 + k0^2]) + 64*k0^6*(-k0 + Sqrt[-k^2 + k0^2]) + 20*k^4*k0^2*(-7*k0 + 4*Sqrt[-k^2 + k0^2]) - 8*k^2*k0^4*(-21*k0 + 17*Sqrt[-k^2 + k0^2])))/(840*k^5*k0^4)
Další Hankelovy transformace pro kappa=5 Former-commit-id: cc20e7f5dbf8651a81543f84ac066d011e84082b 2018-01-23 00:52:10 +02:00			(-(k^6(-35 + 8Sqrt[1 + k^2/(c - Ik0)^2])(c - Ik0) + 20k^4(-7 + 4Sqrt[1 + k^2/(c - Ik0)^2])(c - Ik0)^3 + 8k^2(-21 + 17Sqrt[1 + k^2/(c - Ik0)^2])(c - Ik0)^5 + 64(-1 + Sqrt[1 + k^2/(c - Ik0)^2])(c - Ik0)^7)/(168k^5) + (k^6(-35 + 8Sqrt[1 + k^2/(2c - Ik0)^2])(2c - Ik0) + 20k^4(-7 + 4Sqrt[1 + k^2/(2c - Ik0)^2])(2c - Ik0)^3 + 8k^2(-21 + 17Sqrt[1 + k^2/(2c - Ik0)^2])(2c - Ik0)^5 + 64(-1 + Sqrt[1 + k^2/(2c - Ik0)^2])(2c - Ik0)^7)/(84k^5) - (k^6(-35 + 8Sqrt[1 + k^2/(3c - Ik0)^2])(3c - Ik0) + 20k^4(-7 + 4Sqrt[1 + k^2/(3c - Ik0)^2])(3c - Ik0)^3 + 8k^2(-21 + 17Sqrt[1 + k^2/(3c - Ik0)^2])(3c - Ik0)^5 + 64(-1 + Sqrt[1 + k^2/(3c - Ik0)^2])(3c - Ik0)^7)/(84k^5) + (k^6(-35 + 8Sqrt[1 + k^2/(4c - Ik0)^2])(4c - Ik0) + 20k^4(-7 + 4Sqrt[1 + k^2/(4c - Ik0)^2])(4c - Ik0)^3 + 8k^2(-21 + 17Sqrt[1 + k^2/(4c - Ik0)^2])(4c - Ik0)^5 + 64(-1 + Sqrt[1 + k^2/(4c - Ik0)^2])(4c - Ik0)^7)/(168k^5) - (k^6(-35 + 8Sqrt[1 + k^2/(5c - Ik0)^2])(5c - Ik0) + 20k^4(-7 + 4Sqrt[1 + k^2/(5c - Ik0)^2])(5c - Ik0)^3 + 8k^2(-21 + 17Sqrt[1 + k^2/(5c - Ik0)^2])(5c - Ik0)^5 + 64(-1 + Sqrt[1 + k^2/(5c - Ik0)^2])(5c - Ik0)^7)/(840k^5) + (I/840(k^6(35k0 - 8Sqrt[-k^2 + k0^2]) + 64k0^6(-k0 + Sqrt[-k^2 + k0^2]) + 20k^4k0^2(-7k0 + 4Sqrt[-k^2 + k0^2]) - 8k^2k0^4(-21k0 + 17Sqrt[-k^2 + k0^2])))/k^5)/k0^4
			(-(Power(k,6)(-35 + 8Sqrt(1 + Power(k,2)/Power(c - Complex(0,1)k0,2)))(c - Complex(0,1)k0) + 20Power(k,4)(-7 + 4Sqrt(1 + Power(k,2)/Power(c - Complex(0,1)k0,2)))Power(c - Complex(0,1)k0,3) + 8Power(k,2)(-21 + 17Sqrt(1 + Power(k,2)/Power(c - Complex(0,1)k0,2)))Power(c - Complex(0,1)k0,5) + 64(-1 + Sqrt(1 + Power(k,2)/Power(c - Complex(0,1)k0,2)))Power(c - Complex(0,1)k0,7))/(168.Power(k,5)) + (Power(k,6)(-35 + 8Sqrt(1 + Power(k,2)/Power(2c - Complex(0,1)k0,2)))(2c - Complex(0,1)k0) + 20Power(k,4)(-7 + 4Sqrt(1 + Power(k,2)/Power(2c - Complex(0,1)k0,2)))Power(2c - Complex(0,1)k0,3) + 8Power(k,2)(-21 + 17Sqrt(1 + Power(k,2)/Power(2c - Complex(0,1)k0,2)))Power(2c - Complex(0,1)k0,5) + 64(-1 + Sqrt(1 + Power(k,2)/Power(2c - Complex(0,1)k0,2)))Power(2c - Complex(0,1)k0,7))/(84.Power(k,5)) - (Power(k,6)(-35 + 8Sqrt(1 + Power(k,2)/Power(3c - Complex(0,1)k0,2)))(3c - Complex(0,1)k0) + 20Power(k,4)(-7 + 4Sqrt(1 + Power(k,2)/Power(3c - Complex(0,1)k0,2)))Power(3c - Complex(0,1)k0,3) + 8Power(k,2)(-21 + 17Sqrt(1 + Power(k,2)/Power(3c - Complex(0,1)k0,2)))Power(3c - Complex(0,1)k0,5) + 64(-1 + Sqrt(1 + Power(k,2)/Power(3c - Complex(0,1)k0,2)))Power(3c - Complex(0,1)k0,7))/(84.Power(k,5)) + (Power(k,6)(-35 + 8Sqrt(1 + Power(k,2)/Power(4c - Complex(0,1)k0,2)))(4c - Complex(0,1)k0) + 20Power(k,4)(-7 + 4Sqrt(1 + Power(k,2)/Power(4c - Complex(0,1)k0,2)))Power(4c - Complex(0,1)k0,3) + 8Power(k,2)(-21 + 17Sqrt(1 + Power(k,2)/Power(4c - Complex(0,1)k0,2)))Power(4c - Complex(0,1)k0,5) + 64(-1 + Sqrt(1 + Power(k,2)/Power(4c - Complex(0,1)k0,2)))Power(4c - Complex(0,1)k0,7))/(168.Power(k,5)) - (Power(k,6)(-35 + 8Sqrt(1 + Power(k,2)/Power(5c - Complex(0,1)k0,2)))(5c - Complex(0,1)k0) + 20Power(k,4)(-7 + 4Sqrt(1 + Power(k,2)/Power(5c - Complex(0,1)k0,2)))Power(5c - Complex(0,1)k0,3) + 8Power(k,2)(-21 + 17Sqrt(1 + Power(k,2)/Power(5c - Complex(0,1)k0,2)))Power(5c - Complex(0,1)k0,5) + 64(-1 + Sqrt(1 + Power(k,2)/Power(5c - Complex(0,1)k0,2)))Power(5c - Complex(0,1)k0,7))/(840.Power(k,5)) + (Complex(0,0.0011904761904761906)(Power(k,6)(35k0 - 8Sqrt(-Power(k,2) + Power(k0,2))) + 64Power(k0,6)(-k0 + Sqrt(-Power(k,2) + Power(k0,2))) + 20Power(k,4)Power(k0,2)(-7k0 + 4Sqrt(-Power(k,2) + Power(k0,2))) - 8Power(k,2)Power(k0,4)(-21k0 + 17Sqrt(-Power(k,2) + Power(k0,2)))))/Power(k,5))/Power(k0,4)
			`SeriesData[k, Infinity, {(24c^5)/k0^4, (-525c^6)/(2k0^4) + ((105I)c^5)/k0^3, (1280c^7)/k0^4 - ((960I)c^6)/k0^3 - (192c^5)/k0^2, (-315(75c^8 - (80I)c^7k0 - 30c^6k0^2 + (4I)c^5k0^3))/(8k0^4), 0, (231(2025c^10 - (3310I)c^9k0 - 2250c^8k0^2 + (800I)c^7k0^3 + 150c^6k0^4 - (12I)c^5k0^5))/(32k0^4), 0, (-429(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^6(-35 + 8Sqrt[1 + k^2/(c - Ik0)^2])(c - Ik0) + 20k^4(-7 + 4Sqrt[1 + k^2/(c - Ik0)^2])(c - Ik0)^3 + 8k^2(-21 + 17Sqrt[1 + k^2/(c - Ik0)^2])(c - Ik0)^5 + 64(-1 + Sqrt[1 + k^2/(c - Ik0)^2])(c - Ik0)^7) - 10(k^6(-35 + 8Sqrt[1 + k^2/(2c - Ik0)^2])(2c - Ik0) + 20k^4(-7 + 4Sqrt[1 + k^2/(2c - Ik0)^2])(2c - Ik0)^3 + 8k^2(-21 + 17Sqrt[1 + k^2/(2c - Ik0)^2])(2c - Ik0)^5 + 64(-1 + Sqrt[1 + k^2/(2c - Ik0)^2])(2c - Ik0)^7) + 10(k^6(-35 + 8Sqrt[1 + k^2/(3c - Ik0)^2])(3c - Ik0) + 20k^4(-7 + 4Sqrt[1 + k^2/(3c - Ik0)^2])(3c - Ik0)^3 + 8k^2(-21 + 17Sqrt[1 + k^2/(3c - Ik0)^2])(3c - Ik0)^5 + 64(-1 + Sqrt[1 + k^2/(3c - Ik0)^2])(3c - Ik0)^7) - 5(k^6(-35 + 8Sqrt[1 + k^2/(4c - Ik0)^2])(4c - Ik0) + 20k^4(-7 + 4Sqrt[1 + k^2/(4c - Ik0)^2])(4c - Ik0)^3 + 8k^2(-21 + 17Sqrt[1 + k^2/(4c - Ik0)^2])(4c - Ik0)^5 + 64(-1 + Sqrt[1 + k^2/(4c - Ik0)^2])(4c - Ik0)^7) + k^6(-35 + 8Sqrt[1 + k^2/(5c - Ik0)^2])(5c - Ik0) + 20k^4(-7 + 4Sqrt[1 + k^2/(5c - Ik0)^2])(5c - Ik0)^3 + 8k^2(-21 + 17Sqrt[1 + k^2/(5c - Ik0)^2])(5c - Ik0)^5 + 64(-1 + Sqrt[1 + k^2/(5c - Ik0)^2])(5c - Ik0)^7 - I(k^6(35k0 - 8Sqrt[-k^2 + k0^2]) + 64k0^6(-k0 + Sqrt[-k^2 + k0^2]) + 20k^4k0^2(-7k0 + 4Sqrt[-k^2 + k0^2]) - 8k^2k0^4(-21k0 + 17Sqrt[-k^2 + k0^2])))/(840k^5*k0^4)