qpms/besseltransforms/ksmall/5-5-4

(-(k^6*(-35 + 16*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0) + 2*k^4*(-35 + 24*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^3 + 8*k^2*(-7 + 6*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^5 + 16*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^7)/(336*k^4) + (k^6*(-35 + 16*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0) + 2*k^4*(-35 + 24*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^3 + 8*k^2*(-7 + 6*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^5 + 16*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^7)/(168*k^4) - (k^6*(-35 + 16*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0) + 2*k^4*(-35 + 24*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^3 + 8*k^2*(-7 + 6*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^5 + 16*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^7)/(168*k^4) + (k^6*(-35 + 16*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0) + 2*k^4*(-35 + 24*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^3 + 8*k^2*(-7 + 6*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^5 + 16*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^7)/(336*k^4) - (k^6*(-35 + 16*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0) + 2*k^4*(-35 + 24*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^3 + 8*k^2*(-7 + 6*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^5 + 16*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^7)/(1680*k^4) + (I/1680*(k^6*(35*k0 - 16*Sqrt[-k^2 + k0^2]) + 16*k0^6*(-k0 + Sqrt[-k^2 + k0^2]) - 8*k^2*k0^4*(-7*k0 + 6*Sqrt[-k^2 + k0^2]) + 2*k^4*k0^2*(-35*k0 + 24*Sqrt[-k^2 + k0^2])))/k^4)/k0^5
(-(Power(k,6)*(-35 + 16*Sqrt(1 + Power(k,2)/Power(c - Complex(0,1)*k0,2)))*(c - Complex(0,1)*k0) + 2*Power(k,4)*(-35 + 24*Sqrt(1 + Power(k,2)/Power(c - Complex(0,1)*k0,2)))*Power(c - Complex(0,1)*k0,3) + 8*Power(k,2)*(-7 + 6*Sqrt(1 + Power(k,2)/Power(c - Complex(0,1)*k0,2)))*Power(c - Complex(0,1)*k0,5) + 16*(-1 + Sqrt(1 + Power(k,2)/Power(c - Complex(0,1)*k0,2)))*Power(c - Complex(0,1)*k0,7))/(336.*Power(k,4)) + (Power(k,6)*(-35 + 16*Sqrt(1 + Power(k,2)/Power(2*c - Complex(0,1)*k0,2)))*(2*c - Complex(0,1)*k0) + 2*Power(k,4)*(-35 + 24*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)*(-7 + 6*Sqrt(1 + Power(k,2)/Power(2*c - Complex(0,1)*k0,2)))*Power(2*c - Complex(0,1)*k0,5) + 16*(-1 + Sqrt(1 + Power(k,2)/Power(2*c - Complex(0,1)*k0,2)))*Power(2*c - Complex(0,1)*k0,7))/(168.*Power(k,4)) - (Power(k,6)*(-35 + 16*Sqrt(1 + Power(k,2)/Power(3*c - Complex(0,1)*k0,2)))*(3*c - Complex(0,1)*k0) + 2*Power(k,4)*(-35 + 24*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)*(-7 + 6*Sqrt(1 + Power(k,2)/Power(3*c - Complex(0,1)*k0,2)))*Power(3*c - Complex(0,1)*k0,5) + 16*(-1 + Sqrt(1 + Power(k,2)/Power(3*c - Complex(0,1)*k0,2)))*Power(3*c - Complex(0,1)*k0,7))/(168.*Power(k,4)) + (Power(k,6)*(-35 + 16*Sqrt(1 + Power(k,2)/Power(4*c - Complex(0,1)*k0,2)))*(4*c - Complex(0,1)*k0) + 2*Power(k,4)*(-35 + 24*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)*(-7 + 6*Sqrt(1 + Power(k,2)/Power(4*c - Complex(0,1)*k0,2)))*Power(4*c - Complex(0,1)*k0,5) + 16*(-1 + Sqrt(1 + Power(k,2)/Power(4*c - Complex(0,1)*k0,2)))*Power(4*c - Complex(0,1)*k0,7))/(336.*Power(k,4)) - (Power(k,6)*(-35 + 16*Sqrt(1 + Power(k,2)/Power(5*c - Complex(0,1)*k0,2)))*(5*c - Complex(0,1)*k0) + 2*Power(k,4)*(-35 + 24*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)*(-7 + 6*Sqrt(1 + Power(k,2)/Power(5*c - Complex(0,1)*k0,2)))*Power(5*c - Complex(0,1)*k0,5) + 16*(-1 + Sqrt(1 + Power(k,2)/Power(5*c - Complex(0,1)*k0,2)))*Power(5*c - Complex(0,1)*k0,7))/(1680.*Power(k,4)) + (Complex(0,0.0005952380952380953)*(Power(k,6)*(35*k0 - 16*Sqrt(-Power(k,2) + Power(k0,2))) + 16*Power(k0,6)*(-k0 + Sqrt(-Power(k,2) + Power(k0,2))) - 8*Power(k,2)*Power(k0,4)*(-7*k0 + 6*Sqrt(-Power(k,2) + Power(k0,2))) + 2*Power(k,4)*Power(k0,2)*(-35*k0 + 24*Sqrt(-Power(k,2) + Power(k0,2)))))/Power(k,4))/Power(k0,5)
SeriesData[k, Infinity, {(4*c^5)/k0^5, (-75*c^6)/(2*k0^5) + ((15*I)*c^5)/k0^4, (160*c^7)/k0^5 - ((120*I)*c^6)/k0^4 - (24*c^5)/k0^3, (-35*(75*c^8 - (80*I)*c^7*k0 - 30*c^6*k0^2 + (4*I)*c^5*k0^3))/(8*k0^5), 0, (21*(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*k0^5), 0, (-33*(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*k0^5)}, 2, 11, 1]
-(5*(k^6*(-35 + 16*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0) + 2*k^4*(-35 + 24*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^3 + 8*k^2*(-7 + 6*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^5 + 16*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^7) - 10*(k^6*(-35 + 16*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0) + 2*k^4*(-35 + 24*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^3 + 8*k^2*(-7 + 6*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^5 + 16*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^7) + 10*(k^6*(-35 + 16*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0) + 2*k^4*(-35 + 24*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^3 + 8*k^2*(-7 + 6*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^5 + 16*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^7) - 5*(k^6*(-35 + 16*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0) + 2*k^4*(-35 + 24*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^3 + 8*k^2*(-7 + 6*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^5 + 16*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^7) + k^6*(-35 + 16*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0) + 2*k^4*(-35 + 24*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^3 + 8*k^2*(-7 + 6*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^5 + 16*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^7 - I*(k^6*(35*k0 - 16*Sqrt[-k^2 + k0^2]) + 16*k0^6*(-k0 + Sqrt[-k^2 + k0^2]) - 8*k^2*k0^4*(-7*k0 + 6*Sqrt[-k^2 + k0^2]) + 2*k^4*k0^2*(-35*k0 + 24*Sqrt[-k^2 + k0^2])))/(1680*k^4*k0^5)
Další Hankelovy transformace pro kappa=5 Former-commit-id: cc20e7f5dbf8651a81543f84ac066d011e84082b 2018-01-23 00:52:10 +02:00			(-(k^6(-35 + 16Sqrt[1 + k^2/(c - Ik0)^2])(c - Ik0) + 2k^4(-35 + 24Sqrt[1 + k^2/(c - Ik0)^2])(c - Ik0)^3 + 8k^2(-7 + 6Sqrt[1 + k^2/(c - Ik0)^2])(c - Ik0)^5 + 16(-1 + Sqrt[1 + k^2/(c - Ik0)^2])(c - Ik0)^7)/(336k^4) + (k^6(-35 + 16Sqrt[1 + k^2/(2c - Ik0)^2])(2c - Ik0) + 2k^4(-35 + 24Sqrt[1 + k^2/(2c - Ik0)^2])(2c - Ik0)^3 + 8k^2(-7 + 6Sqrt[1 + k^2/(2c - Ik0)^2])(2c - Ik0)^5 + 16(-1 + Sqrt[1 + k^2/(2c - Ik0)^2])(2c - Ik0)^7)/(168k^4) - (k^6(-35 + 16Sqrt[1 + k^2/(3c - Ik0)^2])(3c - Ik0) + 2k^4(-35 + 24Sqrt[1 + k^2/(3c - Ik0)^2])(3c - Ik0)^3 + 8k^2(-7 + 6Sqrt[1 + k^2/(3c - Ik0)^2])(3c - Ik0)^5 + 16(-1 + Sqrt[1 + k^2/(3c - Ik0)^2])(3c - Ik0)^7)/(168k^4) + (k^6(-35 + 16Sqrt[1 + k^2/(4c - Ik0)^2])(4c - Ik0) + 2k^4(-35 + 24Sqrt[1 + k^2/(4c - Ik0)^2])(4c - Ik0)^3 + 8k^2(-7 + 6Sqrt[1 + k^2/(4c - Ik0)^2])(4c - Ik0)^5 + 16(-1 + Sqrt[1 + k^2/(4c - Ik0)^2])(4c - Ik0)^7)/(336k^4) - (k^6(-35 + 16Sqrt[1 + k^2/(5c - Ik0)^2])(5c - Ik0) + 2k^4(-35 + 24Sqrt[1 + k^2/(5c - Ik0)^2])(5c - Ik0)^3 + 8k^2(-7 + 6Sqrt[1 + k^2/(5c - Ik0)^2])(5c - Ik0)^5 + 16(-1 + Sqrt[1 + k^2/(5c - Ik0)^2])(5c - Ik0)^7)/(1680k^4) + (I/1680(k^6(35k0 - 16Sqrt[-k^2 + k0^2]) + 16k0^6(-k0 + Sqrt[-k^2 + k0^2]) - 8k^2k0^4(-7k0 + 6Sqrt[-k^2 + k0^2]) + 2k^4k0^2(-35k0 + 24Sqrt[-k^2 + k0^2])))/k^4)/k0^5
			(-(Power(k,6)(-35 + 16Sqrt(1 + Power(k,2)/Power(c - Complex(0,1)k0,2)))(c - Complex(0,1)k0) + 2Power(k,4)(-35 + 24Sqrt(1 + Power(k,2)/Power(c - Complex(0,1)k0,2)))Power(c - Complex(0,1)k0,3) + 8Power(k,2)(-7 + 6Sqrt(1 + Power(k,2)/Power(c - Complex(0,1)k0,2)))Power(c - Complex(0,1)k0,5) + 16(-1 + Sqrt(1 + Power(k,2)/Power(c - Complex(0,1)k0,2)))Power(c - Complex(0,1)k0,7))/(336.Power(k,4)) + (Power(k,6)(-35 + 16Sqrt(1 + Power(k,2)/Power(2c - Complex(0,1)k0,2)))(2c - Complex(0,1)k0) + 2Power(k,4)(-35 + 24Sqrt(1 + Power(k,2)/Power(2c - Complex(0,1)k0,2)))Power(2c - Complex(0,1)k0,3) + 8Power(k,2)(-7 + 6Sqrt(1 + Power(k,2)/Power(2c - Complex(0,1)k0,2)))Power(2c - Complex(0,1)k0,5) + 16(-1 + Sqrt(1 + Power(k,2)/Power(2c - Complex(0,1)k0,2)))Power(2c - Complex(0,1)k0,7))/(168.Power(k,4)) - (Power(k,6)(-35 + 16Sqrt(1 + Power(k,2)/Power(3c - Complex(0,1)k0,2)))(3c - Complex(0,1)k0) + 2Power(k,4)(-35 + 24Sqrt(1 + Power(k,2)/Power(3c - Complex(0,1)k0,2)))Power(3c - Complex(0,1)k0,3) + 8Power(k,2)(-7 + 6Sqrt(1 + Power(k,2)/Power(3c - Complex(0,1)k0,2)))Power(3c - Complex(0,1)k0,5) + 16(-1 + Sqrt(1 + Power(k,2)/Power(3c - Complex(0,1)k0,2)))Power(3c - Complex(0,1)k0,7))/(168.Power(k,4)) + (Power(k,6)(-35 + 16Sqrt(1 + Power(k,2)/Power(4c - Complex(0,1)k0,2)))(4c - Complex(0,1)k0) + 2Power(k,4)(-35 + 24Sqrt(1 + Power(k,2)/Power(4c - Complex(0,1)k0,2)))Power(4c - Complex(0,1)k0,3) + 8Power(k,2)(-7 + 6Sqrt(1 + Power(k,2)/Power(4c - Complex(0,1)k0,2)))Power(4c - Complex(0,1)k0,5) + 16(-1 + Sqrt(1 + Power(k,2)/Power(4c - Complex(0,1)k0,2)))Power(4c - Complex(0,1)k0,7))/(336.Power(k,4)) - (Power(k,6)(-35 + 16Sqrt(1 + Power(k,2)/Power(5c - Complex(0,1)k0,2)))(5c - Complex(0,1)k0) + 2Power(k,4)(-35 + 24Sqrt(1 + Power(k,2)/Power(5c - Complex(0,1)k0,2)))Power(5c - Complex(0,1)k0,3) + 8Power(k,2)(-7 + 6Sqrt(1 + Power(k,2)/Power(5c - Complex(0,1)k0,2)))Power(5c - Complex(0,1)k0,5) + 16(-1 + Sqrt(1 + Power(k,2)/Power(5c - Complex(0,1)k0,2)))Power(5c - Complex(0,1)k0,7))/(1680.Power(k,4)) + (Complex(0,0.0005952380952380953)(Power(k,6)(35k0 - 16Sqrt(-Power(k,2) + Power(k0,2))) + 16Power(k0,6)(-k0 + Sqrt(-Power(k,2) + Power(k0,2))) - 8Power(k,2)Power(k0,4)(-7k0 + 6Sqrt(-Power(k,2) + Power(k0,2))) + 2Power(k,4)Power(k0,2)(-35k0 + 24Sqrt(-Power(k,2) + Power(k0,2)))))/Power(k,4))/Power(k0,5)
			`SeriesData[k, Infinity, {(4c^5)/k0^5, (-75c^6)/(2k0^5) + ((15I)c^5)/k0^4, (160c^7)/k0^5 - ((120I)c^6)/k0^4 - (24c^5)/k0^3, (-35(75c^8 - (80I)c^7k0 - 30c^6k0^2 + (4I)c^5k0^3))/(8k0^5), 0, (21(2025c^10 - (3310I)c^9k0 - 2250c^8k0^2 + (800I)c^7k0^3 + 150c^6k0^4 - (12I)c^5k0^5))/(32k0^5), 0, (-33(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*k0^5)}, 2, 11, 1]`
			-(5(k^6(-35 + 16Sqrt[1 + k^2/(c - Ik0)^2])(c - Ik0) + 2k^4(-35 + 24Sqrt[1 + k^2/(c - Ik0)^2])(c - Ik0)^3 + 8k^2(-7 + 6Sqrt[1 + k^2/(c - Ik0)^2])(c - Ik0)^5 + 16(-1 + Sqrt[1 + k^2/(c - Ik0)^2])(c - Ik0)^7) - 10(k^6(-35 + 16Sqrt[1 + k^2/(2c - Ik0)^2])(2c - Ik0) + 2k^4(-35 + 24Sqrt[1 + k^2/(2c - Ik0)^2])(2c - Ik0)^3 + 8k^2(-7 + 6Sqrt[1 + k^2/(2c - Ik0)^2])(2c - Ik0)^5 + 16(-1 + Sqrt[1 + k^2/(2c - Ik0)^2])(2c - Ik0)^7) + 10(k^6(-35 + 16Sqrt[1 + k^2/(3c - Ik0)^2])(3c - Ik0) + 2k^4(-35 + 24Sqrt[1 + k^2/(3c - Ik0)^2])(3c - Ik0)^3 + 8k^2(-7 + 6Sqrt[1 + k^2/(3c - Ik0)^2])(3c - Ik0)^5 + 16(-1 + Sqrt[1 + k^2/(3c - Ik0)^2])(3c - Ik0)^7) - 5(k^6(-35 + 16Sqrt[1 + k^2/(4c - Ik0)^2])(4c - Ik0) + 2k^4(-35 + 24Sqrt[1 + k^2/(4c - Ik0)^2])(4c - Ik0)^3 + 8k^2(-7 + 6Sqrt[1 + k^2/(4c - Ik0)^2])(4c - Ik0)^5 + 16(-1 + Sqrt[1 + k^2/(4c - Ik0)^2])(4c - Ik0)^7) + k^6(-35 + 16Sqrt[1 + k^2/(5c - Ik0)^2])(5c - Ik0) + 2k^4(-35 + 24Sqrt[1 + k^2/(5c - Ik0)^2])(5c - Ik0)^3 + 8k^2(-7 + 6Sqrt[1 + k^2/(5c - Ik0)^2])(5c - Ik0)^5 + 16(-1 + Sqrt[1 + k^2/(5c - Ik0)^2])(5c - Ik0)^7 - I(k^6(35k0 - 16Sqrt[-k^2 + k0^2]) + 16k0^6(-k0 + Sqrt[-k^2 + k0^2]) - 8k^2k0^4(-7k0 + 6Sqrt[-k^2 + k0^2]) + 2k^4k0^2(-35k0 + 24Sqrt[-k^2 + k0^2])))/(1680k^4*k0^5)