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qpms/besseltransforms/ksmall/5-4-3

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Další Hankelovy transformace pro kappa=5 Former-commit-id: cc20e7f5dbf8651a81543f84ac066d011e84082b
2018-01-23 00:52:10 +02:00
(-(k^4*(-15 + 8*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0) + 4*k^2*(-5 + 4*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^3 + 8*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^5)/(24*k^3) + (k^4*(-15 + 8*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0) + 4*k^2*(-5 + 4*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^3 + 8*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^5)/(12*k^3) - (k^4*(-15 + 8*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0) + 4*k^2*(-5 + 4*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^3 + 8*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^5)/(12*k^3) + (k^4*(-15 + 8*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0) + 4*k^2*(-5 + 4*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^3 + 8*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^5)/(24*k^3) - (k^4*(-15 + 8*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0) + 4*k^2*(-5 + 4*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^3 + 8*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^5)/(120*k^3) + (I/120*(k^4*(15*k0 - 8*Sqrt[-k^2 + k0^2]) + 8*k0^4*(k0 - Sqrt[-k^2 + k0^2]) + 4*k^2*k0^2*(-5*k0 + 4*Sqrt[-k^2 + k0^2])))/k^3)/k0^4
(-(Power(k,4)*(-15 + 8*Sqrt(1 + Power(k,2)/Power(c - Complex(0,1)*k0,2)))*(c - Complex(0,1)*k0) + 4*Power(k,2)*(-5 + 4*Sqrt(1 + Power(k,2)/Power(c - Complex(0,1)*k0,2)))*Power(c - Complex(0,1)*k0,3) + 8*(-1 + Sqrt(1 + Power(k,2)/Power(c - Complex(0,1)*k0,2)))*Power(c - Complex(0,1)*k0,5))/(24.*Power(k,3)) + (Power(k,4)*(-15 + 8*Sqrt(1 + Power(k,2)/Power(2*c - Complex(0,1)*k0,2)))*(2*c - Complex(0,1)*k0) + 4*Power(k,2)*(-5 + 4*Sqrt(1 + Power(k,2)/Power(2*c - Complex(0,1)*k0,2)))*Power(2*c - Complex(0,1)*k0,3) + 8*(-1 + Sqrt(1 + Power(k,2)/Power(2*c - Complex(0,1)*k0,2)))*Power(2*c - Complex(0,1)*k0,5))/(12.*Power(k,3)) - (Power(k,4)*(-15 + 8*Sqrt(1 + Power(k,2)/Power(3*c - Complex(0,1)*k0,2)))*(3*c - Complex(0,1)*k0) + 4*Power(k,2)*(-5 + 4*Sqrt(1 + Power(k,2)/Power(3*c - Complex(0,1)*k0,2)))*Power(3*c - Complex(0,1)*k0,3) + 8*(-1 + Sqrt(1 + Power(k,2)/Power(3*c - Complex(0,1)*k0,2)))*Power(3*c - Complex(0,1)*k0,5))/(12.*Power(k,3)) + (Power(k,4)*(-15 + 8*Sqrt(1 + Power(k,2)/Power(4*c - Complex(0,1)*k0,2)))*(4*c - Complex(0,1)*k0) + 4*Power(k,2)*(-5 + 4*Sqrt(1 + Power(k,2)/Power(4*c - Complex(0,1)*k0,2)))*Power(4*c - Complex(0,1)*k0,3) + 8*(-1 + Sqrt(1 + Power(k,2)/Power(4*c - Complex(0,1)*k0,2)))*Power(4*c - Complex(0,1)*k0,5))/(24.*Power(k,3)) - (Power(k,4)*(-15 + 8*Sqrt(1 + Power(k,2)/Power(5*c - Complex(0,1)*k0,2)))*(5*c - Complex(0,1)*k0) + 4*Power(k,2)*(-5 + 4*Sqrt(1 + Power(k,2)/Power(5*c - Complex(0,1)*k0,2)))*Power(5*c - Complex(0,1)*k0,3) + 8*(-1 + Sqrt(1 + Power(k,2)/Power(5*c - Complex(0,1)*k0,2)))*Power(5*c - Complex(0,1)*k0,5))/(120.*Power(k,3)) + (Complex(0,0.008333333333333333)*(Power(k,4)*(15*k0 - 8*Sqrt(-Power(k,2) + Power(k0,2))) + 8*Power(k0,4)*(k0 - Sqrt(-Power(k,2) + Power(k0,2))) + 4*Power(k,2)*Power(k0,2)*(-5*k0 + 4*Sqrt(-Power(k,2) + Power(k0,2)))))/Power(k,3))/Power(k0,4)
SeriesData[k, Infinity, {(8*c^5)/k0^4, (-75*c^6)/(2*k0^4) + ((15*I)*c^5)/k0^3, 0, (35*(75*c^8 - (80*I)*c^7*k0 - 30*c^6*k0^2 + (4*I)*c^5*k0^3))/(8*k0^4), 0, (-63*(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, (165*(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^4*(-15 + 8*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0) + 4*k^2*(-5 + 4*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^3 + 8*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^5) - 10*(k^4*(-15 + 8*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0) + 4*k^2*(-5 + 4*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^3 + 8*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^5) + 10*(k^4*(-15 + 8*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0) + 4*k^2*(-5 + 4*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^3 + 8*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^5) - 5*(k^4*(-15 + 8*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0) + 4*k^2*(-5 + 4*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^3 + 8*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^5) + k^4*(-15 + 8*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0) + 4*k^2*(-5 + 4*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^3 + 8*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^5 - I*(k^4*(15*k0 - 8*Sqrt[-k^2 + k0^2]) + 8*k0^4*(k0 - Sqrt[-k^2 + k0^2]) + 4*k^2*k0^2*(-5*k0 + 4*Sqrt[-k^2 + k0^2])))/(120*k^3*k0^4)