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qpms/besseltransforms/ksmall/5-2-3

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Další Hankelovy transformace pro kappa=5 Former-commit-id: cc20e7f5dbf8651a81543f84ac066d011e84082b
2018-01-23 00:52:10 +02:00
((-5*(k^2*(-3 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0) + 4*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^3))/(3*k^3) + (10*(k^2*(-3 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0) + 4*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^3))/(3*k^3) - (10*(k^2*(-3 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0) + 4*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^3))/(3*k^3) + (5*(k^2*(-3 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0) + 4*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^3))/(3*k^3) - (k^2*(-3 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0) + 4*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^3)/(3*k^3) - (I/3*(4*k0^2*(k0 - Sqrt[-k^2 + k0^2]) + k^2*(-3*k0 + Sqrt[-k^2 + k0^2])))/k^3)/k0^2
((-5*(Power(k,2)*(-3 + Sqrt(1 + Power(k,2)/Power(c - Complex(0,1)*k0,2)))*(c - Complex(0,1)*k0) + 4*(-1 + Sqrt(1 + Power(k,2)/Power(c - Complex(0,1)*k0,2)))*Power(c - Complex(0,1)*k0,3)))/(3.*Power(k,3)) + (10*(Power(k,2)*(-3 + Sqrt(1 + Power(k,2)/Power(2*c - Complex(0,1)*k0,2)))*(2*c - Complex(0,1)*k0) + 4*(-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,3)) - (10*(Power(k,2)*(-3 + Sqrt(1 + Power(k,2)/Power(3*c - Complex(0,1)*k0,2)))*(3*c - Complex(0,1)*k0) + 4*(-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,3)) + (5*(Power(k,2)*(-3 + Sqrt(1 + Power(k,2)/Power(4*c - Complex(0,1)*k0,2)))*(4*c - Complex(0,1)*k0) + 4*(-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,3)) - (Power(k,2)*(-3 + Sqrt(1 + Power(k,2)/Power(5*c - Complex(0,1)*k0,2)))*(5*c - Complex(0,1)*k0) + 4*(-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,3)) - (Complex(0,0.3333333333333333)*(4*Power(k0,2)*(k0 - Sqrt(-Power(k,2) + Power(k0,2))) + Power(k,2)*(-3*k0 + Sqrt(-Power(k,2) + Power(k0,2)))))/Power(k,3))/Power(k0,2)
SeriesData[k, Infinity, {(525*c^6)/(2*k0^2) - ((105*I)*c^5)/k0, 0, (14175*c^6)/4 - (70875*c^8)/(8*k0^2) + ((9450*I)*c^7)/k0 - (945*I)/2*c^5*k0, 0, (3465*(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)}, 6, 11, 1]
-(5*k^2*(-3 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0) + 20*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^3 - 10*k^2*(-3 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0) - 40*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^3 + 10*k^2*(-3 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0) + 40*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^3 - 5*k^2*(-3 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0) - 20*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^3 + k^2*(-3 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0) + 4*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^3 + (4*I)*k0^2*(k0 - Sqrt[-k^2 + k0^2]) + I*k^2*(-3*k0 + Sqrt[-k^2 + k0^2]))/(3*k^3*k0^2)