5 lines
6.3 KiB
Plaintext
5 lines
6.3 KiB
Plaintext
((-5*(k^4 - 4*k^2*(-2 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^2 - 8*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^4))/(k^4*Sqrt[1 + k^2/(c - I*k0)^2]*(c - I*k0)) + (10*(k^4 - 4*k^2*(-2 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^2 - 8*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^4))/(k^4*Sqrt[1 + k^2/(2*c - I*k0)^2]*(2*c - I*k0)) - (10*(k^4 - 4*k^2*(-2 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^2 - 8*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^4))/(k^4*Sqrt[1 + k^2/(3*c - I*k0)^2]*(3*c - I*k0)) + (5*(k^4 - 4*k^2*(-2 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^2 - 8*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^4))/(k^4*Sqrt[1 + k^2/(4*c - I*k0)^2]*(4*c - I*k0)) - (k^4 - 4*k^2*(-2 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^2 - 8*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^4)/(k^4*Sqrt[1 + k^2/(5*c - I*k0)^2]*(5*c - I*k0)) + ((4*I)*k*k0*(k^2 - 2*k0^2) + (k*(k^4 - 8*k^2*k0^2 + 8*k0^4))/Sqrt[k^2 - k0^2])/k^5)/k0
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((-5*(Power(k,4) - 4*Power(k,2)*(-2 + Sqrt(1 + Power(k,2)/Power(c - Complex(0,1)*k0,2)))*Power(c - Complex(0,1)*k0,2) - 8*(-1 + Sqrt(1 + Power(k,2)/Power(c - Complex(0,1)*k0,2)))*Power(c - Complex(0,1)*k0,4)))/(Power(k,4)*Sqrt(1 + Power(k,2)/Power(c - Complex(0,1)*k0,2))*(c - Complex(0,1)*k0)) + (10*(Power(k,4) - 4*Power(k,2)*(-2 + Sqrt(1 + Power(k,2)/Power(2*c - Complex(0,1)*k0,2)))*Power(2*c - Complex(0,1)*k0,2) - 8*(-1 + Sqrt(1 + Power(k,2)/Power(2*c - Complex(0,1)*k0,2)))*Power(2*c - Complex(0,1)*k0,4)))/(Power(k,4)*Sqrt(1 + Power(k,2)/Power(2*c - Complex(0,1)*k0,2))*(2*c - Complex(0,1)*k0)) - (10*(Power(k,4) - 4*Power(k,2)*(-2 + Sqrt(1 + Power(k,2)/Power(3*c - Complex(0,1)*k0,2)))*Power(3*c - Complex(0,1)*k0,2) - 8*(-1 + Sqrt(1 + Power(k,2)/Power(3*c - Complex(0,1)*k0,2)))*Power(3*c - Complex(0,1)*k0,4)))/(Power(k,4)*Sqrt(1 + Power(k,2)/Power(3*c - Complex(0,1)*k0,2))*(3*c - Complex(0,1)*k0)) + (5*(Power(k,4) - 4*Power(k,2)*(-2 + Sqrt(1 + Power(k,2)/Power(4*c - Complex(0,1)*k0,2)))*Power(4*c - Complex(0,1)*k0,2) - 8*(-1 + Sqrt(1 + Power(k,2)/Power(4*c - Complex(0,1)*k0,2)))*Power(4*c - Complex(0,1)*k0,4)))/(Power(k,4)*Sqrt(1 + Power(k,2)/Power(4*c - Complex(0,1)*k0,2))*(4*c - Complex(0,1)*k0)) - (Power(k,4) - 4*Power(k,2)*(-2 + Sqrt(1 + Power(k,2)/Power(5*c - Complex(0,1)*k0,2)))*Power(5*c - Complex(0,1)*k0,2) - 8*(-1 + Sqrt(1 + Power(k,2)/Power(5*c - Complex(0,1)*k0,2)))*Power(5*c - Complex(0,1)*k0,4))/(Power(k,4)*Sqrt(1 + Power(k,2)/Power(5*c - Complex(0,1)*k0,2))*(5*c - Complex(0,1)*k0)) + (Complex(0,4)*k*k0*(Power(k,2) - 2*Power(k0,2)) + (k*(Power(k,4) - 8*Power(k,2)*Power(k0,2) + 8*Power(k0,4)))/Sqrt(Power(k,2) - Power(k0,2)))/Power(k,5))/k0
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SeriesData[k, Infinity, {-(1/(k*k0)), (k - (4*I)*k0)/(k*k0), (I/2*(8*k - (15*I)*k0))/k, (-15*k*k0 + (16*I)*k0^2)/(2*k), ((-8*I)*k0^3 - (5*((4*(c - I*k0)^5)/k + (3*(c - I*k0)^4*(c/k - (I*k0)/k))/8))/(c - I*k0) + (10*((4*(2*c - I*k0)^5)/k + (3*(2*c - I*k0)^4*((2*c)/k - (I*k0)/k))/8))/(2*c - I*k0) - (10*((4*(3*c - I*k0)^5)/k + (3*(3*c - I*k0)^4*((3*c)/k - (I*k0)/k))/8))/(3*c - I*k0) + (5*((4*(4*c - I*k0)^5)/k + (3*(4*c - I*k0)^4*((4*c)/k - (I*k0)/k))/8))/(4*c - I*k0) + ((-4*(5*c - I*k0)^5)/k - (3*(5*c - I*k0)^4*((5*c)/k - (I*k0)/k))/8)/(5*c - I*k0))/k0, ((35*k0^4)/8 - (5*((3*(c - I*k0)^6)/(2*k) - (3*(c - I*k0)^5*(c/k - (I*k0)/k))/2))/(c - I*k0) + (10*((3*(2*c - I*k0)^6)/(2*k) - (3*(2*c - I*k0)^5*((2*c)/k - (I*k0)/k))/2))/(2*c - I*k0) - (10*((3*(3*c - I*k0)^6)/(2*k) - (3*(3*c - I*k0)^5*((3*c)/k - (I*k0)/k))/2))/(3*c - I*k0) + (5*((3*(4*c - I*k0)^6)/(2*k) - (3*(4*c - I*k0)^5*((4*c)/k - (I*k0)/k))/2))/(4*c - I*k0) + ((-3*(5*c - I*k0)^6)/(2*k) + (3*(5*c - I*k0)^5*((5*c)/k - (I*k0)/k))/2)/(5*c - I*k0))/k0, ((-5*((-4*(c - I*k0)^7)/k + (43*(c - I*k0)^6*(c/k - (I*k0)/k))/16))/(c - I*k0) + (10*((-4*(2*c - I*k0)^7)/k + (43*(2*c - I*k0)^6*((2*c)/k - (I*k0)/k))/16))/(2*c - I*k0) - (10*((-4*(3*c - I*k0)^7)/k + (43*(3*c - I*k0)^6*((3*c)/k - (I*k0)/k))/16))/(3*c - I*k0) + (5*((-4*(4*c - I*k0)^7)/k + (43*(4*c - I*k0)^6*((4*c)/k - (I*k0)/k))/16))/(4*c - I*k0) + ((4*(5*c - I*k0)^7)/k - (43*(5*c - I*k0)^6*((5*c)/k - (I*k0)/k))/16)/(5*c - I*k0))/k0, ((21*k0^6)/16 - (5*((5*(c - I*k0)^8)/(2*k) - (5*(c - I*k0)^7*(c/k - (I*k0)/k))/2))/(c - I*k0) + (10*((5*(2*c - I*k0)^8)/(2*k) - (5*(2*c - I*k0)^7*((2*c)/k - (I*k0)/k))/2))/(2*c - I*k0) - (10*((5*(3*c - I*k0)^8)/(2*k) - (5*(3*c - I*k0)^7*((3*c)/k - (I*k0)/k))/2))/(3*c - I*k0) + (5*((5*(4*c - I*k0)^8)/(2*k) - (5*(4*c - I*k0)^7*((4*c)/k - (I*k0)/k))/2))/(4*c - I*k0) + ((-5*(5*c - I*k0)^8)/(2*k) + (5*(5*c - I*k0)^7*((5*c)/k - (I*k0)/k))/2)/(5*c - I*k0))/k0, ((-495*(c - I*k0)^7*(c/k - (I*k0)/k))/128 + (495*(2*c - I*k0)^7*((2*c)/k - (I*k0)/k))/64 - (495*(3*c - I*k0)^7*((3*c)/k - (I*k0)/k))/64 + (495*(4*c - I*k0)^7*((4*c)/k - (I*k0)/k))/128 - (99*(5*c - I*k0)^7*((5*c)/k - (I*k0)/k))/128)/k0, ((99*k0^8)/128 - (5*((-23*(c - I*k0)^10)/(32*k) + (23*(c - I*k0)^9*(c/k - (I*k0)/k))/32))/(c - I*k0) + (10*((-23*(2*c - I*k0)^10)/(32*k) + (23*(2*c - I*k0)^9*((2*c)/k - (I*k0)/k))/32))/(2*c - I*k0) - (10*((-23*(3*c - I*k0)^10)/(32*k) + (23*(3*c - I*k0)^9*((3*c)/k - (I*k0)/k))/32))/(3*c - I*k0) + (5*((-23*(4*c - I*k0)^10)/(32*k) + (23*(4*c - I*k0)^9*((4*c)/k - (I*k0)/k))/32))/(4*c - I*k0) + ((23*(5*c - I*k0)^10)/(32*k) - (23*(5*c - I*k0)^9*((5*c)/k - (I*k0)/k))/32)/(5*c - I*k0))/k0, ((715*(c - I*k0)^9*(c/k - (I*k0)/k))/256 - (715*(2*c - I*k0)^9*((2*c)/k - (I*k0)/k))/128 + (715*(3*c - I*k0)^9*((3*c)/k - (I*k0)/k))/128 - (715*(4*c - I*k0)^9*((4*c)/k - (I*k0)/k))/256 + (143*(5*c - I*k0)^9*((5*c)/k - (I*k0)/k))/256)/k0}, 0, 11, 1]
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((-5*(k^4 - 4*k^2*(-2 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^2 - 8*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^4))/(Sqrt[1 + k^2/(c - I*k0)^2]*(c - I*k0)) + (10*(k^4 - 4*k^2*(-2 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^2 - 8*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^4))/(Sqrt[1 + k^2/(2*c - I*k0)^2]*(2*c - I*k0)) - (10*(k^4 - 4*k^2*(-2 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^2 - 8*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^4))/(Sqrt[1 + k^2/(3*c - I*k0)^2]*(3*c - I*k0)) + (5*(k^4 - 4*k^2*(-2 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^2 - 8*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^4))/(Sqrt[1 + k^2/(4*c - I*k0)^2]*(4*c - I*k0)) - (k^4 - 4*k^2*(-2 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^2 - 8*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^4)/(Sqrt[1 + k^2/(5*c - I*k0)^2]*(5*c - I*k0)) + (4*I)*k0*(k^2 - 2*k0^2) + (k^4 - 8*k^2*k0^2 + 8*k0^4)/Sqrt[k^2 - k0^2])/(k^4*k0)
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