5 lines
6.6 KiB
Plaintext
5 lines
6.6 KiB
Plaintext
((-5*(k^4*(-5 + Sqrt[1 + k^2/(c - I*k0)^2]) + 4*k^2*(-5 + 3*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^2 + 16*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^4))/(k^5*Sqrt[1 + k^2/(c - I*k0)^2]) + (10*(k^4*(-5 + Sqrt[1 + k^2/(2*c - I*k0)^2]) + 4*k^2*(-5 + 3*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^2 + 16*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^4))/(k^5*Sqrt[1 + k^2/(2*c - I*k0)^2]) - (10*(k^4*(-5 + Sqrt[1 + k^2/(3*c - I*k0)^2]) + 4*k^2*(-5 + 3*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^2 + 16*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^4))/(k^5*Sqrt[1 + k^2/(3*c - I*k0)^2]) + (5*(k^4*(-5 + Sqrt[1 + k^2/(4*c - I*k0)^2]) + 4*k^2*(-5 + 3*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^2 + 16*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^4))/(k^5*Sqrt[1 + k^2/(4*c - I*k0)^2]) - (k^4*(-5 + Sqrt[1 + k^2/(5*c - I*k0)^2]) + 4*k^2*(-5 + 3*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^2 + 16*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^4)/(k^5*Sqrt[1 + k^2/(5*c - I*k0)^2]) + (k^5 - 12*k^3*k0^2 + 16*k*k0^4 + (I*k*k0*(5*k^4 - 20*k^2*k0^2 + 16*k0^4))/Sqrt[k^2 - k0^2])/k^6)/k0
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((-5*(Power(k,4)*(-5 + Sqrt(1 + Power(k,2)/Power(c - Complex(0,1)*k0,2))) + 4*Power(k,2)*(-5 + 3*Sqrt(1 + Power(k,2)/Power(c - Complex(0,1)*k0,2)))*Power(c - Complex(0,1)*k0,2) + 16*(-1 + Sqrt(1 + Power(k,2)/Power(c - Complex(0,1)*k0,2)))*Power(c - Complex(0,1)*k0,4)))/(Power(k,5)*Sqrt(1 + Power(k,2)/Power(c - Complex(0,1)*k0,2))) + (10*(Power(k,4)*(-5 + Sqrt(1 + Power(k,2)/Power(2*c - Complex(0,1)*k0,2))) + 4*Power(k,2)*(-5 + 3*Sqrt(1 + Power(k,2)/Power(2*c - Complex(0,1)*k0,2)))*Power(2*c - Complex(0,1)*k0,2) + 16*(-1 + Sqrt(1 + Power(k,2)/Power(2*c - Complex(0,1)*k0,2)))*Power(2*c - Complex(0,1)*k0,4)))/(Power(k,5)*Sqrt(1 + Power(k,2)/Power(2*c - Complex(0,1)*k0,2))) - (10*(Power(k,4)*(-5 + Sqrt(1 + Power(k,2)/Power(3*c - Complex(0,1)*k0,2))) + 4*Power(k,2)*(-5 + 3*Sqrt(1 + Power(k,2)/Power(3*c - Complex(0,1)*k0,2)))*Power(3*c - Complex(0,1)*k0,2) + 16*(-1 + Sqrt(1 + Power(k,2)/Power(3*c - Complex(0,1)*k0,2)))*Power(3*c - Complex(0,1)*k0,4)))/(Power(k,5)*Sqrt(1 + Power(k,2)/Power(3*c - Complex(0,1)*k0,2))) + (5*(Power(k,4)*(-5 + Sqrt(1 + Power(k,2)/Power(4*c - Complex(0,1)*k0,2))) + 4*Power(k,2)*(-5 + 3*Sqrt(1 + Power(k,2)/Power(4*c - Complex(0,1)*k0,2)))*Power(4*c - Complex(0,1)*k0,2) + 16*(-1 + Sqrt(1 + Power(k,2)/Power(4*c - Complex(0,1)*k0,2)))*Power(4*c - Complex(0,1)*k0,4)))/(Power(k,5)*Sqrt(1 + Power(k,2)/Power(4*c - Complex(0,1)*k0,2))) - (Power(k,4)*(-5 + Sqrt(1 + Power(k,2)/Power(5*c - Complex(0,1)*k0,2))) + 4*Power(k,2)*(-5 + 3*Sqrt(1 + Power(k,2)/Power(5*c - Complex(0,1)*k0,2)))*Power(5*c - Complex(0,1)*k0,2) + 16*(-1 + Sqrt(1 + Power(k,2)/Power(5*c - Complex(0,1)*k0,2)))*Power(5*c - Complex(0,1)*k0,4))/(Power(k,5)*Sqrt(1 + Power(k,2)/Power(5*c - Complex(0,1)*k0,2))) + (Power(k,5) - 12*Power(k,3)*Power(k0,2) + 16*k*Power(k0,4) + (Complex(0,1)*k*k0*(5*Power(k,4) - 20*Power(k,2)*Power(k0,2) + 16*Power(k0,4)))/Sqrt(Power(k,2) - Power(k0,2)))/Power(k,6))/k0
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SeriesData[k, Infinity, {-(1/(k*k0)), (k - (5*I)*k0)/(k*k0), (I*(5*k - (12*I)*k0))/k, (-24*k*k0 + (35*I)*k0^2)/(2*k), ((-125*(5*c - I*k0)^4)/(8*k) - (35*I)/2*k0^3 - (3*(5*c - I*k0)^3*((5*c)/k - (I*k0)/k))/8 - 5*((125*(c - I*k0)^4)/(8*k) + (3*(c - I*k0)^3*(c/k - (I*k0)/k))/8) + 10*((125*(2*c - I*k0)^4)/(8*k) + (3*(2*c - I*k0)^3*((2*c)/k - (I*k0)/k))/8) - 10*((125*(3*c - I*k0)^4)/(8*k) + (3*(3*c - I*k0)^3*((3*c)/k - (I*k0)/k))/8) + 5*((125*(4*c - I*k0)^4)/(8*k) + (3*(4*c - I*k0)^3*((4*c)/k - (I*k0)/k))/8))/k0, ((6*(5*c - I*k0)^5)/k + 16*k0^4 + (15*(5*c - I*k0)^4*((5*c)/k - (I*k0)/k))/8 - 5*((-6*(c - I*k0)^5)/k - (15*(c - I*k0)^4*(c/k - (I*k0)/k))/8) + 10*((-6*(2*c - I*k0)^5)/k - (15*(2*c - I*k0)^4*((2*c)/k - (I*k0)/k))/8) - 10*((-6*(3*c - I*k0)^5)/k - (15*(3*c - I*k0)^4*((3*c)/k - (I*k0)/k))/8) + 5*((-6*(4*c - I*k0)^5)/k - (15*(4*c - I*k0)^4*((4*c)/k - (I*k0)/k))/8))/k0, ((35*(5*c - I*k0)^6)/(8*k) + (63*I)/8*k0^5 - (35*(5*c - I*k0)^5*((5*c)/k - (I*k0)/k))/8 - 5*((-35*(c - I*k0)^6)/(8*k) + (35*(c - I*k0)^5*(c/k - (I*k0)/k))/8) + 10*((-35*(2*c - I*k0)^6)/(8*k) + (35*(2*c - I*k0)^5*((2*c)/k - (I*k0)/k))/8) - 10*((-35*(3*c - I*k0)^6)/(8*k) + (35*(3*c - I*k0)^5*((3*c)/k - (I*k0)/k))/8) + 5*((-35*(4*c - I*k0)^6)/(8*k) + (35*(4*c - I*k0)^5*((4*c)/k - (I*k0)/k))/8))/k0, ((-8*(5*c - I*k0)^7)/k + (95*(5*c - I*k0)^6*((5*c)/k - (I*k0)/k))/16 - 5*((8*(c - I*k0)^7)/k - (95*(c - I*k0)^6*(c/k - (I*k0)/k))/16) + 10*((8*(2*c - I*k0)^7)/k - (95*(2*c - I*k0)^6*((2*c)/k - (I*k0)/k))/16) - 10*((8*(3*c - I*k0)^7)/k - (95*(3*c - I*k0)^6*((3*c)/k - (I*k0)/k))/16) + 5*((8*(4*c - I*k0)^7)/k - (95*(4*c - I*k0)^6*((4*c)/k - (I*k0)/k))/16))/k0, ((585*(5*c - I*k0)^8)/(128*k) + (33*I)/16*k0^7 - (585*(5*c - I*k0)^7*((5*c)/k - (I*k0)/k))/128 - 5*((-585*(c - I*k0)^8)/(128*k) + (585*(c - I*k0)^7*(c/k - (I*k0)/k))/128) + 10*((-585*(2*c - I*k0)^8)/(128*k) + (585*(2*c - I*k0)^7*((2*c)/k - (I*k0)/k))/128) - 10*((-585*(3*c - I*k0)^8)/(128*k) + (585*(3*c - I*k0)^7*((3*c)/k - (I*k0)/k))/128) + 5*((-585*(4*c - I*k0)^8)/(128*k) + (585*(4*c - I*k0)^7*((4*c)/k - (I*k0)/k))/128))/k0, ((715*(c - I*k0)^8*(c/k - (I*k0)/k))/128 - (715*(2*c - I*k0)^8*((2*c)/k - (I*k0)/k))/64 + (715*(3*c - I*k0)^8*((3*c)/k - (I*k0)/k))/64 - (715*(4*c - I*k0)^8*((4*c)/k - (I*k0)/k))/128 + (143*(5*c - I*k0)^8*((5*c)/k - (I*k0)/k))/128)/k0, ((-77*(5*c - I*k0)^10)/(64*k) + (143*I)/128*k0^9 + (77*(5*c - I*k0)^9*((5*c)/k - (I*k0)/k))/64 - 5*((77*(c - I*k0)^10)/(64*k) - (77*(c - I*k0)^9*(c/k - (I*k0)/k))/64) + 10*((77*(2*c - I*k0)^10)/(64*k) - (77*(2*c - I*k0)^9*((2*c)/k - (I*k0)/k))/64) - 10*((77*(3*c - I*k0)^10)/(64*k) - (77*(3*c - I*k0)^9*((3*c)/k - (I*k0)/k))/64) + 5*((77*(4*c - I*k0)^10)/(64*k) - (77*(4*c - I*k0)^9*((4*c)/k - (I*k0)/k))/64))/k0}, 0, 11, 1]
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(k^4 - (5*(k^4*(-5 + Sqrt[1 + k^2/(c - I*k0)^2]) + 4*k^2*(-5 + 3*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^2 + 16*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^4))/Sqrt[1 + k^2/(c - I*k0)^2] + (10*(k^4*(-5 + Sqrt[1 + k^2/(2*c - I*k0)^2]) + 4*k^2*(-5 + 3*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^2 + 16*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^4))/Sqrt[1 + k^2/(2*c - I*k0)^2] - (10*(k^4*(-5 + Sqrt[1 + k^2/(3*c - I*k0)^2]) + 4*k^2*(-5 + 3*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^2 + 16*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^4))/Sqrt[1 + k^2/(3*c - I*k0)^2] + (5*(k^4*(-5 + Sqrt[1 + k^2/(4*c - I*k0)^2]) + 4*k^2*(-5 + 3*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^2 + 16*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^4))/Sqrt[1 + k^2/(4*c - I*k0)^2] - (k^4*(-5 + Sqrt[1 + k^2/(5*c - I*k0)^2]) + 4*k^2*(-5 + 3*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^2 + 16*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^4)/Sqrt[1 + k^2/(5*c - I*k0)^2] - 12*k^2*k0^2 + 16*k0^4 + (I*k0*(5*k^4 - 20*k^2*k0^2 + 16*k0^4))/Sqrt[k^2 - k0^2])/(k^5*k0)
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