3 lines
2.4 KiB
Plaintext
3 lines
2.4 KiB
Plaintext
(-14*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0) + 42*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0) - 70*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0) + 70*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0) - 42*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0) + 14*(-1 + Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0) - 2*(-1 + Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0) + k*Sqrt[Pi]*(Piecewise[{{0, k^2/k0^2 <= 1}}, (2*Sqrt[k^2 - k0^2])/(k*Sqrt[Pi])] + I*Piecewise[{{(2*k0)/(k*Sqrt[Pi]), k0^2/k^2 < 1}, {(2*(k0 - Sqrt[-k^2 + k0^2]))/(k*Sqrt[Pi]), k0^2/k^2 > 1}}, 0]))/(2*k*k0^2)
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Piecewise[{{SeriesData[k, Infinity, {(11025*c^8)/(2*k0^2) - ((1575*I)*c^7)/k0, 0, (-33075*(98*c^10 - (77*I)*c^9*k0 - 21*c^8*k0^2 + (2*I)*c^7*k0^3))/(4*k0^2)}, 8, 11, 1], (k0 <= 0 && k^2/k0^2 > 1) || k0 > 0}}, SeriesData[k, Infinity, {-k0^(-2), 0, 1/2, 0, ((7*c*(c - I*k0)^3)/8 - (21*c*(2*c - I*k0)^3)/4 + (105*c*(3*c - I*k0)^3)/8 - (35*c*(4*c - I*k0)^3)/2 + (105*c*(5*c - I*k0)^3)/8 - (21*c*(6*c - I*k0)^3)/4 + (7*c*(7*c - I*k0)^3)/8 - (7*I)/8*(c - I*k0)^3*k0 + (21*I)/8*(2*c - I*k0)^3*k0 - (35*I)/8*(3*c - I*k0)^3*k0 + (35*I)/8*(4*c - I*k0)^3*k0 - (21*I)/8*(5*c - I*k0)^3*k0 + (7*I)/8*(6*c - I*k0)^3*k0 - I/8*(7*c - I*k0)^3*k0)/k0^2, 0, ((-7*c*(c - I*k0)^5)/16 + (21*c*(2*c - I*k0)^5)/8 - (105*c*(3*c - I*k0)^5)/16 + (35*c*(4*c - I*k0)^5)/4 - (105*c*(5*c - I*k0)^5)/16 + (21*c*(6*c - I*k0)^5)/8 - (7*c*(7*c - I*k0)^5)/16 + (7*I)/16*(c - I*k0)^5*k0 - (21*I)/16*(2*c - I*k0)^5*k0 + (35*I)/16*(3*c - I*k0)^5*k0 - (35*I)/16*(4*c - I*k0)^5*k0 + (21*I)/16*(5*c - I*k0)^5*k0 - (7*I)/16*(6*c - I*k0)^5*k0 + I/16*(7*c - I*k0)^5*k0)/k0^2, 0, ((35*c*(c - I*k0)^7)/128 - (105*c*(2*c - I*k0)^7)/64 + (525*c*(3*c - I*k0)^7)/128 - (175*c*(4*c - I*k0)^7)/32 + (525*c*(5*c - I*k0)^7)/128 - (105*c*(6*c - I*k0)^7)/64 + (35*c*(7*c - I*k0)^7)/128 - (35*I)/128*(c - I*k0)^7*k0 + (105*I)/128*(2*c - I*k0)^7*k0 - (175*I)/128*(3*c - I*k0)^7*k0 + (175*I)/128*(4*c - I*k0)^7*k0 - (105*I)/128*(5*c - I*k0)^7*k0 + (35*I)/128*(6*c - I*k0)^7*k0 - (5*I)/128*(7*c - I*k0)^7*k0)/k0^2, 0, ((-49*c*(c - I*k0)^9)/256 + (147*c*(2*c - I*k0)^9)/128 - (735*c*(3*c - I*k0)^9)/256 + (245*c*(4*c - I*k0)^9)/64 - (735*c*(5*c - I*k0)^9)/256 + (147*c*(6*c - I*k0)^9)/128 - (49*c*(7*c - I*k0)^9)/256 + (49*I)/256*(c - I*k0)^9*k0 - (147*I)/256*(2*c - I*k0)^9*k0 + (245*I)/256*(3*c - I*k0)^9*k0 - (245*I)/256*(4*c - I*k0)^9*k0 + (147*I)/256*(5*c - I*k0)^9*k0 - (49*I)/256*(6*c - I*k0)^9*k0 + (7*I)/256*(7*c - I*k0)^9*k0)/k0^2}, 0, 11, 1]]
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