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- For[count = 1, count <= 50, count++,
- {a, b, e, f} = RandomReal[{0, 10}, 4, WorkingPrecision -> 50];
- {c, g, d, h} = RandomInteger[{1, 10}, 4];
- I1 = NIntegrate[1/(a + b x^c)^d 1/(e + f x^g)^h, {x, 0, Infinity},
- WorkingPrecision -> 30];
- I2 = 1/(b c ) 1/(f g ) (-1)^(
- d + h)/((d - 1)! (h - 1)!) (D[
- Exp[-I Pi (2 - 1/c - 1/g)] (b/xi)^(1 - 1/c) (f/eta)^(1 - 1/g)
- Sum[( -1/c Log[ xi/b ] + 1/g Log[eta/f ] + (
- I [Pi] (c - g - 2 g p + 2 c q))/(c g)) (-1)^(
- 2 p/c + 2 q/g)/((xi/b)^(1/c)
- Exp[(I Pi (2 p + 1))/c] - (eta/f)^(1/g)
- Exp[(I Pi (2 q + 1))/g]), {p, 0, c - 1}, {q, 0,
- g - 1}], {xi, d - 1}, {eta, h - 1}] /. {xi :> a, eta :> e});
- If[Abs[I2/I1 - 1] > 10^(-3),
- Print["mismatch..", {a, b, e, f, c, g, d, h}]; Break[]];
- PrintTemporary[count];
- ];
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