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Link to original content: https://doi.org/10.1007/s11075-009-9265-4
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Numerical evaluation of Goursat’s infinite integral

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Abstract

The infinite integral \(\int_0^{\infty}x\,dx/(1+x^6\sin^2x)\) converges but is hard to evaluate because the integrand f(x) = x/(1 + x 6sin2 x) is a non-convergent and unbounded function, indeed f() = → ∞ (k→ ∞). We present an efficient method to evaluate the above integral in high accuracy and actually obtain an approximate value in up to 73 significant digits on an octuple precision system in C++.

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Correspondence to Takemitsu Hasegawa.

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Dedicated to the memory of Professor Hideo Toda.

Technical details omitted in this paper are given in [12].

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Hatano, Y., Ninomiya, I., Sugiura, H. et al. Numerical evaluation of Goursat’s infinite integral. Numer Algor 52, 213–224 (2009). https://doi.org/10.1007/s11075-009-9265-4

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  • DOI: https://doi.org/10.1007/s11075-009-9265-4

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