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arXiv · 1004.2445

The Cauchy-Schlomilch transformation

T. Amdeberhan·M. L. Glasser·M. C. Jones·V. H. Moll·R. Posey·D. Varela
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Abstract

The Cauchy-Schlömilch transformation states that for a function $f$ and $a, \, b > 0$, the integral of $f(x^{2})$ and $af((ax-bx^{-1})^{2}$ over the interval $[0, \infty)$ are the same. This elementary result is used to evaluate many non-elementary definite integrals, most of which cannot be obtained by symbolic packages. Applications to probability distributions is also given.

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T. Amdeberhan, M. L. Glasser, M. C. Jones, V. H. Moll, R. Posey, D. Varela. 2010-04-14. The Cauchy-Schlomilch transformation. https://arxiv.org/abs/1004.2445

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