The Cauchy-Schlomilch transformation

2010/04/14 by Amdeberhan, T., Glasser, M. L., Jones, M. C. +3
#33 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics

paper · doi:10.48550/arxiv.1004.2445

Abstract

The Cauchy-Schlömilch transformation states that for a function f and a, b > 0, the integral of f(x²) and af((ax-bx^-1)² over the interval [0, ∞) 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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