The Cauchy–Schlömilch transformation

Amdeberhan, T.; Glasser, M. L.; Jones, M. C.; Moll, V.; Posey, R. and Varela, D. (2019). The Cauchy–Schlömilch transformation. Integral Transforms and Special Functions (Early Access).

DOI: https://doi.org/10.1080/10652469.2019.1637432

Abstract

The Cauchy–Schlömilch transformation states that for a function f and a, b>0, the integral of ƒ(ᵡ2) and aƒ((aᵡ−bᵡ−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 are also given.

Viewing alternatives

Metrics

Public Attention

Altmetrics from Altmetric

Number of Citations

Citations from Dimensions

Item Actions

Export

About

Recommendations