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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 (Digital Object Identifier) Link: https://doi.org/10.1080/10652469.2019.1637432
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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.

Item Type: Journal Item
Copyright Holders: 2019 Informa UK Limited, trading as Taylor & Francis Group
ISSN: 1065-2469
Keywords: Definite integrals; transformations; Laplace integral; error function; elliptic integrals; Bessel function; Riemann zeta function
Academic Unit/School: Faculty of Science, Technology, Engineering and Mathematics (STEM)
Related URLs:
Item ID: 62455
Depositing User: ORO Import
Date Deposited: 15 Jul 2019 08:26
Last Modified: 31 Jul 2019 09:53
URI: http://oro.open.ac.uk/id/eprint/62455
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