Article
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An Improper Integral with a Square Root
Feng Qi
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Version 1
: Received: 20 October 2016 / Approved: 21 October 2016 / Online: 21 October 2016 (08:29:08 CEST)
How to cite: Qi, F. An Improper Integral with a Square Root. Preprints 2016, 2016100089 (doi: 10.20944/preprints201610.0089.v1). Qi, F. An Improper Integral with a Square Root. Preprints 2016, 2016100089 (doi: 10.20944/preprints201610.0089.v1).
Abstract
In the paper, the author presents explicit and unified expressions for a sequence of improper integrals in terms of the beta functions and the Wallis ratios. Hereafter, the author derives integral representations for the Catalan numbers originating from combinatorics.
Subject Areas
improper integral; explicit expression; unified expression; beta function; Wallis ratio; integral representation; Catalan number
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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Commenter: Feng Qi
The commenter has declared there is no conflict of interests.
Feng Qi, An improper integral, the beta function, the Wallis ratio, and the Catalan numbers, Problemy Analiza--Issues of Analysis 7 (25) (2018), in press; Available online at https://doi.org/10.15393/j3.art.2018.????