Article
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An Improper Integral with a Square Root
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Version 1
: Received: 20 October 2016 / Approved: 21 October 2016 / Online: 21 October 2016 (08:29:08 CEST)
A peer-reviewed article of this Preprint also exists.
Feng Qi, An improper integral, the beta function, the Wallis ratio, and the Catalan numbers, Problemy Analiza--Issues of Analysis 7 (25) (2018), no. 1, 104--115; Available online at https://doi.org/10.15393/j3.art.2018.4370. Feng Qi, An improper integral, the beta function, the Wallis ratio, and the Catalan numbers, Problemy Analiza--Issues of Analysis 7 (25) (2018), no. 1, 104--115; Available online at https://doi.org/10.15393/j3.art.2018.4370.
Journal reference: Problemy Analiza--Issues of Analysis 2018, 7, 104-115
DOI: 10.15393/j3.art.2018.4370
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.
Keywords
improper integral; explicit expression; unified expression; beta function; Wallis ratio; integral representation; Catalan number
Subject
MATHEMATICS & COMPUTER SCIENCE, Analysis
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:
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.????
Commenter: Feng Qi
Commenter's Conflict of Interests: I am the author
Feng Qi, An improper integral, the beta function, the Wallis ratio, and the Catalan numbers, Problemy Analiza--Issues of Analysis 7 (25) (2018), no. 1, in press; Available online at https://doi.org/10.15393/j3.art.2018.4370
Commenter:
Commenter's Conflict of Interests: I am the author
Commenter: Feng Qi
Commenter's Conflict of Interests: I am the author
Commenter:
Commenter's Conflict of Interests: I am the author
Feng Qi, An improper integral, the beta function, the Wallis ratio, and the Catalan numbers, Problemy Analiza—Issues of Analysis 7 (25) (2018), no. 1, 104—115; Available online at https://doi.org/10.15393/j3.art.2018.4370
Commenter:
Commenter's Conflict of Interests: I am the author
Feng Qi, An improper integral, the beta function, the Wallis ratio, and the Catalan numbers, Problemy Analiza—Issues of Analysis 7 (25) (2018), no. 1, 104—115; Available online at https://doi.org/10.15393/j3.art.2018.4370