Preprint Article Version 1 This version is not peer-reviewed

An Improper Integral with a Square Root

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

Readers' Comments and Ratings (1)

Comment 1
Received: 22 April 2018
Commenter: Feng Qi
The commenter has declared there is no conflict of interests.
Comment: This preprint has been accepted for publication as

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.????
+ Respond to this comment
Leave a public comment
Send a private comment to the author(s)
Rate this article
Views 0
Downloads 0
Comments 1
Metrics 0
Leave a public comment

×
Alerts
Notify me about updates to this article or when a peer-reviewed version is published.