Preprint Article Version 1 This version not peer reviewed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