ARTICLE | doi:10.20944/preprints201610.0089.v1
Subject: Mathematics & Computer Science, Analysis Keywords: improper integral; explicit expression; unified expression; beta function; Wallis ratio; integral representation; Catalan number
Online: 21 October 2016 (08:29:08 CEST)
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.