Submitted:
20 October 2016
Posted:
21 October 2016
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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
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