Article
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Integral Representations of Catalan Numbers and Their Applications
Version 1
: Received: 6 April 2017 / Approved: 7 April 2017 / Online: 7 April 2017 (04:27:13 CEST)
A peer-reviewed article of this Preprint also exists.
Abstract
In the paper, the authors survey integral representations of the Catalan numbers and the Catalan–Qi function, discuss equivalent relations between these integral representations, supply alternative and new proofs of several integral representations, collect applications of some integral representations, and present sums of several power series whose coefficients involve the Catalan numbers.
Keywords
Catalan number; integral representation; equivalent relation; application; sum of power series; Catalan--Qi function; Catalan--Qi number; beta function
Subject
Computer Science and Mathematics, 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: Feng Qi
Commenter's Conflict of Interests: I am the first author of this paper.
Feng Qi and Bai-Ni Guo, Integral representations of the Catalan numbers and their applications, Mathematics 5 (2017), no. 3, Article 40, 31 pages; Available online at http://dx.doi.org/10.3390/math5030040.
Commenter:
Commenter's Conflict of Interests: I am the first and corresponding author for this manuscript
Feng Qi and Bai-Ni Guo, Integral representations of the Catalan numbers and their applications, Mathematics 5 (2017), no. 3, Article 40, 31 pages; Available online at http://dx.doi.org/10.3390/math5030040
Commenter: Feng Qi
Commenter's Conflict of Interests: I am the first and corresponding author