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Mathematics 2017, 5(3), 40; doi:10.3390/math5030040

Integral Representations of the Catalan Numbers and Their Applications

1,2,3,* and 4
1
Institute of Mathematics, Henan Polytechnic University, Jiaozuo 454010, Henan Province, China
2
College of Mathematics, Inner Mongolia University for Nationalities, Tongliao 028043, Inner Mongolia Autonomous Region, China
3
Department of Mathematics, College of Science, Tianjin Polytechnic University, Tianjin 300387, China
4
School of Mathematics and Informatics, Henan Polytechnic University, Jiaozuo 454010, Henan Province, China
*
Author to whom correspondence should be addressed.
Academic Editor: Hari M. Srivastava
Received: 22 May 2017 / Accepted: 25 July 2017 / Published: 3 August 2017
View Full-Text   |   Download PDF [347 KB, uploaded 3 August 2017]

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. View Full-Text
Keywords: Catalan number; integral representation; equivalent relation; application; sum of power series; Catalan–Qi function; Catalan–Qi number; beta function Catalan number; integral representation; equivalent relation; application; sum of power series; Catalan–Qi function; Catalan–Qi number; beta function
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. (CC BY 4.0).

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MDPI and ACS Style

Qi, F.; Guo, B.-N. Integral Representations of the Catalan Numbers and Their Applications. Mathematics 2017, 5, 40.

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