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Mathematics
Volume 5
Issue 3
10.3390/math5030040
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Review

Integral Representations of the Catalan Numbers and Their Applications

by
Feng Qi
1,2,3,* and
Bai-Ni Guo
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.
Mathematics 2017, 5(3), 40; https://doi.org/10.3390/math5030040
Submission received: 22 May 2017 / Accepted: 25 July 2017 / Published: 3 August 2017
Versions Notes

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 Catalan number; integral representation; equivalent relation; application; sum of power series; Catalan–Qi function; Catalan–Qi number; beta function

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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. https://doi.org/10.3390/math5030040

AMA Style

Qi F, Guo B-N. Integral Representations of the Catalan Numbers and Their Applications. Mathematics. 2017; 5(3):40. https://doi.org/10.3390/math5030040

Chicago/Turabian Style

Qi, Feng, and Bai-Ni Guo. 2017. "Integral Representations of the Catalan Numbers and Their Applications" Mathematics 5, no. 3: 40. https://doi.org/10.3390/math5030040

APA Style

Qi, F., & Guo, B.-N. (2017). Integral Representations of the Catalan Numbers and Their Applications. Mathematics, 5(3), 40. https://doi.org/10.3390/math5030040

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