Integral Representations of the Catalan Numbers and Their Applications
Institute of Mathematics, Henan Polytechnic University, Jiaozuo 454010, Henan Province, China
College of Mathematics, Inner Mongolia University for Nationalities, Tongliao 028043, Inner Mongolia Autonomous Region, China
Department of Mathematics, College of Science, Tianjin Polytechnic University, Tianjin 300387, China
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
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.
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.
Qi F, Guo B-N. Integral Representations of the Catalan Numbers and Their Applications. Mathematics. 2017; 5(3):40.
Qi, Feng; Guo, Bai-Ni. 2017. "Integral Representations of the Catalan Numbers and Their Applications." Mathematics 5, no. 3: 40.
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