A further generalization of the Catalan numbers and its explicit formula and integral representation-Reference-Cited by-同舟云学术

A further generalization of the Catalan numbers and its explicit formula and integral representation

Published:2023 Issue:19 Volume:37 Page:6505-6524
ISSN:0354-5180
Container-title:Filomat
language:en
Short-container-title:Filomat

Author:

Li Wen-Hui¹,Kouba Omran²,Kaddoura Issam³,Qi Feng⁴

Affiliation:

1. School of Economics, Henan Kaifeng College of Science Technology and Communication, Kaifeng, Henan, China

2. Department of Mathematics, Higher Institute for Applied Sciences and Technology, Damascus, Syria

3. Department of Mathematics, School of Arts and Sciences, International University of Beirut, Lebanese International University, Beirut, Lebanon

4. Institute of Mathematics, Henan Polytechnic University, Jiaozuo, Henan, China + Independent Researcher, Dallas, USA

Abstract

In the paper, motivated by the generating function of the Catalan numbers in combinatorial number theory and with the aid of Cauchy?s integral formula in complex analysis, the authors generalize the Catalan numbers and its generating function, establish an explicit formula and an integral representation for the generalization of the Catalan numbers and corresponding generating function, and derive several integral formulas and combinatorial identities.

Publisher

National Library of Serbia

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