A Brief Survey and an Analytic Generalization of the Catalan Numbers and Their Integral Representations-Reference-Cited by-同舟云学术

A Brief Survey and an Analytic Generalization of the Catalan Numbers and Their Integral Representations

Published:2023-04-14 Issue:8 Volume:11 Page:1870
ISSN:2227-7390
Container-title:Mathematics
language:en
Short-container-title:Mathematics

Author:

Cao Jian¹^ORCID,Li Wen-Hui²^ORCID,Niu Da-Wei³^ORCID,Qi Feng⁴^ORCID,Zhao Jiao-Lian⁵^ORCID

Affiliation:

1. School of Mathematics, Hangzhou Normal University, Hangzhou 311121, China

2. School of Economics, Henan Kaifeng College of Science Technology and Communication, Kaifeng 475001, China

3. Department of Science, Henan University of Animal Husbandry and Economy, Zhengzhou 450046, China

4. Institute of Mathematics, Henan Polytechnic University, Jiaozuo 454010, China

5. School of Mathematics and Statistics, Weinan Normal University, Weinan 714000, China

Abstract

In the paper, the authors briefly survey several generalizations of the Catalan numbers in combinatorial number theory, analytically generalize the Catalan numbers, establish an integral representation of the analytic generalization of the Catalan numbers by virtue of Cauchy’s integral formula in the theory of complex functions, and point out potential directions for further study.

Funder

Zhejiang Provincial Natural Science Foundation

National Natural Science Foundation of China

Publisher

MDPI AG

Subject

General Mathematics,Engineering (miscellaneous),Computer Science (miscellaneous)

Link

https://www.mdpi.com/2227-7390/11/8/1870/pdf

Reference61 articles.

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2. Koshy, T. (2009). Catalan Numbers with Applications, Oxford University Press.

3. Spivey, M.Z. (2019). Discrete Mathematics and Its Applications, CRC Press.

4. Roman, S. (2015). An Introduction to Catalan Numbers, Birkhäuser-Springer. With a foreword by Richard Stanley, Compact Textbook in Mathematics.

5. Qi, F., and Guo, B.-N. (2017). Integral representations of the Catalan numbers and their applications. Mathematics, 5.

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