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

被引：1
|
作者：
Cao, Jian [1 ]
Li, Wen-Hui [2 ]
Niu, Da-Wei [3 ]
Qi, Feng [4 ]
Zhao, Jiao-Lian [5 ]
机构：
[1] Hangzhou Normal Univ, Sch Math, Hangzhou 311121, Peoples R China
[2] Henan Kaifeng Coll Sci Technol & Commun, Sch Econ, Kaifeng 475001, Peoples R China
[3] Henan Univ Anim Husb & Econ, Dept Sci, Zhengzhou 450046, Peoples R China
[4] Henan Polytech Univ, Inst Math, Jiaozuo 454010, Peoples R China
[5] Weinan Normal Univ, Sch Math & Stat, Weinan 714000, Peoples R China
来源：
MATHEMATICS | 2023年 / 11卷 / 08期
基金：
中国国家自然科学基金;
关键词：
Catalan number; generalized Catalan function; generalized Catalan number; Cauchy's integral formula; generalization; generating function; integral representation; DIFFERENTIAL-EQUATIONS; BELL POLYNOMIALS; IDENTITIES; FORMULAS; QI; INVERSE;
D O I：
10.3390/math11081870
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
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.
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页数：16
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