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

被引:5
作者
Li, Wen -Hui [1 ]
Kouba, Omran [2 ]
Kaddoura, Issam [3 ]
Qi, Feng [4 ]
机构
[1] Henan Kaifeng Coll Sci Technol & Commun, Sch Econ, Kaifeng 475001, Henan, Peoples R China
[2] Higher Inst Appl Sci & Technol, Dept Math, POB 31983, Damascus, Syria
[3] Lebanese Int Univ, Int Univ Beirut, Sch Arts & Sci, Dept Math, Beirut, Lebanon
[4] Henan Polytech Univ, Inst Math, Jiaozuo 454010, Henan, Peoples R China
关键词
Catalan number; Catalan-Qi number; Generating function; Generalization; Explicit formula; Integral representation; Cauchy?s integral formula; Integral formula; Combinatorial identity; Gamma function; BELL POLYNOMIALS; IDENTITIES; INVERSE;
D O I
10.2298/FIL2319505L
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
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.
引用
收藏
页码:6505 / 6524
页数:20
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