Integral Representations of the Catalan Numbers and Their Applications

被引：36

作者：

Qi, Feng ^{[1
,2
,3
]}

Guo, Bai-Ni ^{[4
]}

机构：

[1] Henan Polytech Univ, Inst Math, Jiaozuo 454010, Henan, Peoples R China

[2] Inner Mongolia Univ Nationalities, Coll Math, Tongliao 028043, Inner Mongolia, Peoples R China

[3] Tianjin Polytech Univ, Coll Sci, Dept Math, Tianjin 300387, Peoples R China

[4] Henan Polytech Univ, Sch Math & Informat, Jiaozuo 454010, Henan, Peoples R China

来源：

MATHEMATICS | 2017年 / 5卷 / 03期

关键词：

Catalan number; integral representation; equivalent relation; application; sum of power series; Catalan-Qi function; Catalan-Qi number; beta function; WALLIS FORMULA; QI NUMBERS; GAMMA FUNCTIONS; IDENTITIES; SERIES; RATIO; PRESENTATIONS; INEQUALITIES; ANALOGS;

D O I：

10.3390/math5030040

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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.

引用

页数：31

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