A Simple Proof And Some Applications Of An Integral Representation For The Catalan Numbers

被引：0
|
作者：
Stewart, Sean M. [1 ]
机构：
[1] King Abdullah Univ Sci & Technol KAUST, Phys Sci & Engn Div, Thuwal 239556900, Saudi Arabia
来源：
APPLIED MATHEMATICS E-NOTES | 2022年 / 22卷
关键词：
PARAMETRIC INTEGRALS; PRESENTATIONS;
D O I：
暂无
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
A simple proof for an integral representation of the Catalan numbers that makes use of an ordinary generating function approach and relies on essentially nothing beyond elementary integral calculus is presented. Application of the integral representation given is then made in the evaluation of a family of infinite sums consisting of products between the central binomial coefficient and the bicentral binomial coefficient.
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页码：637 / 643
页数：7
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