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

Sean M. Stewart

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

Sean M. Stewart

Physical Sciences and Engineering

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

Abstract

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 coeffi cient and the bicentral binomial coeffi cient.

Original language	English (US)
Pages (from-to)	637-643
Number of pages	7
Journal	Applied Mathematics E - Notes
Volume	22
State	Published - Jan 1 2022

Bibliographical note

KAUST Repository Item: Exported on 2022-12-08
Acknowledgements: The author is grateful to Sangchul Lee for the conjectured expression for the integral Ik appearing in (18) which expresses its value explicitly in terms of a simple positive rational n

ASJC Scopus subject areas

Applied Mathematics

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https://repository.kaust.edu.sa/bitstream/10754/686276/1/Sean-Stewart-Catalan-Integral-Representation.pdf

Cite this

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abstract = "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 coeffi cient and the bicentral binomial coeffi cient.",

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AB - 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 coeffi cient and the bicentral binomial coeffi cient.

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UR - https://www.emis.de/journals/AMEN/2022/AMEN-211007.pdf

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

Abstract

Bibliographical note

ASJC Scopus subject areas

Access to Document

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