AN IMPROPER INTEGRAL, THE BETA FUNCTION, THE WALLIS RATIO, AND THE CATALAN NUMBERS

AN IMPROPER INTEGRAL, THE BETA FUNCTION, THE WALLIS RATIO, AND THE CATALAN NUMBERS

In the paper we present closed and unified expressions for a sequence of improper integrals in terms of the beta function and the Wallis ratio. Hereafter, we derive integral representations for the Catalan numbers originating from combinatorics

Bibliographic Details
Main Author: Qi Feng
Format: Article
Language:English
Published: Petrozavodsk State University 2018-06-01
Series:Проблемы анализа
Subjects:
improper integral ◆ closed expression ◆ unified expression ◆ beta function ◆ Wallis ratio ◆ integral representation ◆ Catalan number
Online Access:http://issuesofanalysis.petrsu.ru/article/genpdf.php?id=4370&lang=ru
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spelling doaj-6fd6fbc86d2c45fe95433c22f2265c722021-07-02T08:18:59ZengPetrozavodsk State UniversityПроблемы анализа2306-34242306-34322018-06-017(25)110411510.15393/j3.art.2018.4370AN IMPROPER INTEGRAL, THE BETA FUNCTION, THE WALLIS RATIO, AND THE CATALAN NUMBERSQi Feng0 Institute of Mathematics, Henan Polytechnic University; College of Mathematics, Inner Mongolia University for Nationalities; Department of Mathematics, College of Science Tianjin Polytechnic University In the paper we present closed and unified expressions for a sequence of improper integrals in terms of the beta function and the Wallis ratio. Hereafter, we derive integral representations for the Catalan numbers originating from combinatoricshttp://issuesofanalysis.petrsu.ru/article/genpdf.php?id=4370&lang=ruimproper integral ◆ closed expression ◆ unified expression ◆ beta function ◆ Wallis ratio ◆ integral representation ◆ Catalan number
collection DOAJ
language English
format Article
sources DOAJ
author Qi Feng
spellingShingle Qi Feng
AN IMPROPER INTEGRAL, THE BETA FUNCTION, THE WALLIS RATIO, AND THE CATALAN NUMBERS
Проблемы анализа
improper integral ◆ closed expression ◆ unified expression ◆ beta function ◆ Wallis ratio ◆ integral representation ◆ Catalan number
author_facet Qi Feng
author_sort Qi Feng
title AN IMPROPER INTEGRAL, THE BETA FUNCTION, THE WALLIS RATIO, AND THE CATALAN NUMBERS
title_short AN IMPROPER INTEGRAL, THE BETA FUNCTION, THE WALLIS RATIO, AND THE CATALAN NUMBERS
title_full AN IMPROPER INTEGRAL, THE BETA FUNCTION, THE WALLIS RATIO, AND THE CATALAN NUMBERS
title_fullStr AN IMPROPER INTEGRAL, THE BETA FUNCTION, THE WALLIS RATIO, AND THE CATALAN NUMBERS
title_full_unstemmed AN IMPROPER INTEGRAL, THE BETA FUNCTION, THE WALLIS RATIO, AND THE CATALAN NUMBERS
title_sort improper integral, the beta function, the wallis ratio, and the catalan numbers
publisher Petrozavodsk State University
series Проблемы анализа
issn 2306-3424
2306-3432
publishDate 2018-06-01
description In the paper we present closed and unified expressions for a sequence of improper integrals in terms of the beta function and the Wallis ratio. Hereafter, we derive integral representations for the Catalan numbers originating from combinatorics
topic improper integral ◆ closed expression ◆ unified expression ◆ beta function ◆ Wallis ratio ◆ integral representation ◆ Catalan number
url http://issuesofanalysis.petrsu.ru/article/genpdf.php?id=4370&lang=ru
work_keys_str_mv AT qifeng animproperintegralthebetafunctionthewallisratioandthecatalannumbers
AT qifeng improperintegralthebetafunctionthewallisratioandthecatalannumbers
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