Qi Feng, “An improper integral, the beta function, the Wallis ratio, and the Catalan numbers”, Пробл. анал. Issues Anal., 2018, том 7(25), выпуск 1,страницы 104

Эта публикация цитируется в 10 статьях

An improper integral, the beta function, the Wallis ratio, and the Catalan numbers

Qi Feng^abc

^a Department of Mathematics, College of Science, Tianjin Polytechnic University, Tianjin, 300387, China
^b College of Mathematics, Inner Mongolia University for Nationalities, Tongliao, Inner Mongolia, 028043, China
^c Institute of Mathematics, Henan Polytechnic University, Jiaozuo, Henan, 454010, China

Аннотация: 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.

Ключевые слова: improper integral; closed expression; unified expression; beta function; Wallis ratio; integral representation; Catalan number.

УДК: 519.58

MSC: Primary 11B65; Secondary 11B75, 11B83, 26A39, 26A42, 33B15

Поступила в редакцию: 22.01.2018
Исправленный вариант: 28.04.2018
Принята в печать: 30.04.2018

Язык публикации: английский

DOI: 10.15393/j3.art.2018.4370