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

• 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
• ISSN: 2306-3424; 2306-3432

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