A note on two known sums involving central binomial coefficients with an application

한국수학교육학회지시리즈B:순수및응용수학 / Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, (P)1226-0657; (E)2287-6081

2022, v.29 no.2, pp.171-177

https://doi.org/https://doi.org/10.7468/jksmeb.2022.29.2.171

Lim, Dongkyu (Department of Mathematics Education, Andong National University)
Rathie, Arjun Kumar (Department of Mathematics, Vedant College of Engineering & Technology, Rajasthan Technical University)

Lim, Dongkyu, & Rathie, Arjun Kumar. (2022). A NOTE ON TWO KNOWN SUMS INVOLVING CENTRAL BINOMIAL COEFFICIENTS WITH AN APPLICATION. 한국수학교육학회지시리즈B:순수및응용수학, 29(2), 171-177, https://doi.org/https://doi.org/10.7468/jksmeb.2022.29.2.171

복사

Abstract

The aim of this note is to establish two known sums involving central binomial coefficients via a hypergeometric series approach. As an application, we discover two new closed-form evaluations of generalized hypergeometric function.

keywords: sum, series, alternating series, central binomial coefficient, proof, generalized hypergeometric function

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Vol.29 No.2

A NOTE ON TWO KNOWN SUMS INVOLVING CENTRAL BINOMIAL COEFFICIENTS WITH AN APPLICATION

A note on two known sums involving central binomial coefficients with an application

Abstract

한국수학교육학회지시리즈B:순수및응용수학