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  • P-ISSN1226-0657
  • E-ISSN2287-6081
  • KCI

ISSN : 1226-0657

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Vol.30 No.2

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A Note on Two New Closed­form Evaluations of the Generalized Hypergeometric Function $_5F_4$ with Argument $1/256$

Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics / Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, (P)1226-0657; (E)2287-6081
2023, v.30 no.2, pp.131-138
https://doi.org/https://doi.org/10.7468/jksmeb.2023.30.2.131
B. R. Srivatsa Kumar
Dongkyu Lim
Arjun K. Rathie
B., R. S. K. , Dongkyu, L. , & Arjun, K. R. (2023). A Note on Two New Closed­form Evaluations of the Generalized Hypergeometric Function $_5F_4$ with Argument $1/256$. Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, 30(2), 131-138, https://doi.org/https://doi.org/10.7468/jksmeb.2023.30.2.131

Abstract

The aim of this note is to provide two new and interesting closed-form evaluations of the generalized hypergeometric function <sub>5</sub>F<sub>4</sub> with argument <TEX>$\frac{1}{256}$</TEX>. This is achieved by means of separating a generalized hypergeometric function into even and odd components together with the use of two known sums (one each) involving reciprocals of binomial coefficients obtained earlier by Trif and Sprugnoli. In the end, the results are written in terms of two interesting combinatorial identities.

keywords
Generalized hypergeometric function, central binomial coefficients, Combinatorial sum, Reciprocals

Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics

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