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  • P-ISSN3059-0604
  • E-ISSN3059-1309
  • KCI

ISSN : 3059-0604

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Vol.30 No.2

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A NOTE ON TWO NEW CLOSED-FORM EVALUATIONS OF THE GENERALIZED HYPERGEOMETRIC FUNCTION 5F4 WITH ARGUMENT $\frac{1}{256}$

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

한국수학교육학회지시리즈B:순수및응용수학 / Journal of the Korean Society of Mathematical Education Series B: Theoretical Mathematics and Pedagogical Mathematics, (P)3059-0604; (E)3059-1309
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 (Department of Mathematics, Manipal Institute of Technology, Manipal Academy of Higher Education)
Dongkyu Lim (Department of Mathematics Education, Andong National University)
Arjun K. Rathie (Department of Mathematics, Vedant College of Engineering and Technology (Rajasthan Technical University))
B. R. Srivatsa Kumar, Dongkyu Lim, & Arjun K. Rathie. (2023). A NOTE ON TWO NEW CLOSED-FORM EVALUATIONS OF THE GENERALIZED HYPERGEOMETRIC FUNCTION <sub>5</sub>F<sub>4</sub> WITH ARGUMENT <TEX>$\frac{1}{256}$</TEX>, 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 5F4 with argument $\frac{1}{256}$. 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

한국수학교육학회지시리즈B:순수및응용수학

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