The Pure and Applied Mathematics (한국수학교육학회지시리즈B:순수및응용수학)

Korean Society of Mathematical Education (한국수학교육학회)
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A NOTE ON TWO NEW CLOSED-FORM EVALUATIONS OF THE GENERALIZED HYPERGEOMETRIC FUNCTION 5F4 WITH ARGUMENT $\frac{1}{256}$

  • 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))
  • Received : 2022.02.04
  • Accepted : 2022.12.25
  • Published : 2023.05.31
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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.

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Acknowledgement

The referees have reviewed the paper very carefully. The authors express their deep thanks for the comments. The work of D. Lim was partially supported by the National Research Foundation of Korea (NRF) grant funded by the Korean government (MSIT) NRF-2021R1C1C1010902.

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