A NOTE ON A NEW AND GENERAL SUMMATION FORMULA FOR THE GENERALIZED HYPERGEOMETRIC SERIES $_4F_3(1)$

Print ISSN: 2319-1023 | Online ISSN: 2582-5461 | Total Downloads : 11

Volume : 11 , Issue : 2
DOI: https://doi.org/10.56827/JRSMMS.2024.1102.10
Author :
Madhav Prasad Poudel (School of Engineering, Pokhara University, Kaski, Pokhara, NEPAL)
Vijay Yadav (Department of Mathematics, SPDT College, Andheri East, Mumbai 400059, Maharashtra, INDIA)
Arjun K. Rathie (Department of Mathematics, Vedant College of Engineering & Technology (Rajasthan Technical University) Tulsi, Jakhamund, Bundi, Rajasthan, INDIA)

Abstract

The main purpose of this note is to demonstrate how one can obtain a new and general summation formula for the generalized hypergeometric series $_4F_3(1)$. This is achieved by employing two generalizations of the Gauss's second summation theorems obtained earlier by Rakha and Rathie in an identity due to Bailey. Several results obtained earlier by Ali et al. follow special cases of our main findings.

Keywords and Phrases

Generalized hypergeometric function, Gauss summation formula, Generalization, Bailey identity.

A.M.S. subject classification

33C20.

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