An Identity Involving Product of Generalized Hypergeometric Series 2F2

Yong Sup Kim; Junesang Choi; Arjun Kumar Rathie

doi:10.5666/KMJ.2019.59.2.293

Article

KYUNGPOOK Math. J. 2019; 59(2): 293-299

Published online June 23, 2019

An Identity Involving Product of Generalized Hypergeometric Series ₂F₂

Yong Sup Kim, Junesang Choi^∗, Arjun Kumar Rathie

Department of Mathematics Education, Wonkwang University, Iksan 54538, Republic of Korea
e-mail : yspkim@wonkwang.ac.kr

Department of Mathematics, Dongguk University, Gyeongju 38066, Republic of Korea
e-mail : junesang@mail.dongguk.ac.kr

Department of Mathematics, Vedant College of Engineering & Technology (Rajasthan Technical University), Bundi, Rajasthan State, India
e-mail : arjunkumarrathie@gmail.com

Received: August 27, 2018; Revised: October 16, 2019; Accepted: October 16, 2018

Abstract

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Abstract

A number of identities associated with the product of generalized hypergeometric series have been investigated. In this paper, we aim to establish an identity involving the product of the generalized hypergeometric series ₂F₂. We do this using the generalized Kummer-type II transformation due to Rathie and Pogany and another identity due to Bailey. The result presented here, being general, can be reduced to a number of relatively simple identities involving the product of generalized hypergeometric series, some of which are observed to correspond to known ones.

Keywords: generalized hypergeometric series, Kummer-type I transformation, Kummer-type II transformation, Gauss’s summation theorem for ₂F₁(1), Watson summation theorem for ₃F₂