Bulletin of the
Korean Mathematical Society
BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

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Bull. Korean Math. Soc. 2013; 50(5): 1673-1681

Printed September 1, 2013

https://doi.org/10.4134/BKMS.2013.50.5.1673

Copyright © The Korean Mathematical Society.

Certain hypergeometric identities deducible by using the beta integral method

Junesang Choi, Arjun K. Rathie, and Hari M. Srivastava

Dongguk University, Central University of Kerala, University of Victoria

Abstract

The main objective of this paper is to show how one can obtain eleven new and interesting hypergeometric identities in the form of a single result from the old ones by mainly employing the known beta integral method which was recently introduced and used in a systematic manner by Krattenthaler and Rao \cite{Kr-Ra}. The results are derived with the help of a generalization of a well-known hypergeometric transformation formula due to Kummer. Several identities including one obtained earlier by Krattenthaler and Rao \cite{Kr-Ra} follow as special cases of our main results.

Keywords: generalized hypergeometric function ${}_pF_q$, Gamma function, Pochhammer symbol, Beta integral method, Kummer's formula, generalization of Kummer's formula

MSC numbers: Primary 33C70, 33C06; Secondary 33C90, 33C05