Bulletin of the
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Bull. Korean Math. Soc. 2009; 46(6): 1201-1211

Printed November 1, 2009

https://doi.org/10.4134/BKMS.2009.46.6.1201

Copyright © The Korean Mathematical Society.

Applications of generalized Kummer's summation theorem for the series ${}_{2}F_{1}$

Yong Sup Kim and Arjun K. Rathie

Wonkwang University and Vedant College of Engineering and Technology

Abstract

The aim of this research paper is to establish generalizations of classical Dixon's theorem for the series ${}_{3}F_{2}$, a result due to Bailey involving product of generalized hypergeometric series and certain very interesting summations due to Ramanujan. The results are derived with the help of generalized Kummer's summation theorem for the series ${}_{2}F_{1}$ obtained earlier by Lavoie, Grondin, and Rathie.

Keywords: generalized Kummer's theorem, generalized Dixon's theorem, generalized Whipple's theorem

MSC numbers: 33C05, 33C20

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