Six unified results for reducibility of the Srivastava's triple hypergeometric series \(H_A\)

Volume 10, Issue 6, pp 3038--3045 http://dx.doi.org/10.22436/jnsa.010.06.18

Publication Date: June 25, 2017 Submission Date: October 26, 2016

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Authors

Junesang Choi - Department of Mathematics, Dongguk University, Gyeongju 38066, Republic of Korea. Arjun K. Rathie - Department of Mathematics, School of Physical Sciences, Central University of Kerala, Kasaragod-671316, Kerala, India.

Abstract

We aim to provide six unified results for reducibility of the Srivastava’s triple hypergeometric series \(H_A\). The results are obtained with the help of generalizations of classical summation theorems due to Kummer, Gauss second and Bailey for the series \(_2F_1\) which have recently been published. Our main findings are also shown to be specialized to yield several known results.

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Keywords

• Gamma function
• hypergeometric function
• generalized hypergeometric function
• summation theorems
• Appell’s function \(F_1\)
• triple hypergeometric series \(H_A\).

MSC

•  33C60
•  33C65
•  33C05
•  33C70

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