On a New Class of Unified Reduction Formulas for Srivastava’s General Triple Hypergeometric Function $F^{(3)}[x, y, z]$
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Authors: Y. S. KIM, A. KILICMAN AND A. K. RATHIE
DOI: 10.46793/KgJMat2001.065K
Abstract:
Very recently, by applying the so called Beta integral method to the well-known hypergeometric identities due to Bailey and Ramanujan, Choi et al. [Reduction formula for Srivastava’s triple hypergeometric series F(3)[x,y,z], Kyungpook Math. J. 55 (2015), 439–447] have obtained three interesting reduction formulas for the Srivastava’s triple hypergeometric series F(3)[x,y,z].
The aim of this paper is to provide three unified reduction formulas for the Srivastava’s triple hypergeometric series F(3)[x,y,z] from which as many as reduction formulas desired (including those obtained by Choi et al.) can be deduced.
In the end, three unified relationships between Srivastava’s triple hypergeometric series and Kampé de Fériet function have also been given.
Keywords:
Generalized hypergeometric function pFq, gamma function, Pochhammer symbol, beta integral, Kampé de Fériet function, Srivastava’s triple hypergeometric series F(3)[x,y,z].
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