Kyungpook Mathematical Journal 2015; 55(2): 439-447
Published online June 23, 2015
Copyright © Kyungpook Mathematical Journal.
Reduction Formulas for Srivastava's Triple Hypergeometric Series $F^{(3)}[x, y, z]$
Junesang Choi1, Xiaoxia Wang2 and Arjun K. Rathie3
1Department of Mathematics, Dongguk University, Gyeongju 780-714, Republic of Korea
2Department of Mathematics, Shanghai University, Shanghai, 200444, P. R. China
3Department of Mathematics, School of Mathematical $&$ Physical Sciences, Central University of Kerala, Riverside Transit Campus, Padennakad P.O. Nileshwar, Kasaragod-671 328, India
Very recently the authors have obtained a very interesting reduction formula for the Srivastava's triple hypergeometric series $F^{(3)}(x,,y,,z)$ by applying the so-called Beta integral method to the Henrici's triple product formula for the hypergeometric series. In this sequel, we also present three more interesting reduction formulas for the function
$F^{(3)}(x,,y,,z)$ by using the well known identities due to Bailey and Ramanujan. The results established here are simple,
easily derived and (potentially) useful.
Keywords: Generalized hypergeometric function ${}_pF_q$, Gamma function, Pochhammer symbol, Beta integral, Kamp'e
de F'eriet function, Srivastava's triple hypergeometric series $F^{(3)}[x, y, z]$, Henrici's formula