Certain cubic reduction formulas involving hypergeometric functions

Abstract

In this paper, we obtain a new general double infinite series identity (in terms of the sum of three infinite series) involving the bounded sequence of arbitrary complex numbers using Saalschutz summation theorem for terminating Clausen series. As application of our double series identity, we establish two cubic reduction formulas for Srivastava-Daoust double hypergeometric functions in terms of generalized hypergeometric function with suitable convergence conditions. By the theory of analytic continuation, our cubic reduction formula is also valid in -211/25≤R(z)≤3/4 when F(z)=0, using Mathematica software.