A general double-series identity and its application in hypergeometric reduction formulas

Abstract

In this paper, we obtain a general double-series identity involving the bounded sequence of arbitrary complex numbers. As application of our double-series identity, we establish some reduction formulas for Srivastava–Daoust double hypergeometric function and Gaussian generalized hypergeometric function 4F3 . As special cases of our reduction formula for 4F3 lead to some corollaries involving Clausen hypergeometric functions 3F2 . Making suitable adjustment of parameters in reduction formulas for 4F3 and 3F2 , we obtain some results in terms of elementary functions and some special functions like Lerch generalized zeta function and incomplete beta function.