Some summation theorems for generalized hypergeometric functions

Abstract

Essentially, whenever a generalized hypergeometric series can be summed in terms of gamma functions, the result will be important as only a few such summation theorems are available in the literature. In this paper, we apply two identities of generalized hypergeometric series in order to extend some classical summation theorems of hypergeometric functions such as Gauss, Kummer, Dixon, Watson, Whipple, Pfaff-Saalschütz and Dougall formulas and also obtain some new summation theorems in the sequel.