Generating functions for the generalized Gauss hypergeometric functions

摘要

Formulas and identities involving many well-known special functions (such as the Gamma and Beta functions, the Gauss hypergeometric function, and so on) play important rôles in themselves and in their diverse applications. Various families of generating functions have been established by a number of authors in many different ways. In this paper, we aim at establishing some (presumably new) generating functions for the generalized Gauss type hypergeometric type function which is introduced here. We also present some special cases of the main results of this paper.