Some classes of generating functions associated with a certain family of extended and generalized hypergeometric functions

摘要

Recently, Srivastava et al. (2012) [11] introduced and initiated the study of many interesting fundamental properties and characteristics of a certain pair of potentially useful families of the so-called generalized incomplete hypergeometric functions. Ever since then there have appeared many closely-related works dealing essentially with notable developments involving various classes of generalized hypergeometric functions and generalized hypergeometric polynomials, which are defined by means of the corresponding incomplete and other novel extensions of the familiar Pochhammer symbol. Here, in this sequel to some of these earlier works, we first derive two remarkably distinct classes of hypergeometric generating functions and then apply each of them in deducing a family of linear, bilinear and bilateral (or mixed multilateral) generating functions. We also consider various (known or new) special cases and consequences of the results presented in this paper.