Some Generalizations of Pochhammer’s Symbol and their Associated Families of Hypergeometric Functions and Hypergeometric Polynomials

In 2012, H. M. Srivastava et al. [37] introduced and studied a number of interesting fundamental properties and characteristics of a family of potentially useful incomplete hypergeometric functions. The definitions of these incomplete hypergeometric functions were based essentially upon some generalization of the Pochhammer symbol by mean of the incomplete gamma functions γ(s,x) and Γ (s,x). Our principal objective in this article is to present a systematic investigation of several further properties of these incomplete hypergeometric functions and some general classes of the incomplete hypergeometric polynomials which are associated with them. Various (known or new) special cases and consequences of the results presented in this article are considered. Several other generalizations of the Pochhammer symbol and their associated families of hypergeometric functions and hypergeometric polynomials are also briefly pointed out.