Some extended Pochhammer symbols and their applications involving generalized hypergeometric polynomials

Ever since 2012 when Srivastava et al. [22] 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, 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 derive several general families of hypergeometric generating functions by applying (for example) some such combinatorial identities as Gould's identity, which stem essentially from the Lagrange expansion theorem. We also indicate various (known or new) special cases and consequences of the results presented in this paper.