Some Srivastava-Brafman Type Generating Relations For A General Class Of Multi-Index And Multi-Variable Gould-Hopper And Dattoli Type Hypergeometric Polynomials

Abstract

Abstract In this article, we first introduce and study a new family of the multi-index and multi-variable Gould-Hopper and Dattoli type polynomials {Hn(cm, cm-1,…, c3, c2)(a1, a2, …, am} defined by (2.1), which are an extension of different types of Her-mite polynomials defined in section 1. We next consider multi-variable linear, bilinear and bilateral generating relations of the newly defined hypergeometric polynomials, using series iteration techniques. Further, we generalize these generating relations in the forms of multiple series identities involving bounded multiple sequences, Fox-Wright hypergeometric function and Srivastava-Daoust multi-variable hypergeometric function.