Addition Theorems for the Product of Two Generalized Hermite Polynomials and Their Consequences

Abstract

This paper aims to acquire two theorems (believed to be new and not recorded in the literature) for the product of two generalized Hermite polynomials, using suitable generating relations, decomposition of infinite series, Cauchy double-series identity, and series rearrangement technique. Further, we discuss some special cases related to generalized and classical Hermite polynomials.