Generating functions for generalized Hermite polynomials associated with parabolic cylinder functions

ABSTRACT

In this article, we first give some basic properties of generalized Hermite polynomials associated with parabolic cylinder functions. We next use Weisner? group theoretic method and operational rules method to establish new generating functions for these generalized Hermite polynomials. The operational methods we use allow us to obtain unilateral, bilinear and bilateral generating functions by using the same procedure. Applications of generating functions obtained by Weisner? group theoretic method are discussed.