Some properties of generalized multiple Hermite polynomials

Abstract

The purpose of this paper is to introduce and discuss a more general class of multiple Hermite polynomials. In this work, the explicit forms, operational formulas and a recurrence relation are obtained. Furthermore, we derive several families of bilinear, bilateral and mixed multilateral finite series relationships and generating functions for the generalized multiple Hermite polynomials. (C) 2011 Elsevier B.V. All rights reserved.