New Generating Functions for a Class of Generalized Hermite Polynomials

The main object of this paper is to present several (presumably new) families of linear, bilinear, and mixed multilateral generating functions for a certain interesting generalization of the classical Hermite (and Laguerre) polynomials.Some of these generating functions are associated with the Stirling numbers of the second kind. Numerous known or new consequences of the results derived here also considered.