A New Generating Function for Hermite Polynomials

Abstract

This paper presents a new generating function of the form gx,t=∑n=0∞tnHnex for Hermite polynomials and reveals its connection with the incomplete gamma function. Recurrence relations of Hermite polynomials and another version of its contour integral representation are derived from this version of the generating function. New versions of the generating functions for the two-variable Hermite polynomials have been presented.