On a Multivariable Extension of the Hermite and Related Polynomials

Abstract

In this paper, some limit relations between multivariable
Hermite polynomials \((MHP)\) and some other multivariable polyno-
mials are given, a class of multivariable polynomials is defined via
generating function, which include \((MHP)\) and multivariable Gegen-
bauer polynomials \((MGP)\) and with the help of this generating func-
tion various recurrence relations are obtained to this class. Integral
representations of \(MHP\) and \(MGP\) are also given. Furthermore, gene-
ral families of multilinear and multilateral generating functions are
obtained and their applications are presented.