ON A MULTIVARIABLE EXTENSION OF THE HERMITE AND RELATED POLYNOMIALS

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