On a Class of Humbert-Hermite Polynomials

A unified presentation of a class of Humbert’s polynomials in two variables which generalizes the well known class of Gegenbauer, Humbert, Legendre, Chebycheff, Pincherle, Horadam, Kinnsy, Horadam-Pethe, Djordjević , Gould, Milovanović and Djordjević, Pathan and Khan polynomials and many not so called ’named’ polynomials has inspired the present paper and the authors define here generalized Humbert-Hermite polynomials of two variables. Several expansions of Humbert- Hermite polynomials, Hermite-Gegenbaurer (or ultraspherical) polynomials and Hermite- Chebyshev polynomials are proved.