On a class of generalized Humbert-Hermite polynomials via generalized Fibonacci polynomials

Abstract

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, Kinney, Horadam-Pethe, Djordjevi${\acute{c}}$, Gould, Milovanovi${\acute{c}}$ and Djordjevi${\acute{c}}$, Pathan and Khan polynomials and many not so called 'named' polynomials has inspired the present paper. We define here generalized Humbert-Hermite polynomials of two variables. Several expansions of Humbert-Hermite polynomials, Hermite-Gegenbaurer (or ultraspherical) polynomials