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, Djordjević, Gould, Milovanovic and Djordjevi 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 and Hermite–Chebyshev polynomials are proved.