On certain generalized polynomial system associated with Humbert polynomials

Abstract

The object of this paper is to present a unification and generalization of a class of Humbert polynomials which generalizes the well known class of Gegenbauer, Legendre, Pincherle, Horadam, Kinney, Horadam-Pethe, Gould, Milovanovic-Dordevic, Pathan-Khan and many not so well known polynomials. We shall give some basic relations involving the generalized Humbert polynomials and then take up several generating functions, hypergeometric representations and expansions in series of some relatively more familiar polynomials of Legendre, Gegenbauer, Hermite and Laguerre. The results obtained are of general character and include the investigations carried out by several authors including Dilcher, Horadam, Sinha, Shreshtha, Milovanovic-Dordevic and Pathan-Khan.