GENERAL STUDY ON POLYNOMIALS ASSOCIATED WITH HUMBERT POLYNOMIALS

Abstract

In this paper, we address a polynomial associated with Humbert polynomials. The main objects of this paper is to provide a natural further step towards the unified presentation of a class of Humbert’s polynomials which generalizes the well known class of Gegenbauer, Legendre, Pincherle, Horadam, Horadam-Pethe, Gould, Milovanovic Dordevic polynomials 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 finite series representations of some relatively more familiar polynomials Legendre, Gegenbauer, Hermite and Laguerre etc.