On the Generalized Class of Multivariable Humbert-Type Polynomials

Abstract

The present paper deals with the class of multivariable Humbert polynomials having generalization of some well-known polynomials like Gegenbauer, Legendre, Chebyshev, Gould, Sinha, Milovanović-Djordjević, Horadam, Horadam-Pethe, Pathan and Khan, a class of generalized Humbert polynomials in two variables etc. In this paper, we are presenting power series representation, integral representation, and hypergeometric representation of this polynomial. We shall obtain the expansion of the above considering multivariable Humbert polynomial in series of well-known polynomials like Legendre, Hermite, Laguerre and also obtain some generating functions.