A generalized class of Humbert-Hermite polynomials

Abstract

In the recent years, several extensions of class of Humberts polynomial of two variables are established by various authors. Recent study done by Pathan and Khan that introduced Humbert-Hermite polynomial, generalizes the well known class of Humbert, Gegenbauer, Legendre, Chebyshev and many not so named polynomials. Inspired by the research, in this paper authors defined a generalization of class of Humbert - Hermite polynomials. Moreover, several generalizations of Hermite - Gegenbauer polynomials, Hermite – Legendre and Hermite  Chebyshev polynomials are established.