Polynomials associated by Humbert polynomials

Abstract

We define the polynomials $w_{n,m}^{(r,s)}(x)$ where $r+s>1$, $m\geq 2$, which are related with the generalized Humbert polynomials $u_{n,m}^{(r)}(x)$. Here we find many recurrence relations and explicit representations for $w_{n,m}^{(r,s)}(x)$. Also, we present some special classes of the polynomials $u_{n,m}^{(r)}(x)$.