Abstract
In this work, we introduce a differential-difference operator , which includes as particular cases the derivative operator and the Dunkl operator associated with root system of type . We show that the symmetrization of the eigenfunction of this operator is a solution of an inhomogeneous Bessel differential equation. Also we construct an intertwining operator between and the Dunkl operator. As application, we study a polynomials set of Boas and Buck type by using the quasi-monomiality method related to this operator.