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.
Acknowledgements
The authors would like to extend their sincere appreciation to the Deanship of Scientific Research at King Saud University for funding this Research group No (RG-1435-026).
Disclosure statement
No potential conflict of interest was reported by the authors.