Bernoulli–Dunkl and Euler–Dunkl polynomials and their generalizations

Abstract

Bernoulli–Dunkl and Euler–Dunkl polynomials are generalizations of the classical Bernoulli and Euler polynomials, using the Dunkl operator instead of the differential operator. In this paper, we study properties of these polynomials that extend some of the well-known identities in the classical case, such as the Euler–Maclaurin or the Boole summation formulas in the Dunkl context.