Two characterizations of Sheffer-Dunkl sequences

TL;DR

This paper introduces two Stieltjes integral characterizations of Sheffer-Dunkl polynomials, extending classical polynomial characterizations to the Dunkl setting with analogous operators.

Contribution

It provides novel integral characterizations of Sheffer-Dunkl polynomials, bridging classical and Dunkl polynomial theories.

Findings

Two Stieltjes integral formulas for Sheffer-Dunkl polynomials

Extension of classical polynomial characterizations to Dunkl context

New tools for analyzing Sheffer-Dunkl sequences

Abstract

Sheffer polynomials can be characterized using different Stieltjes integrals. These families of polynomials have been recently extended to the Dunkl context. In this way some classical operators as the derivative operator or the difference operator are replaced as analogous operators in the Dunkl universe. In this paper we establish two Stieltjes integrals that help us to characterize the Sheffer-Dunkl polynomials.