Asymptotic behavior of Bernoulli-Dunkland Euler-Dunkl polynomials and their zeros

Abstract

Bernoulli-Dunkl and Euler-Dunkl polynomials have been recently introduced as an extension of Bernoulli and Euler polynomials to the Dunkl context. In this article we study the asymptotic behavior of them and prove their convergence to suitable Bessel functions, which are the functions analogous to sine and cosine in the Dunkl context. Finally, we analyze the behavior of the zeros of the Bernoulli-Dunkl and Euler-Dunkl polynomials.