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December 2021 Asymptotic behavior of Bernoulli-Dunkland Euler-Dunkl polynomials and their zeros
Judit Mínguez Ceniceros, Juan L. Varona
Funct. Approx. Comment. Math. 65(2): 211-226 (December 2021). DOI: 10.7169/facm/1968

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.

Citation

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Judit Mínguez Ceniceros. Juan L. Varona. "Asymptotic behavior of Bernoulli-Dunkland Euler-Dunkl polynomials and their zeros." Funct. Approx. Comment. Math. 65 (2) 211 - 226, December 2021. https://doi.org/10.7169/facm/1968

Information

Published: December 2021
First available in Project Euclid: 13 October 2021

Digital Object Identifier: 10.7169/facm/1968

Subjects:
Primary: 11B68
Secondary: 33C10 , 42C10

Keywords: Appell-Dunkl sequences , asymptotic behavior , Bernoulli-Dunkl polynomials , Bessel functions , distribution of zeros , Euler-Dunkl polynomials , Fourier series , Fourier-Dunkl series

Rights: Copyright © 2021 Adam Mickiewicz University

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Vol.65 • No. 2 • December 2021
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