Bernoulli-Dunkl and Apostol-Euler-Dunkl polynomials with applications to series involving zeros of Bessel functions
Classical Analysis and ODEs
2020-11-10 v1 Number Theory
Abstract
We introduce Bernoulli-Dunkl and Apostol-Euler-Dunkl polynomials as generalizations of Bernoulli and Apostol-Euler polynomials, where the role of the derivative is now played by the Dunkl operator on the real line. We use them to sum a bunch of series involving the zeros of Bessel functions.
Keywords
Cite
@article{arxiv.1608.06976,
title = {Bernoulli-Dunkl and Apostol-Euler-Dunkl polynomials with applications to series involving zeros of Bessel functions},
author = {Óscar Ciaurri and Antonio J. Durán and Mario Pérez and Juan L. Varona},
journal= {arXiv preprint arXiv:1608.06976},
year = {2020}
}
Comments
29 pages