Bernoulli-Dunkl and Apostol-Euler-Dunkl polynomials with applications to series involving zeros of Bessel functions

摘要

We introduce Bernoulli-Dunkl and Apostol-Euler-Dunkl polynomials asgeneralizations of Bernoulli and Apostol-Euler polynomials, where the role ofthe derivative is now played by the Dunkl operator on the real line. We usethem to sum a bunch of series involving the zeros of Bessel functions.