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

  1. Ciaurri, Ó. 1
  2. Durán, A.J. 2
  3. Pérez, M. 3
  4. Varona, J.L. 1
  1. 1 Universidad de La Rioja
    info

    Universidad de La Rioja

    Logroño, España

    ROR https://ror.org/0553yr311

  2. 2 Universidad de Sevilla
    info

    Universidad de Sevilla

    Sevilla, España

    ROR https://ror.org/03yxnpp24

  3. 3 Universidad de Zaragoza
    info

    Universidad de Zaragoza

    Zaragoza, España

    ROR https://ror.org/012a91z28

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Journal:
Journal of Approximation Theory

ISSN: 0021-9045

Year of publication: 2018

Volume: 235

Pages: 20-45

Type: Article

DOI: 10.1016/J.JAT.2018.06.001 SCOPUS: 2-s2.0-85048574893 GOOGLE SCHOLAR

More publications in: Journal of Approximation Theory

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Ortogonalidad, teoría de la aproximación y aplicaciones en física matemática.

2016/00008/001

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 find the sum of many different series involving the zeros of Bessel functions. © 2018 Elsevier Inc.