Appell polynomials as values of special functions

  1. Navas, L.M. 1
  2. Ruiz, F.J. 2
  3. Varona, J.L. 3
  1. 1 Universidad de Salamanca
    info

    Universidad de Salamanca

    Salamanca, España

    ROR https://ror.org/02f40zc51

  2. 2 Universidad de Zaragoza
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    Universidad de Zaragoza

    Zaragoza, España

    ROR https://ror.org/012a91z28

  3. 3 Universidad de La Rioja
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    Universidad de La Rioja

    Logroño, España

    ROR https://ror.org/0553yr311

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Revista:
Journal of Mathematical Analysis and Applications

ISSN: 0022-247X

Año de publicación: 2018

Volumen: 459

Número: 1

Páginas: 419-436

Tipo: Artículo

DOI: 10.1016/J.JMAA.2017.10.049 SCOPUS: 2-s2.0-85035144978 WoS: WOS:000418310900024 GOOGLE SCHOLAR

Otras publicaciones en: Journal of Mathematical Analysis and Applications

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Resumen

We show that there is a large class of Appell sequences {Pn(x)}n=0 ∞ for which there is a function F(s,x), entire in s for fixed x with Rex>0 and satisfying F(−n,x)=Pn(x) for n=0,1,2,…. For example, in the case of Bernoulli and Apostol–Bernoulli polynomials, F is essentially the Hurwitz zeta function and the Lerch transcendent, respectively. We study a subclass of these Appell sequences for which the corresponding special function has a form more closely related to the classical zeta functions, and give some interesting examples of these general constructions. © 2017 Elsevier Inc.