Appell polynomials as values of special functions
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1
Universidad de Salamanca
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2
Universidad de Zaragoza
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3
Universidad de La Rioja
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ISSN: 0022-247X
Ano de publicación: 2018
Volume: 459
Número: 1
Páxinas: 419-436
Tipo: Artigo
Outras publicacións en: Journal of Mathematical Analysis and Applications
Resumo
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.