99351 20230921135440.0 doi 10.5817/AM2019-3-157 sideral 122887 ART-2019-122887 eng Navas, L.M. Existence and reduction of generalized apostol-bernoulli, apostol-euler and apostol-genocchi polynomials 2019 Access copy available to the general public Unrestricted One can find in the mathematical literature many recent papers studying the generalized Apostol-Bernoulli, Apostol-Euler and Apostol-Genocchi polynomials, defined by means of generating functions. In this article we clarify the range of parameters in which these definitions are valid and when they provide essentially different families of polynomials. In particular, we show that, up to multiplicative constants, it is enough to take as the “main family” those given by \[ \Big ( \frac{2}{\lambda e^t+1} \Big )^\alpha e^{xt} = \sum _{n=0}^{\infty } \mathcal{E}^{(\alpha )}_{n}(x;\lambda ) \frac{t^n}{n!}\,, \qquad \lambda \in \mathbb{C}\setminus \lbrace -1\rbrace \,, \] and as an “exceptional family” \[ \Big ( \frac{t}{e^t-1} \Big )^\alpha e^{xt} = \sum _{n=0}^{\infty } \mathcal{B}^{(\alpha )}_{n}(x) \frac{t^n}{n!}\,, \] both of these for $\alpha \in \mathbb{C}$. info:eu-repo/grantAgreement/ES/DGA/E64 info:eu-repo/grantAgreement/ES/MINECO/MTM2015-65888-C4-4-P info:eu-repo/semantics/openAccess by-nc-nd http://creativecommons.org/licenses/by-nc-nd/3.0/es/ 0.237 2019 Mathematics (miscellaneous) 2019 Q3 info:eu-repo/semantics/article info:eu-repo/semantics/publishedVersion Ruiz, F.J. Universidad de Zaragoza (orcid)0000-0001-5364-4799 Varona, J.L. 2006 015 Universidad de Zaragoza Dpto. Matemáticas Área Análisis Matemático 55, 3 (2019), 157-165 Archivum Mathematicum 0044-8753 492974 http://zaguan.unizar.es/record/99351/files/texto_completo.pdf Versión publicada 578543 http://zaguan.unizar.es/record/99351/files/texto_completo.jpg?subformat=icon icon Versión publicada oai:zaguan.unizar.es:99351 articulos driver 2023-09-21-13:31:28 ARTICLE