000099351 001__ 99351
000099351 005__ 20230921135440.0
000099351 0247_ $$2doi$$a10.5817/AM2019-3-157
000099351 0248_ $$2sideral$$a122887
000099351 037__ $$aART-2019-122887
000099351 041__ $$aeng
000099351 100__ $$aNavas, L.M.
000099351 245__ $$aExistence and reduction of generalized apostol-bernoulli, apostol-euler and apostol-genocchi polynomials
000099351 260__ $$c2019
000099351 5060_ $$aAccess copy available to the general public$$fUnrestricted
000099351 5203_ $$aOne 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 $\alpha \in \mathbb{C}$.
000099351 536__ $$9info:eu-repo/grantAgreement/ES/DGA/E64$$9info:eu-repo/grantAgreement/ES/MINECO/MTM2015-65888-C4-4-P
000099351 540__ $$9info:eu-repo/semantics/openAccess$$aby-nc-nd$$uhttp://creativecommons.org/licenses/by-nc-nd/3.0/es/
000099351 592__ $$a0.237$$b2019
000099351 593__ $$aMathematics (miscellaneous)$$c2019$$dQ3
000099351 655_4 $$ainfo:eu-repo/semantics/article$$vinfo:eu-repo/semantics/publishedVersion
000099351 700__ $$0(orcid)0000-0001-5364-4799$$aRuiz, F.J.$$uUniversidad de Zaragoza
000099351 700__ $$aVarona, J.L.
000099351 7102_ $$12006$$2015$$aUniversidad de Zaragoza$$bDpto. Matemáticas$$cÁrea Análisis Matemático
000099351 773__ $$g55, 3 (2019), 157-165$$tArchivum Mathematicum$$x0044-8753
000099351 8564_ $$s492974$$uhttps://zaguan.unizar.es/record/99351/files/texto_completo.pdf$$yVersión publicada
000099351 8564_ $$s578543$$uhttps://zaguan.unizar.es/record/99351/files/texto_completo.jpg?subformat=icon$$xicon$$yVersión publicada
000099351 909CO $$ooai:zaguan.unizar.es:99351$$particulos$$pdriver
000099351 951__ $$a2023-09-21-13:31:28
000099351 980__ $$aARTICLE