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000088373 0247_ $$2doi$$a10.1016/j.jmaa.2019.04.019
000088373 0248_ $$2sideral$$a111415
000088373 037__ $$aART-2019-111415
000088373 041__ $$aeng
000088373 100__ $$aNavas, L.M.
000088373 245__ $$aA note on Appell sequences, Mellin transforms and Fourier series
000088373 260__ $$c2019
000088373 5060_ $$aAccess copy available to the general public$$fUnrestricted
000088373 5203_ $$aA large class of Appell polynomial sequences {p n (x)} n=0 8 are special values at the negative integers of an entire function F(s, x), given by the Mellin transform of the generating function for the sequence. For the Bernoulli and Apostol-Bernoulli polynomials, these are basically the Hurwitz zeta function and the Lerch transcendent. Each of these have well-known Fourier series which are proved in the literature using various techniques. Here we find the latter Fourier series by directly calculating the coefficients in a straightforward manner. We then show that, within the context of Appell sequences, these are the only cases for which the polynomials have uniformly convergent Fourier series. In the more general context of Sheffer sequences, we find that there are other polynomials with uniformly convergent Fourier series. Finally, applying the same ideas to the Fourier transform, considered as the continuous analog of the Fourier series, the Hermite polynomials play a role analogous to that of the Bernoulli polynomials.
000088373 536__ $$9info:eu-repo/grantAgreement/ES/DGA/E64$$9info:eu-repo/grantAgreement/ES/MINECO-FEDER/MTM2015-65888-C4-4-P
000088373 540__ $$9info:eu-repo/semantics/openAccess$$aby-nc-nd$$uhttp://creativecommons.org/licenses/by-nc-nd/3.0/es/
000088373 590__ $$a1.22$$b2019
000088373 592__ $$a1.021$$b2019
000088373 591__ $$aMATHEMATICS$$b77 / 324 = 0.238$$c2019$$dQ1$$eT1
000088373 593__ $$aApplied Mathematics$$c2019$$dQ1
000088373 591__ $$aMATHEMATICS, APPLIED$$b124 / 260 = 0.477$$c2019$$dQ2$$eT2
000088373 593__ $$aAnalysis$$c2019$$dQ2
000088373 655_4 $$ainfo:eu-repo/semantics/article$$vinfo:eu-repo/semantics/acceptedVersion
000088373 700__ $$0(orcid)0000-0001-5364-4799$$aRuiz, F.J.$$uUniversidad de Zaragoza
000088373 700__ $$aVarona, J.L.
000088373 7102_ $$12006$$2015$$aUniversidad de Zaragoza$$bDpto. Matemáticas$$cÁrea Análisis Matemático
000088373 773__ $$g476, 2 (2019), 836-850$$pJ. math. anal. appl.$$tJournal of Mathematical Analysis and Applications$$x0022-247X
000088373 8564_ $$s669151$$uhttps://zaguan.unizar.es/record/88373/files/texto_completo.pdf$$yPostprint
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000088373 951__ $$a2020-07-16-08:47:59
000088373 980__ $$aARTICLE