88373 20200716101429.0 doi 10.1016/j.jmaa.2019.04.019 sideral 111415 ART-2019-111415 eng Navas, L.M. A note on Appell sequences, Mellin transforms and Fourier series 2019 Access copy available to the general public Unrestricted A 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. info:eu-repo/grantAgreement/ES/DGA/E64 info:eu-repo/grantAgreement/ES/MINECO-FEDER/MTM2015-65888-C4-4-P info:eu-repo/semantics/openAccess by-nc-nd http://creativecommons.org/licenses/by-nc-nd/3.0/es/ 1.22 2019 1.021 2019 MATHEMATICS 77 / 324 = 0.238 2019 Q1 T1 Applied Mathematics 2019 Q1 MATHEMATICS, APPLIED 124 / 260 = 0.477 2019 Q2 T2 Analysis 2019 Q2 info:eu-repo/semantics/article info:eu-repo/semantics/acceptedVersion (orcid)0000-0001-5364-4799 Ruiz, F.J. Universidad de Zaragoza Varona, J.L. 2006 015 Universidad de Zaragoza Dpto. Matemáticas Área Análisis Matemático 476, 2 (2019), 836-850 J. math. anal. appl. Journal of Mathematical Analysis and Applications 0022-247X 669151 http://zaguan.unizar.es/record/88373/files/texto_completo.pdf Postprint 54107 http://zaguan.unizar.es/record/88373/files/texto_completo.jpg?subformat=icon icon Postprint oai:zaguan.unizar.es:88373 articulos driver 2020-07-16-08:47:59 ARTICLE