101608 20210902121724.0 doi 10.1515/fca-2020-0025 sideral 118189 ART-2020-118189 eng Ferreira, E.M. Reflection properties of zeta related functions in terms of fractional derivatives 2020 Access copy available to the general public Unrestricted We prove that the Weyl fractional derivative is a useful instrument to express certain properties of the zeta related functions. Specifically, we show that a known reflection property of the Hurwitz zeta function ¿(n, a) of integer first argument can be extended to the more general case of ¿(s, a), with complex s, by replacement of the ordinary derivative of integer order by Weyl fractional derivative of complex order. Besides, ¿(s, a) with (s) > 2 is essentially the Weyl (s-2)-derivative of ¿(2, a). These properties of the Hurwitz zeta function can be immediately transferred to a family of polygamma functions of complex order defined in a natural way. Finally, we discuss the generalization of a recently unveiled reflection property of the Lerch''s transcendent. info:eu-repo/grantAgreement/ES/DGA-UZ/E24-1 info:eu-repo/grantAgreement/ES/MICINN/MTM2009-11154 info:eu-repo/semantics/openAccess All rights reserved http://www.europeana.eu/rights/rr-f/ 3.126 2020 MATHEMATICS 10 / 330 = 0.03 2020 Q1 T1 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS 27 / 108 = 0.25 2020 Q1 T1 MATHEMATICS, APPLIED 22 / 265 = 0.083 2020 Q1 T1 1.397 2020 Applied Mathematics 2020 Q1 Analysis 2020 Q1 info:eu-repo/semantics/article info:eu-repo/semantics/acceptedVersion Kohara, A.K. Sesma, J. Universidad de Zaragoza (orcid)0000-0002-3837-8303 2004 405 Universidad de Zaragoza Dpto. Física Teórica Área Física Teórica 23, 2 (2020), 520-533 Fract. Calc. Appl. Anal. Fractional Calculus and Applied Analysis 1311-0454 116661 http://zaguan.unizar.es/record/101608/files/texto_completo.pdf Postprint 1037749 http://zaguan.unizar.es/record/101608/files/texto_completo.jpg?subformat=icon icon Postprint oai:zaguan.unizar.es:101608 articulos driver 2021-09-02-09:30:55 ARTICLE