Reflection properties of zeta related functions in terms of fractional derivatives
Resumen: 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.
Idioma: Inglés
DOI: 10.1515/fca-2020-0025
Año: 2020
Publicado en: Fractional Calculus and Applied Analysis 23, 2 (2020), 520-533
ISSN: 1311-0454

Factor impacto JCR: 3.126 (2020)
Categ. JCR: MATHEMATICS rank: 10 / 330 = 0.03 (2020) - Q1 - T1
Categ. JCR: MATHEMATICS, INTERDISCIPLINARY APPLICATIONS rank: 27 / 108 = 0.25 (2020) - Q1 - T1
Categ. JCR: MATHEMATICS, APPLIED rank: 22 / 265 = 0.083 (2020) - Q1 - T1

Factor impacto SCIMAGO: 1.397 - Applied Mathematics (Q1) - Analysis (Q1)

Financiación: info:eu-repo/grantAgreement/ES/DGA-UZ/E24-1
Financiación: info:eu-repo/grantAgreement/ES/MICINN/MTM2009-11154
Tipo y forma: Article (PostPrint)
Área (Departamento): Área Física Teórica (Dpto. Física Teórica)

Rights Reserved All rights reserved by journal editor

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