Fractional Calculus of the Lerch Zeta Function

Detalhes bibliográficos
Autor(a) principal: Guariglia, Emanuel [UNESP]
Data de Publicação: 2022
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Institucional da UNESP
Texto Completo: http://dx.doi.org/10.1007/s00009-021-01971-7
http://hdl.handle.net/11449/239879
Resumo: This paper deals with the fractional derivative of the Lerch zeta function. We compute the fractional derivative of the Lerch zeta function using a complex generalization of the Grünwald–Letnikov derivative. This definition of fractional derivative, fulfilling the generalized Leibniz rule, allows us to derive a functional equation for the fractional derivative of the Lerch zeta function. This functional equation is rewritten in a simplified form that reduces its computational cost. Furthermore, we prove an approximate functional equation for the fractional derivative of the Lerch zeta function.
id UNSP_181baf8689ec3b6f653f2180b004e2ec
oai_identifier_str oai:repositorio.unesp.br:11449/239879
network_acronym_str UNSP
network_name_str Repositório Institucional da UNESP
repository_id_str 2946
spelling Fractional Calculus of the Lerch Zeta Functioncomputational costfunctional equationgeneralized Leibniz ruleGrünwald–Letnikov fractional derivativeLerch zeta functionThis paper deals with the fractional derivative of the Lerch zeta function. We compute the fractional derivative of the Lerch zeta function using a complex generalization of the Grünwald–Letnikov derivative. This definition of fractional derivative, fulfilling the generalized Leibniz rule, allows us to derive a functional equation for the fractional derivative of the Lerch zeta function. This functional equation is rewritten in a simplified form that reduces its computational cost. Furthermore, we prove an approximate functional equation for the fractional derivative of the Lerch zeta function.Institute of Biosciences Letters and Exact Sciences São Paulo State University (UNESP), Rua Cristóvão Colombo 2265, SPInstitute of Biosciences Letters and Exact Sciences São Paulo State University (UNESP), Rua Cristóvão Colombo 2265, SPUniversidade Estadual Paulista (UNESP)Guariglia, Emanuel [UNESP]2023-03-01T19:51:34Z2023-03-01T19:51:34Z2022-06-01info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articlehttp://dx.doi.org/10.1007/s00009-021-01971-7Mediterranean Journal of Mathematics, v. 19, n. 3, 2022.1660-54541660-5446http://hdl.handle.net/11449/23987910.1007/s00009-021-01971-72-s2.0-85128193784Scopusreponame:Repositório Institucional da UNESPinstname:Universidade Estadual Paulista (UNESP)instacron:UNESPengMediterranean Journal of Mathematicsinfo:eu-repo/semantics/openAccess2023-03-01T19:51:34Zoai:repositorio.unesp.br:11449/239879Repositório InstitucionalPUBhttp://repositorio.unesp.br/oai/requestopendoar:29462024-08-05T21:08:59.741083Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP)false
dc.title.none.fl_str_mv Fractional Calculus of the Lerch Zeta Function
title Fractional Calculus of the Lerch Zeta Function
spellingShingle Fractional Calculus of the Lerch Zeta Function
Guariglia, Emanuel [UNESP]
computational cost
functional equation
generalized Leibniz rule
Grünwald–Letnikov fractional derivative
Lerch zeta function
title_short Fractional Calculus of the Lerch Zeta Function
title_full Fractional Calculus of the Lerch Zeta Function
title_fullStr Fractional Calculus of the Lerch Zeta Function
title_full_unstemmed Fractional Calculus of the Lerch Zeta Function
title_sort Fractional Calculus of the Lerch Zeta Function
author Guariglia, Emanuel [UNESP]
author_facet Guariglia, Emanuel [UNESP]
author_role author
dc.contributor.none.fl_str_mv Universidade Estadual Paulista (UNESP)
dc.contributor.author.fl_str_mv Guariglia, Emanuel [UNESP]
dc.subject.por.fl_str_mv computational cost
functional equation
generalized Leibniz rule
Grünwald–Letnikov fractional derivative
Lerch zeta function
topic computational cost
functional equation
generalized Leibniz rule
Grünwald–Letnikov fractional derivative
Lerch zeta function
description This paper deals with the fractional derivative of the Lerch zeta function. We compute the fractional derivative of the Lerch zeta function using a complex generalization of the Grünwald–Letnikov derivative. This definition of fractional derivative, fulfilling the generalized Leibniz rule, allows us to derive a functional equation for the fractional derivative of the Lerch zeta function. This functional equation is rewritten in a simplified form that reduces its computational cost. Furthermore, we prove an approximate functional equation for the fractional derivative of the Lerch zeta function.
publishDate 2022
dc.date.none.fl_str_mv 2022-06-01
2023-03-01T19:51:34Z
2023-03-01T19:51:34Z
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
dc.type.driver.fl_str_mv info:eu-repo/semantics/article
format article
status_str publishedVersion
dc.identifier.uri.fl_str_mv http://dx.doi.org/10.1007/s00009-021-01971-7
Mediterranean Journal of Mathematics, v. 19, n. 3, 2022.
1660-5454
1660-5446
http://hdl.handle.net/11449/239879
10.1007/s00009-021-01971-7
2-s2.0-85128193784
url http://dx.doi.org/10.1007/s00009-021-01971-7
http://hdl.handle.net/11449/239879
identifier_str_mv Mediterranean Journal of Mathematics, v. 19, n. 3, 2022.
1660-5454
1660-5446
10.1007/s00009-021-01971-7
2-s2.0-85128193784
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv Mediterranean Journal of Mathematics
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.source.none.fl_str_mv Scopus
reponame:Repositório Institucional da UNESP
instname:Universidade Estadual Paulista (UNESP)
instacron:UNESP
instname_str Universidade Estadual Paulista (UNESP)
instacron_str UNESP
institution UNESP
reponame_str Repositório Institucional da UNESP
collection Repositório Institucional da UNESP
repository.name.fl_str_mv Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP)
repository.mail.fl_str_mv
_version_ 1808129291317149696

Registros relacionados