Fractional calculus, zeta functions and Shannon entropy

Detalhes bibliográficos
Autor(a) principal: Guariglia, Emanuel [UNESP]
Data de Publicação: 2021
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Institucional da UNESP
Texto Completo: http://dx.doi.org/10.1515/math-2021-0010
http://hdl.handle.net/11449/206373
Resumo: This paper deals with the fractional calculus of zeta functions. In particular, the study is focused on the Hurwitz ζ \zeta function. All the results are based on the complex generalization of the Grünwald-Letnikov fractional derivative. We state and prove the functional equation together with an integral representation by Bernoulli numbers. Moreover, we treat an application in terms of Shannon entropy.
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spelling Fractional calculus, zeta functions and Shannon entropyBernoulli numbersfractional derivativefunctional equationHurwitz ζ functionShannon entropyThis paper deals with the fractional calculus of zeta functions. In particular, the study is focused on the Hurwitz ζ \zeta function. All the results are based on the complex generalization of the Grünwald-Letnikov fractional derivative. We state and prove the functional equation together with an integral representation by Bernoulli numbers. Moreover, we treat an application in terms of Shannon entropy.Institute of Biosciences Letters and Exact Sciences São Paulo State University (UNESP), Rua Cristóvão Colombo 2265Institute of Biosciences Letters and Exact Sciences São Paulo State University (UNESP), Rua Cristóvão Colombo 2265Universidade Estadual Paulista (Unesp)Guariglia, Emanuel [UNESP]2021-06-25T10:30:57Z2021-06-25T10:30:57Z2021-01-01info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/article87-100http://dx.doi.org/10.1515/math-2021-0010Open Mathematics, v. 19, n. 1, p. 87-100, 2021.2391-5455http://hdl.handle.net/11449/20637310.1515/math-2021-00102-s2.0-85106314924Scopusreponame:Repositório Institucional da UNESPinstname:Universidade Estadual Paulista (UNESP)instacron:UNESPengOpen Mathematicsinfo:eu-repo/semantics/openAccess2021-10-23T04:23:53Zoai:repositorio.unesp.br:11449/206373Repositório InstitucionalPUBhttp://repositorio.unesp.br/oai/requestopendoar:29462024-08-05T21:00:01.147993Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP)false
dc.title.none.fl_str_mv Fractional calculus, zeta functions and Shannon entropy
title Fractional calculus, zeta functions and Shannon entropy
spellingShingle Fractional calculus, zeta functions and Shannon entropy
Guariglia, Emanuel [UNESP]
Bernoulli numbers
fractional derivative
functional equation
Hurwitz ζ function
Shannon entropy
title_short Fractional calculus, zeta functions and Shannon entropy
title_full Fractional calculus, zeta functions and Shannon entropy
title_fullStr Fractional calculus, zeta functions and Shannon entropy
title_full_unstemmed Fractional calculus, zeta functions and Shannon entropy
title_sort Fractional calculus, zeta functions and Shannon entropy
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 Bernoulli numbers
fractional derivative
functional equation
Hurwitz ζ function
Shannon entropy
topic Bernoulli numbers
fractional derivative
functional equation
Hurwitz ζ function
Shannon entropy
description This paper deals with the fractional calculus of zeta functions. In particular, the study is focused on the Hurwitz ζ \zeta function. All the results are based on the complex generalization of the Grünwald-Letnikov fractional derivative. We state and prove the functional equation together with an integral representation by Bernoulli numbers. Moreover, we treat an application in terms of Shannon entropy.
publishDate 2021
dc.date.none.fl_str_mv 2021-06-25T10:30:57Z
2021-06-25T10:30:57Z
2021-01-01
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/10.1515/math-2021-0010
Open Mathematics, v. 19, n. 1, p. 87-100, 2021.
2391-5455
http://hdl.handle.net/11449/206373
10.1515/math-2021-0010
2-s2.0-85106314924
url http://dx.doi.org/10.1515/math-2021-0010
http://hdl.handle.net/11449/206373
identifier_str_mv Open Mathematics, v. 19, n. 1, p. 87-100, 2021.
2391-5455
10.1515/math-2021-0010
2-s2.0-85106314924
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv Open Mathematics
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv 87-100
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_ 1808129271750721536

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