Fractional calculus, zeta functions and Shannon entropy

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 in...

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Autor principal:	Guariglia Emanuel
Formato:	article
Lenguaje:	EN
Publicado:	De Gruyter 2021
Materias:	hurwitz ζ function fractional derivative functional equation bernoulli numbers shannon entropy 11m35 26a33 11b68 34k37 49k99 Mathematics QA1-939
Acceso en línea:	https://doaj.org/article/273f1b236fe041dc9df29eef9db5a373
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id	oai:doaj.org-article:273f1b236fe041dc9df29eef9db5a373
record_format	dspace
spelling	oai:doaj.org-article:273f1b236fe041dc9df29eef9db5a3732021-12-05T14:10:52ZFractional calculus, zeta functions and Shannon entropy2391-545510.1515/math-2021-0010https://doaj.org/article/273f1b236fe041dc9df29eef9db5a3732021-04-01T00:00:00Zhttps://doi.org/10.1515/math-2021-0010https://doaj.org/toc/2391-5455This 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.Guariglia EmanuelDe Gruyterarticlehurwitz ζ functionfractional derivativefunctional equationbernoulli numbersshannon entropy11m3526a3311b6834k3749k99MathematicsQA1-939ENOpen Mathematics, Vol 19, Iss 1, Pp 87-100 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	hurwitz ζ function fractional derivative functional equation bernoulli numbers shannon entropy 11m35 26a33 11b68 34k37 49k99 Mathematics QA1-939
spellingShingle	hurwitz ζ function fractional derivative functional equation bernoulli numbers shannon entropy 11m35 26a33 11b68 34k37 49k99 Mathematics QA1-939 Guariglia Emanuel Fractional calculus, zeta functions and 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.
format	article
author	Guariglia Emanuel
author_facet	Guariglia Emanuel
author_sort	Guariglia Emanuel
title	Fractional calculus, zeta functions and 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
publisher	De Gruyter
publishDate	2021
url	https://doaj.org/article/273f1b236fe041dc9df29eef9db5a373
work_keys_str_mv	AT guarigliaemanuel fractionalcalculuszetafunctionsandshannonentropy
_version_	1718371641217515520

Fractional calculus, zeta functions and Shannon entropy

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