Fractional calculus, zeta functions and Shannon entropy
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Data
2021-01-01
Autores
Guariglia, Emanuel [UNESP]
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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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Bernoulli numbers, fractional derivative, functional equation, Hurwitz ζ function, Shannon entropy
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Open Mathematics, v. 19, n. 1, p. 87-100, 2021.