A single parameter Hermite-Pade series representation for Apery's constant

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dc.contributor.authorSoria Lorente, Anier
dc.contributor.authorBerres, Stefan
dc.date2020
dc.date.accessioned2021-10-04T17:39:45Z
dc.date.available2021-10-04T17:39:45Z
dc.description.abstractInspired by the results of Rhin and Viola (2001), the purpose of this work is to elaborate on a series representation for zeta (3) which only depends on one single integer parameter. This is accomplished by deducing a Hermite-Pade approximation problem using ideas of Sorokin (1998). As a consequence we get a new recurrence relation for the approximation of zeta (3) as well as a corresponding new continued fraction expansion for zeta (3), which do no reproduce Apery's phenomenon, i.e., though the approaches are different, they lead to the same sequence of Diophantine approximations to zeta (3). Finally, the convergence rates of several series representations of zeta (3) are compared.
dc.description.versionPreprint
dc.identifier.citationNotes on Number Theory and Discrete Mathematics, Vol.26, N°3, 1-32, 2020
dc.identifier.doi10.7546/nntdm.2020.26.3.107-134
dc.identifier.urihttp://repositoriodigital.uct.cl/handle/10925/4210
dc.language.isoen
dc.publisherThe Publishing House of Bulgarian Academy of Sciences
dc.rightsObra bajo licencia Creative Commons Atribución 4.0 Internacional
dc.sourceNotes on Number Theory and Discrete Mathematics (Bulgaria)
dc.subjectConstante de Apéry
dc.subjectFunción zeta de Riemann
dc.subject.englishRiemann zeta function
dc.subject.englishApery's theorem
dc.subject.englishHermite-Pade approximation problem
dc.subject.englishRecurrence relation
dc.subject.englishContinued fraction expansion
dc.subject.englishSeries representation
dc.titleA single parameter Hermite-Pade series representation for Apery's constant
dc.typeArtículo de Revista
uct.catalogadorbmc
uct.comunidadIngeniería
uct.facultadFacultad de Ingeniería
uct.indizacionESCI
uct.indizacionCrossRef
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