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

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datacite.alternateIdentifier.citationNotes on Number Theory and Discrete Mathematics, Vol.26, N°3, 1-32, 2020
datacite.alternateIdentifier.doi10.7546/nntdm.2020.26.3.107-134
datacite.creatorSoria Lorente, Anier
datacite.creatorBerres, Stefan
datacite.date2020
datacite.subjectConstante de Apéry
datacite.subjectFunción zeta de Riemann
datacite.subject.englishRiemann zeta function
datacite.subject.englishApery's theorem
datacite.subject.englishHermite-Pade approximation problem
datacite.subject.englishRecurrence relation
datacite.subject.englishContinued fraction expansion
datacite.subject.englishSeries representation
datacite.titleA single parameter Hermite-Pade series representation for Apery's constant
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.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)
oaire.resourceTypeArtículo de Revista
oaire.versionPreprint
uct.catalogadorbmc
uct.comunidadIngeniería
uct.facultadFacultad de Ingeniería
uct.indizacionESCI
uct.indizacionCrossRef
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