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.26,107-134,2020
datacite.alternateIdentifier.doi10.7546/nntdm.2020.26.3.107-134
datacite.creatorSoria-Lorente, Anier
datacite.creatorBerres, Stefan
datacite.date2020
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.accessioned2021-04-30T17:07:20Z
dc.date.available2021-04-30T17:07:20Z
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/10925/4105
dc.language.isoen
dc.publisherBULGARIAN ACAD SCIENCE
dc.sourceNOTES ON NUMBER THEORY AND DISCRETE MATHEMATICS
oaire.resourceTypeArticle
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uct.indizacionESCI
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