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.accessioned2021-04-30T17:07:20Z
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.citationNOTES ON NUMBER THEORY AND DISCRETE MATHEMATICS,Vol.26,107-134,2020
dc.identifier.doi10.7546/nntdm.2020.26.3.107-134
dc.identifier.urihttp://repositoriodigital.uct.cl/handle/10925/4105
dc.language.isoen
dc.publisherBULGARIAN ACAD SCIENCE
dc.sourceNOTES ON NUMBER THEORY AND DISCRETE MATHEMATICS
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.typeArticle
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