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

 dc.contributor.author Soria-Lorente, Anier dc.contributor.author Berres, Stefan dc.date 2020 dc.date.accessioned 2021-04-30T17:07:20Z dc.date.available 2021-04-30T17:07:20Z dc.description.abstract Inspired 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.citation NOTES ON NUMBER THEORY AND DISCRETE MATHEMATICS,Vol.26,107-134,2020 dc.identifier.doi 10.7546/nntdm.2020.26.3.107-134 dc.identifier.uri http://repositoriodigital.uct.cl/handle/10925/4105 dc.language.iso en dc.publisher BULGARIAN ACAD SCIENCE dc.source NOTES ON NUMBER THEORY AND DISCRETE MATHEMATICS dc.subject.english Riemann zeta function dc.subject.english Apery's theorem dc.subject.english Hermite-Pade approximation problem dc.subject.english Recurrence relation dc.subject.english Continued fraction expansion dc.subject.english Series representation dc.title A single parameter Hermite-Pade series representation for Apery's constant dc.type Article uct.catalogador WOS uct.indizacion ESCI