A single parameter Hermite-Pade series representation for Apery's constant
A single parameter Hermite-Pade series representation for Apery's constant
Authors
Soria-Lorente, Anier
Berres, Stefan
Berres, Stefan
Profesor GuĆa
Authors
Date
Datos de publicaciĆ³n:
10.7546/nntdm.2020.26.3.107-134
NOTES ON NUMBER THEORY AND DISCRETE MATHEMATICS,Vol.26,107-134,2020
NOTES ON NUMBER THEORY AND DISCRETE MATHEMATICS,Vol.26,107-134,2020
Tipo de recurso
Article
Keywords
Materia geogrƔfica
Collections
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.