A note on the finitization of Abelian and Tauberian theorems

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Abstract

We present finitary formulations of two well known results concerning infinite series, namely Abel's theorem, which establishes that if a series converges to some limit then its Abel sum converges to the same limit, and Tauber's theorem, which presents a simple condition under which the converse holds. Our approach is inspired by proof theory, and in particular Gödel's functional interpretation, which we use to establish quantitative versions of both of these results.

Original languageEnglish
Pages (from-to)300-310
Number of pages11
JournalMathematical Logic Quarterly
Volume66
Issue number3
Early online date28 Sep 2020
DOIs
Publication statusPublished - 7 Oct 2020

ASJC Scopus subject areas

  • Logic

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