A note on the finitization of Abelian and Tauberian theorems
Logic
2019-10-18 v1
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 G\"{o}del's functional interpretation, which we use to establish quantitative version of both of these results.
Keywords
Cite
@article{arxiv.1910.07926,
title = {A note on the finitization of Abelian and Tauberian theorems},
author = {Thomas Powell},
journal= {arXiv preprint arXiv:1910.07926},
year = {2019}
}