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arXiv · 1910.07926

A note on the finitization of Abelian and Tauberian theorems

Thomas Powell
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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 version of both of these results.

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Thomas Powell. 2019-10-17. A note on the finitization of Abelian and Tauberian theorems. https://arxiv.org/abs/1910.07926

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