Some geometric series for Euler's constant
Number Theory
2026-05-18 v4 Combinatorics
Abstract
We provide representations of Euler's constant as series which converge geometrically fast (but use coefficients whose computation induces a quadratic cost). The asymptotic oscillations of these coefficients are discussed.
Cite
@article{arxiv.2603.29998,
title = {Some geometric series for Euler's constant},
author = {Jean-François Burnol},
journal= {arXiv preprint arXiv:2603.29998},
year = {2026}
}
Comments
20 pages, 2 figures. The e_m's appeared decades ago in theoretical computer science. This version obtains O(1/m) for the error bound in their asymptotic