Some geometric series for Euler's constant

Fuente: arXiv
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Main Author: Burnol, Jean-François
Format: Preprint
Published: 2026
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_version_ 1866918534844514304
author Burnol, Jean-François
author_facet Burnol, Jean-François
contents We provide representations of Euler's constant $γ=0.577...$ as series which converge geometrically fast (but use a certain sequence whose computation induces a quadratic cost). The asymptotic oscillations of these coefficients are determined to all orders. A result of independent interest, about sufficient conditions for the validity, in the case of unbounded parameters, for the Tricomi-Erdélyi asymptotic expansion of the ratio of two Gamma functions, is established for that purpose.
format Preprint
id arxiv_https___arxiv_org_abs_2603_29998
institution arXiv
publishDate 2026
record_format arxiv
spellingShingle Some geometric series for Euler's constant
Burnol, Jean-François
Number Theory
Combinatorics
11Y60, 11B83, 33B15, 41A60 (Primary) 05A16, 11B68, 11M41, 30E15, 60C05 (Secondary)
We provide representations of Euler's constant $γ=0.577...$ as series which converge geometrically fast (but use a certain sequence whose computation induces a quadratic cost). The asymptotic oscillations of these coefficients are determined to all orders. A result of independent interest, about sufficient conditions for the validity, in the case of unbounded parameters, for the Tricomi-Erdélyi asymptotic expansion of the ratio of two Gamma functions, is established for that purpose.
title Some geometric series for Euler's constant
topic Number Theory
Combinatorics
11Y60, 11B83, 33B15, 41A60 (Primary) 05A16, 11B68, 11M41, 30E15, 60C05 (Secondary)
url https://arxiv.org/abs/2603.29998