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arXiv · 2603.29998

Some geometric series for Euler's constant

Jean-François Burnol
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Abstract

We provide representations of Euler's constant $\gamma=0.577...$ 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-Erd\'elyi asymptotic expansion of the ratio of two Gamma functions, is established for that purpose.

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Jean-François Burnol. 2026-03-31. Some geometric series for Euler's constant. https://arxiv.org/abs/2603.29998

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