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arXiv · 2610.13919

An Infinite Family of Apéry-like Recurrences for Euler's Constant

Rotem Kalisch·Tali Monderer·Elyasheev Leibtag·Shachar Weinbaum·Michael Shalyt·Ido Kaminer
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Abstract

Euler's constant $γ$, also known as the Euler-Mascheroni constant, remains one of the most elusive constants in mathematics. Despite extensive study, its irrationality is still unproven, and Apéry-like approximations of it are remarkably scarce. We present a novel identity that expresses $γ$ in terms of a Meijer G-function and its first few derivatives. This identity is then generalized and used to systematically generate infinitely many Apéry-like approximations of $γ$ using a Conservative Matrix Field construction based on the Meijer G-function.

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Rotem Kalisch, Tali Monderer, Elyasheev Leibtag, Shachar Weinbaum, Michael Shalyt, Ido Kaminer. 2026-10-09. An Infinite Family of Apéry-like Recurrences for Euler's Constant. https://arxiv.org/abs/2610.13919

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