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An Infinite Family of Apéry-like Recurrences for Euler's Constant
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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BibTeX
@misc{kalisch2026infinite,
title = {{An Infinite Family of Apéry-like Recurrences for Euler's Constant}},
author = {Rotem Kalisch and Tali Monderer and Elyasheev Leibtag and Shachar Weinbaum and Michael Shalyt and Ido Kaminer},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.13919},
eprint = {2610.13919},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.13919},
}
RIS
TY - UNPB
TI - An Infinite Family of Apéry-like Recurrences for Euler's Constant
AU - Rotem Kalisch
AU - Tali Monderer
AU - Elyasheev Leibtag
AU - Shachar Weinbaum
AU - Michael Shalyt
AU - Ido Kaminer
PY - 2026
DA - 2026/10/09
PB - arXiv
DO - 10.48550/arxiv.2610.13919
UR - https://arxiv.org/abs/2610.13919
AB - 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.
ER -