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Catalan's constant is irrational
Abstract
Whether the constant G=∑k=0∞((−1)k)/((2k+1)2)=1/12−1/32+1/52−1/72+⋯ introduced by Catalan in the nineteen century is irrational, is a long-standing open problem. In this paper we prove the irrationality of G via using suitable weights.
Related
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BibTeX
@misc{sun2026catalans,
title = {{Catalan's constant is irrational}},
author = {Zhi-Wei Sun},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.04176},
eprint = {2609.04176},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.04176},
}
RIS
TY - UNPB
TI - Catalan's constant is irrational
AU - Zhi-Wei Sun
PY - 2026
DA - 2026/09/03
PB - arXiv
DO - 10.48550/arxiv.2609.04176
UR - https://arxiv.org/abs/2609.04176
AB - Whether the constant G=∑_k=0^∞((−1)^k)/((2k+1)^2)=1/1^2−1/3^2+1/5^2−1/7^2+⋯ introduced by Catalan in the nineteen century is irrational, is a long-standing open problem. In this paper we prove the irrationality of G via using suitable weights.
ER -