Year: 2026
Type: preprint
Abstract: Whether the constant $$G=\sum_{k=0}^\infty\frac{(-1)^k}{(2k+1)^2}=\frac1{1^2}-\frac1{3^2}+\frac1{5^2}-\frac1{7^2}+\cdots$$ 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.
Source: arXiv (Cornell University)
Author: Sun, Zhi-Wei
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7208711918
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