Paper
Catalan's constant is irrational
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. · Authors: Zhi-Wei Sun · Published 2026-09-03 · arXiv:2609.04176
- Published
- 2026-09-03
- Authors
- 1
- arXiv
- 2609.04176
- Category
- math.GM
Abstract
arXiv:2609.04176
Zhi-Wei Sun
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.