Catalan's constant is irrational (proof with the help of AI)

Mathematics > General Mathematics

Title:Catalan's constant is irrational

View PDF HTML (experimental)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.

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