Catalan's constant

Catalan's constant is $$G=\displaystyle\sum_{k=0}^{\infty} \dfrac{(-1)^k}{(2k+1)^2} = 0.915 965 594 177 219 015 054 603 514 932 384 110 774 \ldots.$$ This means that Catalan's constant can be expressed as $\beta(2)$ where $\beta$ is the Dirichlet beta function.

Properties

Proposition: The following formula holds: $$K=\beta(2),$$ where $K$ is Catalan's constant and $\beta$ denotes the Dirichlet beta function. where

Proof: proof goes here █