Catalan's constant

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

Properties

Catalan's constant using Dirichlet beta
Catalan's constant using Legendre chi
Catalan's constant using Hurwitz zeta