Catalan's constant

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