Central Binomial coefficient series and Catalan Constant

In this blog entry we will prove the following result:


\begin{align*}
\sum_{n=0}^\infty \frac{\binom{2n}{n}}{2^{2n}}\frac{\sqrt{2}}{(2n+1)^2}&=G+\frac{\pi\ln(2)}{4}
\end{align*}


Click here for the proof.

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