A Beautiful Double Sum from @infseriesbot
I saw this beautiful result below and gave it a try, here is my solution: After partial fraction decomposition Recall Digamma´s integral representation We get Now, recall integral representation of the Dilogarithm function Swapping order of integration Change variable Now use the fact that for Corollary We have shown right in the beginning of the proof that The integral on the RHS of the equation above is an integral representation of , the harmonic number.Therefore we may right and we conclude that Apendix Proof that Recall the series representation of the digamma function derived from the Weierstrass infinite product of the gamma function Proof that Proof that L...