hello, I just found this formula for Catalan constant , is this known ? /infinity \ /infinity \ | ----- | | ----- | | \ 1 | | \ 1 | 11 | ) -------------------| - 71/2 | ) ---------------------| | / 2 | | / 2 | | ----- n (cosh(Pi n) - 1)| | ----- n (cosh(2 Pi n) - 1)| \ n = 1 / \ n = 1 / /infinity \ | ----- | | \ 1 | + 11 | ) ---------------------| | / 2 | | ----- n (cosh(4 Pi n) - 1)| \ n = 1 / gives : 11*Sum(1/n^2/(cosh(Pi*n)-1),n = 1 .. infinity)-71/2*Sum(1/n^2/(cosh(2*Pi*n)-1), n = 1 .. infinity)+11*Sum(1/n^2/(cosh(4*Pi*n)-1),n = 1 .. infinity) when lprinted and evalf(%) gives : 0.91596559417721901505460351493238411077414937428167213426649811962176301977\ 625476947935651292611510624857442261919619957903589881... I think it is valid, one thing I know : I never saw it before. if I am not mistaking, that formula can be used to compute catalan constant to a high precision. I have others that are of interest here : http://pictor.math.uqam.ca/~plouffe/inspired3.pdf a html version is available also at http://pictor.math.uqam.ca/~plouffe/ see the middle of the page some of the text is in french but formulas are in universal language with <sigma> of course, this is a draft of course. some findings are related to Eisenstein series, that I find simpler to grasp in some way. ah yes, I have also found a generalization of Ramanujan formula for rational arguments, as you will see in the documents, instead of having only the cases with 4n+1 there is now a general formula for all odd index as you will see. bonne lecture, simon plouffe