Hello, about the '1' that appears in the formulas : there is a bunch of formulas for 0 too, that explains why I do not have it for 1. If you look closely to the formulas for 1, these formulas are the Eisenstein series reformulated, since the exponent 5, 9,13 where already known I looked for formulas for 3,7,11,15... actualy there are formulas for them BUT it uses 2 arguments instead of 1 : the coefficients are the SAME as the ones for eisenstein series, the trick is to see these formulas as particular Lambert series with the x replaced by exp(pi). Also, I find it really fascinating that I can find one formula for Pi and 1/Pi, Pi^2 and 1/Pi^2, by reverting the exponent for n. Catalan constant is <b(2)>, there are no formulas for b(4), b(6), etc. These are Dirichlet series, like b(4) = sum((-1)^(n+1)/(2*n+1)^4,n=1..infinity), no formulas for 1/b(4) and 1/b(6) either. one for Catalan but NONE for 1/Catalan, this is strange isn't ? I have tried with sinh, and all sorts of variants to find where was the bug about that : there are none, it seems that 1/Catalan cannot be found using these sums and I can't say or see why. simon plouffe