Hello, I think all rational values are feasible in terms of the Gamma function : let me explain, since the rhs of sum(1/n/(exp(Pi*n*a/b)-1),n=1..infinity) = a product of gammas, then by taking the log we should get a linear combination of log(GAMMA(p/q)), p and q being well chosen, The main difficulty is that for small a/b like 2/7 then the degree of the algebraic portion of the gamma's could be of a very high degree, that does mean : p and q have to be chosen in a wide range of values, so even with PSLQ, LLL (the one you like most) it won't give the general solution but only small and easy cases. already with the case of 2/7 computed by Bill Gosper, is already of a fairly high degree, at least 28 ? Also, a technical detail : the sum is something like 1+ 240 *something, of course the <1> has to be removed before taking the log, if not : it won't work, it has to be a pure product of GAMMA(p/q) values. In other words for values like 2/13, or foolishly 2/163 that one is just plain impossible to get with that method in my opinion. also, (to bill gosper), I will change my home page to include your formula for 2/7 and if there is enough place the case 2/13 as well. I am preparing a paper about that , it should come out soon, and with proper credit of course, best regards, simon plouffe