I didn't realize we could do these. Sum[Csch[n*x]^2, {n, 1, Infinity}] == 1/6 + Derivative[0, 1, 0][EllipticThetaPrime][1, Pi/3, E^(-x/3)]/ (6*Sqrt[3]*DedekindEta[(I*x)/Pi]) Mma doesn't realize it either: In[517]:= % /. x -> 1/2 Out[517]= False Yet In[518]:= List @@ %% /. x -> 1/2 Out[518]= {4 (-1 + QPolyGamma[1, 1, Sqrt[E]] + QPolyGamma[1, 1 - 2 I Pi, Sqrt[E]]), (0,1,0) Pi 1 EllipticThetaPrime [1, --, ----] 3 1/6 1 E - + --------------------------------------} 6 I 6 Sqrt[3] DedekindEta[----] 2 Pi In[519]:= N[%, 33] Out[519]= {4.74640293405957128234200051279399 + 0.*10^-35 I, 4.74640293405957128234200051279836} --rwg