In http://arxiv.org/abs/math/0212035, Alan Sokal (of Social Text infamy) uses (q;q)_oo ~ e^(pi^2/ln q). Far closer (1% for -.23<q<1): li (sqrt(q)) 2 ------------ log(q) %e (q; q) = ----------------- inf 1 ---------------- 1 24 (------- - 1) sqrt(q) q Note the strange whiff of q^(1/24) even though it wasn't in the product. Mma draws a nice lily pad for ParametricPlot3D[{r*Cos[\[Theta]], r*Sin[\[Theta]], Abs[DedekindEta[Log[q]/2/I/Pi]/q^(1/24) - E^(PolyLog[2, Sqrt[q]]/Log[q] + Log[q]/24/(1 - 1/Sqrt[q])) /. q -> r*E^(I*\[Theta])]}, {r, .01, .99}, {\[Theta], 0, 2Pi}] (Mma defines DedekindEta[tau], not [q].) --rwg GASOLINIC LOGICIANS