I plotted Dan's function S(x) = x - x^2 + x^4 - x^8 + x^16 ... for x near 1. To get a nice scaling, I did S(1-exp(-x)). It looks periodic: sinusoidal oscillations, 0.500 +- 0.003, period 1.39 ?=? 2 log(2). Maple bombs at x=37.5, so the plots end there. Then I tried f(1-exp(-x)) with f(x) = 1 - x + x^2! - x^3! + x^4! ... Again oscillating, but with increasing amplitude and period. Amplitude was 0.5 +- 0.3 when Maple bombed, and period was 5.6. Is there a theory for such functions that explains their values near x = 1 or elsewhere on the natural boundary, in analogy to the theory for modular functions? Gene __________________________________ Do you Yahoo!? Yahoo! Mail - Find what you need with new enhanced search. http://info.mail.yahoo.com/mail_250