Due to fading sensitivity of my "C" key, I inadvertently pasted a Macsyma notebook output section (instead of text) into a Mathematica notebook, and it worked! (I.e., it rendered a bitmap image.) So anyone with an interest in theta functions can now sneak a peek at http://gosper.org/thetpak.html. --rwg Minor correction to couple wk old mail: rwg>The formula I gave [ 2 i n pi -------- i g(n/d) pi d ----------- sqrt(- log(q)) eta(e q) 12 2 pi limit ------------------------------- = e sqrt(----), q -> 1 2 d pi ----------- 2 6 d log(q) e 1 1 g(r) := if integerp(r) then r else - g(---------) - ------------------- mod(r, 1) 2 denom (r) mod(r, 1) + floor(r) + 3 . ]
is good only for 2 |n| < d, n/=0, which is barely enough, with
2 %pi - -------- 6 log(q) eta(q) %e sqrt(- log(q)) -> sqrt(2 %pi),
to describe eta(e^(i t pi)) for rational t.
Actually, we need 2 |n| <= d, which fortunately obtains.