(q shifted factorial, for penciling in to Appendix I of your BHS): %i log(z) %i sqrt(z) theta (---------, sqrt(q)) 1 2 (z; q) = ------------------------------------- = inf q 1/8 (q, -; q) q z inf 2 2 log (z) 2 %pi - -------- ------ 2 %pi z 2 log(q) %pi log(z) log(q) sqrt(- -------) %e theta (----------, %e ) log(q) 1 log(q) --------------------------------------------------------- . q 1/8 (q, -; q) q z inf (q/z;q) might sometimes be easier to compute than (z;q), e.g. for |q| near 1. Theta[1] and (q;q) (which is also a Theta[1]) are relatively easier. --rwg