rwg>Mike Hirschhorn privately remarked that the QPochhammer reflection formula can't be new. I agree, and conjecture that B(asic)H(ypergeometric)S(eries) omitted it to skirt the gigantic subject of theta functions. Partial retraction: Theta functions seem to be mentioned on p12 (only), as applications of the triple product identity (p11) in converting the series definitions of thetas into products, with z -> e^(i t). But ------ rwg>(q shifted factorial [reflection formula], 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 ------ is really just the triple product identity! --rwg INTERMESHES SMITHEREENS