Jim's latest essay, https://mathenchant.wordpress.com/2016/06/16/sri-ramanujan-and-the-secrets-o... cites https://en.wikipedia.org/wiki/Rogers–Ramanujan_continued_fraction, which says Rogers was first to "discover" the continued fraction with unit denominators and geometrically progressing numerators. Presumably, that means he had the infinite product, but how come nobody noticed the publication of such a startling result? Even less clear from the Wikipedium is whether Rogers knew " It can be evaluated explicitly for a broad class of values of its argument." I.e., (as NeilB had to point out to me), the infinite product can be expressed as an algebraic function of Dedekind etas. The article gives two cases: q = e^(-2π) (the one that startled Hardy) and e^(-2√5π). I wonder what Hardy would have thought of this one: 1 -------------------------------------------------- 4/5 (i - 1) i 1 + ---------------------------------------------- 8/5 (i - 1) i 1 + ------------------------------------------ 12/5 (i - 1) i 1 + -------------------------------------- 16/5 (i - 1) i 1 + ---------------------------------- 4 (i - 1) i 1 + ------------------------------ 24/5 (i - 1) i 1 + -------------------------- . . . 1/4 1 6 5 1/5 (- (-9 + Sqrt[5] + -----------------)) 2 Sqrt[GoldenRatio] = ----------------------------------------- 4/25 (i - 1) i ~ 0.8460733945195074 + 0.2172347253807965 i --rwg