* rwg@sdf.lonestar.org <rwg@sdf.lonestar.org> [Aug 25. 2008 13:37]:
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I repeat my plea: Does anybody know where WRI got those valuations of DedekindEta[I] and DedekindEta'[I] that made this all possible? --rwg
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My suggestion in the other mail seems to work (indeed without the eta-plus detour): You need formula 31.1-10a on p.628 of http://www.jjj.de/fxt/#fxtbook (note my eta(q) is defined as prod(n=1,infty, 1-q^n)) and the evaluation of K(k_4) at http://mathworld.wolfram.com/EllipticIntegralSingularValue.html Attached a script, remains to show algebraically that 2^(-5/12) *k^(1/12)*kp^(1/3) * (sqrt(2)+1)^(1/2) == 1 The other evaluations K(k_n) on Eric's page will give you more eta-evaluations, but likely more complicated expressions. I suggest to try k_3 first. Is there a reason that all K(k_n) with n a square only involve gamma(1/4)?