25 Jul
2009
25 Jul
'09
12:35 a.m.
It seems that when x = pi sqrt(rational), (sum(n/(%e^(n*x)-1),n,1,inf)+1/(4*x)-1/24)/eta(%e^-x)^4 inf ==== \ n 1 1 > -------- + --- - -- / n x 4 x 24 ==== e - 1 n = 1 -------------------------- 4 -x eta (e ) is algebraic, but disappointingly messy (sqrt cubic surd) for rational = Beegner > 7, as you can judge by the rational = 44 case in http://gosper.org/nuetas.html . Rational = 11 isn't much better. --rwg