I just got SUM(N/(%E^(2*SQRT(11)*%PI*N)-1),N,1,INF) = -SQRT(22^(1/3)*(2733*SQRT(33)+624899)^(1/3)+22^(1/3)*(624899-2733*SQRT(33))^(1/3)+240)*GAMMA(1/22)*GAMMA(3/22)*GAMMA(5/22)*GAMMA(9/22)*GAMMA(15/22)/(8448*SQRT(11)*%PI^(7/2))-1/(8*SQRT(11)*%PI)+1/24 inf ==== \ n 1/3
---------------------- = - sqrt(22 / 2 sqrt(11) %pi n ==== %e - 1 n = 1
1/3 1/3 1/3 (2733 sqrt(33) + 624899) + 22 (624899 - 2733 sqrt(33)) 1 3 5 9 15 + 240) gamma(--) gamma(--) gamma(--) gamma(--) gamma(--) 22 22 22 22 22 7/2 1 1 /(8448 sqrt(11) %pi ) - -------------- + -- 8 sqrt(11) %pi 24 and closed forms for eta(exp(-2 sqrt(11)pi)) and eta(exp(-2 sqrt(19)pi)). The logderivative sum needs another hour's work. Working toward sqrt(163)pi. --rwg