OFFSET
1,8
LINKS
Daniel Schultz, Cubic theta functions. Adv. Math. 248, 618-697 (2013). p. 72.
Eric Weisstein's MathWorld, Dedekind Eta Function
Wikipedia, Dedekind eta function
FORMULA
theta_3(tau) = eta(tau/3)^3 + 3*eta(3*tau)^3)/eta(tau), where 'eta' is the Dedekind eta modular elliptic function.
theta_3(7*i/sqrt(7)) = (sqrt((1/2)*(5 + sqrt(21))*sqrt((1/2)*(sqrt(3) + sqrt(7))) + 3^(7/4)/2)*Gamma(1/7)*Gamma(2/7)*Gamma(4/7))/(2^(5/2)*3^(1/8)*7^(1/4)*Pi^2) .
EXAMPLE
1.0000003618680136055734464581211946734487733839572780170205672760474...
MATHEMATICA
(Sqrt[(1/2)*(5 + Sqrt[21])*Sqrt[(1/2)*(Sqrt[3] + Sqrt[7])] + 3^(7/4)/2] * Gamma[1/7] * Gamma[2/7] * Gamma[4/7])/(2^(5/2)*3^(1/8)*7^(1/4)*Pi^2) // RealDigits[#, 10, 105]& // First
CROSSREFS
KEYWORD
AUTHOR
Jean-François Alcover, Jun 29 2015
STATUS
approved