OFFSET
1,2
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(i/sqrt(5)) = sqrt((1/6)*(sqrt(3)-1)*(4 + sqrt(3) + 3*sqrt(5))*Gamma(1/20)*Gamma(3/20)*Gamma(7/20)*Gamma(9/20))/(4*Pi^(3/2)).
EXAMPLE
1.36264523128736336628536293370204672389798024012253482799316167682847...
MATHEMATICA
Sqrt[(1/6)*(Sqrt[3]-1)*(4 + Sqrt[3] + 3*Sqrt[5]) * Gamma[1/20] * Gamma[3/20] * Gamma[7/20] * Gamma[9/20]]/(4*Pi^(3/2)) // RealDigits[#, 10, 105]& // First
CROSSREFS
KEYWORD
AUTHOR
Jean-François Alcover, Jun 29 2015
STATUS
approved