OFFSET
1,7
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(5*i/sqrt(5)) = sqrt((1/30)*(1 + 3*sqrt(3) + 3*(sqrt(5) + sqrt(15)))*Gamma(1/20)*Gamma(3/20)*Gamma(7/20)*Gamma(9/20))/(4*Pi^(3/2)).
EXAMPLE
1.00000474760635187188637766879472447144246277056540611713536529453...
MATHEMATICA
Sqrt[(1/30)*(1 + 3*Sqrt[3] + 3*(Sqrt[5] + Sqrt[15])) * Gamma[1/20] * Gamma[3/20] * Gamma[7/20] * Gamma[9/20]]/(4*Pi^(3/2)) // RealDigits[#, 10, 104]& // First
PROG
(PARI) sqrt((1/30)*(1 + 3*sqrt(3) + 3*(sqrt(5) + sqrt(15)))*gamma(1/20)*gamma(3/20)*gamma(7/20)*gamma(9/20))/(4*Pi^(3/2)) \\ Michel Marcus, Jun 29 2015
CROSSREFS
KEYWORD
AUTHOR
Jean-François Alcover, Jun 29 2015
STATUS
approved