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%I #5 Jun 29 2015 10:23:37
%S 1,0,0,0,0,0,0,3,6,1,8,6,8,0,1,3,6,0,5,5,7,3,4,4,6,4,5,8,1,2,1,1,9,4,
%T 6,7,3,4,4,8,7,7,3,3,8,3,9,5,7,2,7,8,0,1,7,0,2,0,5,6,7,2,7,6,0,4,7,4,
%U 0,0,1,8,0,1,0,1,9,6,2,5,1,3,8,1,1,6,7,5,4,5,6,8,9,8,5,5,2,9,5,2,4,7,8,2,1
%N Decimal expansion of theta_3(7*i/sqrt(7)), an explicit particular value of the cubic theta function theta_3.
%H Daniel Schultz, <a href="http://dx.doi.org/10.1016/j.aim.2013.08.021">Cubic theta functions.</a> Adv. Math. 248, 618-697 (2013). p. 72.
%H Eric Weisstein's MathWorld, <a href="http://mathworld.wolfram.com/DedekindEtaFunction.html">Dedekind Eta Function</a>
%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Dedekind_eta_function">Dedekind eta function</a>
%F theta_3(tau) = eta(tau/3)^3 + 3*eta(3*tau)^3)/eta(tau), where 'eta' is the Dedekind eta modular elliptic function.
%F 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) .
%e 1.0000003618680136055734464581211946734487733839572780170205672760474...
%t (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
%Y Cf. A259498, A259499, A259500.
%K nonn,cons,easy
%O 1,8
%A _Jean-François Alcover_, Jun 29 2015
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