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%I #5 Jun 29 2015 10:24:01
%S 1,5,6,3,4,6,8,0,9,4,3,2,7,9,0,0,5,5,2,0,4,9,9,5,8,9,2,4,0,8,9,3,0,0,
%T 9,4,0,6,7,5,1,2,6,0,0,1,8,7,6,7,4,1,2,6,9,7,2,4,1,6,5,3,3,5,1,9,1,6,
%U 9,3,3,4,3,7,1,5,9,0,9,7,0,0,2,2,5,5,3,0,2,1,0,4,3,0,2,6,2,5,6,2,8,3,7,6,1
%N Decimal expansion of theta_3(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(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 1.56346809432790055204995892408930094067512600187674126972416533519...
%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, A259501.
%K nonn,cons,easy
%O 1,2
%A _Jean-François Alcover_, Jun 29 2015
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