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A273083 Decimal expansion of theta_3(0, exp(-5*Pi)), where theta_3 is the 3rd Jacobi theta function.

%I A273083 #11 Sep 08 2022 08:46:16
%S A273083 1,0,0,0,0,0,0,3,0,1,4,0,3,4,5,5,0,7,8,0,1,2,9,2,2,1,5,0,6,5,4,9,0,3,
%T A273083 9,0,8,0,8,0,2,2,3,6,1,7,8,9,5,4,9,4,8,6,6,7,3,4,7,7,7,4,3,7,4,8,7,6,
%U A273083 2,8,2,1,3,3,1,0,3,1,5,1,3,9,6,2,7,4,2,8,0,5,8,1,4,3,4,4,2,8,4,2,9,8,5,5,9
%N A273083 Decimal expansion of theta_3(0, exp(-5*Pi)), where theta_3 is the 3rd Jacobi theta function.
%H A273083 G. C. Greubel, <a href="/A273083/b273083.txt">Table of n, a(n) for n = 1..10000</a>
%H A273083 Wikipedia, <a href="http://en.wikipedia.org/wiki/Theta_function#Explicit_values">Theta function</a>
%F A273083 Equals sqrt(2/5 + 1/sqrt(5)) * Pi^(1/4)/Gamma(3/4).
%e A273083 1.0000003014034550780129221506549039080802236178954948667347...
%p A273083 evalf(sqrt(2/5 + 1/sqrt(5)) * Pi^(1/4)/GAMMA(3/4), 120);
%t A273083 RealDigits[EllipticTheta[3, 0, Exp[-5*Pi]], 10, 105][[1]]
%t A273083 RealDigits[Sqrt[2/5 + 1/Sqrt[5]] * Pi^(1/4)/Gamma[3/4], 10, 105][[1]]
%o A273083 (PARI) th3(x)=1 + 2*suminf(n=1,x^n^2)
%o A273083 th3(exp(-5*Pi)) \\ _Charles R Greathouse IV_, Jun 06 2016
%o A273083 (Magma) C<i> := ComplexField(); Sqrt(2/5 + 1/Sqrt(5))*Pi(C)^(1/4)/Gamma(3/4) // _G. C. Greubel_, Jan 07 2018
%Y A273083 Cf. A175573, A247217, A273081, A273082, A273084.
%K A273083 nonn,cons
%O A273083 1,8
%A A273083 _Vaclav Kotesovec_, May 14 2016