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A273087 Decimal expansion of theta_3(0, exp(-sqrt(2)*Pi)), where theta_3 is the 3rd Jacobi theta function.

%I A273087 #13 Feb 16 2025 08:33:35
%S A273087 1,0,2,3,5,2,3,9,9,9,3,4,1,0,0,5,8,6,3,4,9,7,7,9,8,6,5,6,7,2,4,9,7,1,
%T A273087 8,5,2,5,6,4,9,1,4,6,0,7,9,4,8,7,8,4,7,4,1,8,7,2,1,5,1,9,8,5,8,7,4,1,
%U A273087 3,4,7,9,7,7,6,7,8,4,6,0,3,1,1,1,3,0,2,2,8,5,7,7,4,6,8,7,6,0,1,9,3,3,5,5,0
%N A273087 Decimal expansion of theta_3(0, exp(-sqrt(2)*Pi)), where theta_3 is the 3rd Jacobi theta function.
%H A273087 G. C. Greubel, <a href="/A273087/b273087.txt">Table of n, a(n) for n = 1..5000</a>
%H A273087 Eric Weisstein's MathWorld, <a href="https://mathworld.wolfram.com/JacobiThetaFunctions.html">Jacobi Theta Functions</a>
%H A273087 Wikipedia, <a href="http://en.wikipedia.org/wiki/Theta_function#Explicit_values">Theta function</a>
%F A273087 Equals Gamma(1/8)/(2^(9/8)*sqrt(Pi*Gamma(1/4))).
%e A273087 1.0235239993410058634977986567249718525649146079487847418721...
%p A273087 evalf(GAMMA(1/8)/(2^(9/8)*sqrt(Pi*GAMMA(1/4))), 120);
%t A273087 RealDigits[EllipticTheta[3, 0, Exp[-Sqrt[2]*Pi]], 10, 105][[1]]
%t A273087 RealDigits[Gamma[1/8]/(2^(9/8)*Sqrt[Pi*Gamma[1/4]]), 10, 105][[1]]
%o A273087 (PARI) th3(x)=1 + 2*suminf(n=1,x^n^2)
%o A273087 th3(exp(-sqrt(2)*Pi)) \\ _Charles R Greathouse IV_, Jun 06 2016
%o A273087 (Magma) C<i> := ComplexField(); Gamma(1/8)/(2^(9/8)*Sqrt(Pi(C)*Gamma(1/4))) // _G. C. Greubel_, Jan 07 2018
%Y A273087 Cf. A175573, A247217, A273081, A273082, A273083, A273084, A273086.
%K A273087 nonn,cons
%O A273087 1,3
%A A273087 _Vaclav Kotesovec_, May 14 2016