A273081 - OEIS

%I #13 Sep 08 2022 08:46:16

%S 1,0,0,0,1,6,1,3,9,9,0,3,5,1,4,0,6,9,4,0,2,1,5,0,2,0,7,0,3,8,9,3,9,9,

%T 5,7,3,8,8,7,5,0,8,3,9,1,2,4,2,3,7,5,2,8,9,3,7,2,7,9,9,8,6,3,1,3,9,1,

%U 4,4,3,7,0,4,5,5,1,8,7,4,5,3,4,8,5,1,2,8,5,4,2,4,9,3,0,0,7,1,2,0,4,7,3,7,1

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

%H G. C. Greubel, <a href="/A273081/b273081.txt">Table of n, a(n) for n = 1..10000</a>

%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Theta_function#Explicit_values">Theta function</a>

%F Equals (1 + 2/sqrt(3))^(1/4) * Pi^(1/4) / (3^(1/4) * Gamma(3/4)).

%e 1.0001613990351406940215020703893995738875083912423752893728...

%p evalf((1 + 2/sqrt(3))^(1/4) * Pi^(1/4) / (3^(1/4) * GAMMA(3/4)), 120);

%t RealDigits[EllipticTheta[3, 0, Exp[-3*Pi]], 10, 105][[1]]

%t RealDigits[(1 + 2/Sqrt[3])^(1/4) * Pi^(1/4) / (3^(1/4) * Gamma[3/4]), 10, 105][[1]]

%o (PARI) sqrtn((2/sqrt(3)+1)*Pi/3,4)/gamma(3/4) \\ _Charles R Greathouse IV_, Jun 06 2016

%o (Magma) C<i> := ComplexField(); (1+2/Sqrt(3))^(1/4)*Pi(C)^(1/4)/(3^(1/4) *Gamma(3/4)) // _G. C. Greubel_, Jan 07 2018

%Y Cf. A175573, A247217, A273082, A273083, A273084.

%K nonn,cons

%O 1,6

%A _Vaclav Kotesovec_, May 14 2016