A247217 - OEIS

%I #29 Nov 11 2024 01:57:44

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

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

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

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

%H G. C. Greubel, <a href="/A247217/b247217.txt">Table of n, a(n) for n = 1..10000</a>

%H Eric Weisstein's MathWorld, <a href="http://mathworld.wolfram.com/JacobiThetaFunctions.html">Jacobi Theta Functions</a>

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

%F Equals (4*Pi*sqrt(2) + 6*Pi)^(1/4)/(2*Gamma(3/4)).

%F Equals Sum_{n=-infinity..infinity} exp(-2*Pi*n^2).

%e 1.0037348854877390910476795950669538662079943324445194...

%t RealDigits[(4*Pi*Sqrt[2] + 6*Pi)^(1/4)/(2*Gamma[3/4]), 10, 102] // First

%o (PARI) (4*Pi*sqrt(2) + 6*Pi)^(1/4)/(2*gamma(3/4)) \\ _Michel Marcus_, Nov 26 2014

%o (Magma) C<i> := ComplexField(); (4*Pi(C)*Sqrt(2) + 6*Pi(C))^(1/4)/(2*Gamma(3/4)); // _G. C. Greubel_, Jan 07 2018

%Y Cf. A000122, A175573 (theta_3(0, exp(-Pi))), A273081, A273082, A273083, A273084.

%Y Cf. A273087, A273086.

%K nonn,cons,easy

%O 1,4

%A _Jean-François Alcover_, Nov 26 2014