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A273084
Decimal expansion of theta_3(0, exp(-6*Pi)), where theta_3 is the 3rd Jacobi theta function.
8
1, 0, 0, 0, 0, 0, 0, 0, 1, 3, 0, 2, 4, 8, 2, 4, 2, 7, 2, 1, 5, 9, 8, 0, 1, 4, 5, 6, 4, 2, 4, 3, 3, 0, 2, 3, 0, 9, 0, 6, 7, 4, 5, 7, 3, 2, 5, 4, 1, 4, 6, 0, 4, 1, 5, 7, 5, 1, 1, 4, 8, 0, 1, 1, 9, 0, 4, 5, 9, 3, 4, 8, 2, 3, 9, 1, 1, 1, 3, 6, 1, 2, 5, 1, 7, 1, 1, 8, 6, 0, 8, 8, 8, 1, 0, 9, 2, 6, 4, 0, 4, 4, 6, 7, 4
OFFSET
1,10
LINKS
FORMULA
Equals sqrt(2+sqrt(8+6*sqrt(3)+4*sqrt(6+4*sqrt(3)))) * Pi^(1/4) / (2*3^(3/8)*Gamma(3/4)).
Equals sqrt((A273081^2 + A292888^4/A363018^2)/2). - Vaclav Kotesovec, May 17 2023
EXAMPLE
1.0000000130248242721598014564243302309067457325414604157511...
MAPLE
evalf(sqrt(2 + sqrt(8 + 6*sqrt(3) + 4*sqrt(6 + 4*sqrt(3)))) * Pi^(1/4) / (2*3^(3/8) * GAMMA(3/4)), 120);
MATHEMATICA
RealDigits[EllipticTheta[3, 0, Exp[-6*Pi]], 10, 105][[1]]
RealDigits[Sqrt[2 + Sqrt[8 + 6*Sqrt[3] + 4*Sqrt[6 + 4*Sqrt[3]]]] * Pi^(1/4) / (2*3^(3/8) * Gamma[3/4]), 10, 105][[1]]
PROG
(PARI) th3(x)=1 + 2*suminf(n=1, x^n^2) th3(exp(-6*Pi)) \\ Charles R Greathouse IV, Jun 06 2016
(Magma) C<i> := ComplexField(); Sqrt(2+Sqrt(8+6*Sqrt(3)+4*Sqrt(6 +4*Sqrt(3))))*Pi(C)^(1/4)/(2*3^(3/8)*Gamma(3/4)) // G. C. Greubel, Jan 07 2018
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
Vaclav Kotesovec, May 14 2016
STATUS
approved