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A273081
Decimal expansion of theta_3(0, exp(-3*Pi)), where theta_3 is the 3rd Jacobi theta function.
8
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, 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, 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
OFFSET
1,6
LINKS
FORMULA
Equals (1 + 2/sqrt(3))^(1/4) * Pi^(1/4) / (3^(1/4) * Gamma(3/4)).
EXAMPLE
1.0001613990351406940215020703893995738875083912423752893728...
MAPLE
evalf((1 + 2/sqrt(3))^(1/4) * Pi^(1/4) / (3^(1/4) * GAMMA(3/4)), 120);
MATHEMATICA
RealDigits[EllipticTheta[3, 0, Exp[-3*Pi]], 10, 105][[1]]
RealDigits[(1 + 2/Sqrt[3])^(1/4) * Pi^(1/4) / (3^(1/4) * Gamma[3/4]), 10, 105][[1]]
PROG
(PARI) sqrtn((2/sqrt(3)+1)*Pi/3, 4)/gamma(3/4) \\ Charles R Greathouse IV, Jun 06 2016
(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
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
Vaclav Kotesovec, May 14 2016
STATUS
approved