A273081 Decimal expansion of theta_3(0, exp(-3*Pi)), where theta_3 is the 3rd Jacobi theta function.

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

G. C. Greubel, Table of n, a(n) for n = 1..10000

Wikipedia, Theta function

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

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

Sequence in context: A195478 A259731 A176399 * A181552 A294347 A229606

Adjacent sequences: A273078 A273079 A273080 * A273082 A273083 A273084

Keyword

nonn,cons

Author

Vaclav Kotesovec, May 14 2016

Status

approved