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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 (list; constant; graph; refs; listen; history; text; internal format)
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

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Last modified May 31 02:51 EDT 2020. Contains 334747 sequences. (Running on oeis4.)