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
Examples
1.0001613990351406940215020703893995738875083912423752893728...
Links
- G. C. Greubel, Table of n, a(n) for n = 1..10000
- Wikipedia, Theta function
Programs
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Magma
C := ComplexField(); (1+2/Sqrt(3))^(1/4)*Pi(C)^(1/4)/(3^(1/4) *Gamma(3/4)) // G. C. Greubel, Jan 07 2018
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Maple
evalf((1 + 2/sqrt(3))^(1/4) * Pi^(1/4) / (3^(1/4) * GAMMA(3/4)), 120);
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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]]
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PARI
sqrtn((2/sqrt(3)+1)*Pi/3,4)/gamma(3/4) \\ Charles R Greathouse IV, Jun 06 2016
Formula
Equals (1 + 2/sqrt(3))^(1/4) * Pi^(1/4) / (3^(1/4) * Gamma(3/4)).