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A273083
Decimal expansion of theta_3(0, exp(-5*Pi)), where theta_3 is the 3rd Jacobi theta function.
8
1, 0, 0, 0, 0, 0, 0, 3, 0, 1, 4, 0, 3, 4, 5, 5, 0, 7, 8, 0, 1, 2, 9, 2, 2, 1, 5, 0, 6, 5, 4, 9, 0, 3, 9, 0, 8, 0, 8, 0, 2, 2, 3, 6, 1, 7, 8, 9, 5, 4, 9, 4, 8, 6, 6, 7, 3, 4, 7, 7, 7, 4, 3, 7, 4, 8, 7, 6, 2, 8, 2, 1, 3, 3, 1, 0, 3, 1, 5, 1, 3, 9, 6, 2, 7, 4, 2, 8, 0, 5, 8, 1, 4, 3, 4, 4, 2, 8, 4, 2, 9, 8, 5, 5, 9
OFFSET
1,8
LINKS
FORMULA
Equals sqrt(2/5 + 1/sqrt(5)) * Pi^(1/4)/Gamma(3/4).
EXAMPLE
1.0000003014034550780129221506549039080802236178954948667347...
MAPLE
evalf(sqrt(2/5 + 1/sqrt(5)) * Pi^(1/4)/GAMMA(3/4), 120);
MATHEMATICA
RealDigits[EllipticTheta[3, 0, Exp[-5*Pi]], 10, 105][[1]]
RealDigits[Sqrt[2/5 + 1/Sqrt[5]] * Pi^(1/4)/Gamma[3/4], 10, 105][[1]]
PROG
(PARI) th3(x)=1 + 2*suminf(n=1, x^n^2)
th3(exp(-5*Pi)) \\ Charles R Greathouse IV, Jun 06 2016
(Magma) C<i> := ComplexField(); Sqrt(2/5 + 1/Sqrt(5))*Pi(C)^(1/4)/Gamma(3/4) // G. C. Greubel, Jan 07 2018
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
Vaclav Kotesovec, May 14 2016
STATUS
approved