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A273087
Decimal expansion of theta_3(0, exp(-sqrt(2)*Pi)), where theta_3 is the 3rd Jacobi theta function.
3
1, 0, 2, 3, 5, 2, 3, 9, 9, 9, 3, 4, 1, 0, 0, 5, 8, 6, 3, 4, 9, 7, 7, 9, 8, 6, 5, 6, 7, 2, 4, 9, 7, 1, 8, 5, 2, 5, 6, 4, 9, 1, 4, 6, 0, 7, 9, 4, 8, 7, 8, 4, 7, 4, 1, 8, 7, 2, 1, 5, 1, 9, 8, 5, 8, 7, 4, 1, 3, 4, 7, 9, 7, 7, 6, 7, 8, 4, 6, 0, 3, 1, 1, 1, 3, 0, 2, 2, 8, 5, 7, 7, 4, 6, 8, 7, 6, 0, 1, 9, 3, 3, 5, 5, 0
OFFSET
1,3
LINKS
Eric Weisstein's MathWorld, Jacobi Theta Functions
Wikipedia, Theta function
FORMULA
Equals Gamma(1/8)/(2^(9/8)*sqrt(Pi*Gamma(1/4))).
EXAMPLE
1.0235239993410058634977986567249718525649146079487847418721...
MAPLE
evalf(GAMMA(1/8)/(2^(9/8)*sqrt(Pi*GAMMA(1/4))), 120);
MATHEMATICA
RealDigits[EllipticTheta[3, 0, Exp[-Sqrt[2]*Pi]], 10, 105][[1]]
RealDigits[Gamma[1/8]/(2^(9/8)*Sqrt[Pi*Gamma[1/4]]), 10, 105][[1]]
PROG
(PARI) th3(x)=1 + 2*suminf(n=1, x^n^2)
th3(exp(-sqrt(2)*Pi)) \\ Charles R Greathouse IV, Jun 06 2016
(Magma) C<i> := ComplexField(); Gamma(1/8)/(2^(9/8)*Sqrt(Pi(C)*Gamma(1/4))) // G. C. Greubel, Jan 07 2018
KEYWORD
nonn,cons
AUTHOR
Vaclav Kotesovec, May 14 2016
STATUS
approved