OFFSET
1,3
LINKS
G. C. Greubel, Table of n, a(n) for n = 1..5000
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
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
Vaclav Kotesovec, May 14 2016
STATUS
approved