OFFSET
1,8
LINKS
G. C. Greubel, Table of n, a(n) for n = 1..10000
Wikipedia, Theta function
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