OFFSET
0,2
LINKS
Steven R. Finch, Dirichlet Integral, May 15, 2008. [Cached copy, with permission of the author]
FORMULA
r_0 = (2^(1/4)*K(-sqrt(2)) - K(-1/sqrt(2)))/(2^(1/4)*K(-sqrt(2)) + K(-1/sqrt(2))), where K is the complete elliptic integral of the first kind.
EXAMPLE
0.039492922771663589516403746990814611201066045824307066695...
MAPLE
evalf((EllipticK(sqrt(2-sqrt(2))) - EllipticK(sqrt(sqrt(2)-1))) / (EllipticK(sqrt(2-sqrt(2))) + EllipticK(sqrt(sqrt(2)-1))), 120); # Vaclav Kotesovec, Oct 28 2014
MATHEMATICA
r0 = (2^(1/4)*EllipticK[-Sqrt[2]] - EllipticK[-1/Sqrt[2]])/(2^(1/4)*EllipticK[-Sqrt[2]] + EllipticK[-1/Sqrt[2]]); Join[{0}, RealDigits[r0, 10, 100] // First]
Prepend[RealDigits[2/(1 + EllipticK[Sqrt[2] - 1]/EllipticK[2 - Sqrt[2]]) - 1, 10, 100][[1]], 0] (* Jan Mangaldan, Jan 04 2017 *)
CROSSREFS
KEYWORD
AUTHOR
Jean-François Alcover, Oct 28 2014
STATUS
approved