OFFSET
1,1
LINKS
David H. Bailey, Jonathan M. Borwein, David Broadhurst and M. L. Glasser, Elliptic integral evaluations of Bessel moments, arXiv:0801.0891 [hep-th], 2008.
FORMULA
c(3, 0) = 3*Gamma(1/3)^6/(32*Pi*2^(2/3)).
Equals (1/2)*Pi*K[(1/4)*(2 - Sqrt[3])]*K[(1/4)*(2 + Sqrt[3])], where K(x) is the complete elliptic integral of the first kind.
Also equals sqrt(3) Pi^3/8 3F2(1/2, 1/2, 1/2; 1, 1; 1/4), where 3F2 is the generalized hypergeometric function A263490.
EXAMPLE
6.94882278107962978943643644547082975767485113260989173516238...
MATHEMATICA
c[3, 0] = 3*Gamma[1/3]^6/(32*Pi*2^(2/3));
RealDigits[c[3, 0], 10, 103][[1]]
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
Jean-François Alcover, May 31 2016
STATUS
approved