A273816 - OEIS

%I #11 Jun 14 2016 06:46:00

%S 6,9,4,8,8,2,2,7,8,1,0,7,9,6,2,9,7,8,9,4,3,6,4,3,6,4,4,5,4,7,0,8,2,9,

%T 7,5,7,6,7,4,8,5,1,1,3,2,6,0,9,8,9,1,7,3,5,1,6,2,3,8,0,6,8,8,1,9,1,4,

%U 2,2,3,3,8,1,9,9,8,0,4,1,8,6,8,3,9,9,5,2,3,5,1,8,0,6,0,9,5,5,3,7,1,9,3

%N Decimal expansion the Bessel moment c(3,0) = Integral_{0..inf} K_0(x)^3 dx, where K_0 is the modified Bessel function of the second kind.

%H David H. Bailey, Jonathan M. Borwein, David Broadhurst and M. L. Glasser, <a href="http://arxiv.org/abs/0801.0891">Elliptic integral evaluations of Bessel moments</a>, arXiv:0801.0891 [hep-th], 2008.

%F c(3, 0) = 3*Gamma(1/3)^6/(32*Pi*2^(2/3)).

%F 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.

%F 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.

%e 6.94882278107962978943643644547082975767485113260989173516238...

%t c[3, 0] = 3*Gamma[1/3]^6/(32*Pi*2^(2/3));

%t RealDigits[c[3, 0], 10, 103][[1]]

%Y Cf. A273817 (c(3,1)), A273818 (c(3,2)), A273819 (c(3,3)).

%K nonn,cons

%O 1,1

%A _Jean-François Alcover_, May 31 2016