A273818 - OEIS

%I #8 Jun 01 2016 02:49:51

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

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

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

%N Decimal expansion the Bessel moment c(3,2) = Integral_{0..inf} x^2 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, 2) = Gamma(1/3)^6/(96 Pi 2^(2/3)) - 4 Pi^5 2^(2/3)/(9 Gamma(1/3)^6).

%F Equals sqrt(3) Pi^3/288 3F2(1/2, 1/2, 1/2; 2, 2; 1/4), where 3F2 is the generalized hypergeometric function.

%e 0.188005128918534491477960566306366792062371900057305840128102...

%t c[3, 2] = Gamma[1/3]^6/(96 Pi 2^(2/3)) - 4 Pi^5 2^(2/3)/(9 Gamma[1/3]^6);

%t RealDigits[c[3, 2], 10, 103][[1]]

%Y Cf. A273816 (c(3,0)), A273817 (c(3,1)), A273819 (c(3,3)).

%K nonn,cons

%O 0,2

%A _Jean-François Alcover_, May 31 2016