cp's OEIS Frontend

A273818 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.

%I A273818 #8 Jun 01 2016 02:49:51
%S A273818 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 A273818 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 A273818 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 A273818 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 A273818 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 A273818 c(3, 2) = Gamma(1/3)^6/(96 Pi 2^(2/3)) - 4 Pi^5 2^(2/3)/(9 Gamma(1/3)^6).
%F A273818 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 A273818 0.188005128918534491477960566306366792062371900057305840128102...
%t A273818 c[3, 2] = Gamma[1/3]^6/(96 Pi 2^(2/3)) - 4 Pi^5 2^(2/3)/(9 Gamma[1/3]^6);
%t A273818 RealDigits[c[3, 2], 10, 103][[1]]
%Y A273818 Cf. A273816 (c(3,0)), A273817 (c(3,1)), A273819 (c(3,3)).
%K A273818 nonn,cons
%O A273818 0,2
%A A273818 _Jean-François Alcover_, May 31 2016