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%I #6 Jun 01 2016 02:46:39
%S 1,9,5,7,7,0,6,2,5,2,4,7,2,8,7,9,1,7,2,1,7,4,5,8,0,8,3,2,7,5,5,7,7,2,
%T 3,7,4,1,8,8,2,7,8,9,6,9,6,6,5,2,5,0,2,8,1,9,7,9,3,3,8,4,6,1,6,6,3,5,
%U 2,9,9,2,9,6,9,4,4,4,4,6,2,6,5,5,3,5,2,9,1,1,1,6,3,8,5,8,0,8,5,7,6,8,8,9
%N Decimal expansion the Bessel moment c(4,2) = Integral_{0..inf} x^2 K_0(x)^4 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.
%F c(4,2) = (Pi^4/64)*(4 * 4F3(1/2, 1/2, 1/2, 1/2; 1, 1, 1; 1) - 3 * 4F3(1/2, 1/2, 1/2, 1/2; 2, 1, 1; 1)) - 3*Pi^2/16, where 4F3 is the generalized hypergeometric function.
%e 0.195770625247287917217458083275577237418827896966525028197933846...
%t c[4, 2] = (Pi^4/64)*(4*HypergeometricPFQ[{1/2, 1/2, 1/2, 1/2}, {1, 1, 1}, 1] - 3*HypergeometricPFQ[{1/2, 1/2, 1/2, 1/2}, {2, 1, 1}, 1]) - 3*Pi^2 / 16;
%t RealDigits[c[4, 2], 10, 104][[1]]
%Y Cf. A273816 (c(3,0)), A273817 (c(3,1)), A273818 (c(3,2)), A273819 (c(3,3)), A273839 (c(4,0)), A233091 (c(4,1)), A273841 (c(4,3)).
%K nonn,cons
%O 0,2
%A _Jean-François Alcover_, Jun 01 2016
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