A273839 - OEIS

%I #8 Jun 01 2016 02:46:09

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

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

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

%N Decimal expansion the Bessel moment c(4,0) = Integral_{0..inf} 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(4,0) = (Pi^4/4) Sum_{n>=0} binomial(2n, n)^4/2^(8n).

%F Equals (Pi^4/4) 4F3(1/2, 1/2, 1/2, 1/2; 1, 1, 1; 1), where 4F3 is the generalized hypergeometric function.

%e 27.2413384178059734067099802645579350239978880986182746551229...

%t c[4, 0] = (Pi^4/4)*HypergeometricPFQ[{1/2, 1/2, 1/2, 1/2}, {1, 1, 1}, 1];

%t RealDigits[c[4, 0], 10, 102][[1]]

%Y Cf. A273816 (c(3,0)), A273817 (c(3,1)), A273818 (c(3,2)), A273819 (c(3,3)), A233091 (c(4,1)), A273840 (c(4,2)), A273841 (c(4,3)).

%K nonn,cons

%O 2,1

%A _Jean-François Alcover_, Jun 01 2016