A273986 - OEIS

%I #5 Jun 06 2016 05:42:53

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

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

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

%N Decimal expansion of the odd Bessel moment s(5,5) (see the referenced paper about the elliptic integral evaluations of Bessel moments).

%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, page 21.

%F s(5,5) = Integral_{0..inf} x^5*BesselI_0(x)*BesselK_0(x)^4 dx.

%F Equals Pi^2 (4/15)^3 (43 C - 19/(40 C)) (conjectural, where C is A273959).

%e 0.054514253132761880363033919802009596877614349544575913649940264634...

%t s[5, 5] = NIntegrate[x^5*BesselI[0, x]*BesselK[0, x]^4, {x, 0, Infinity}, WorkingPrecision -> 103];

%t Join[{0}, RealDigits[s[5, 5]][[1]]]

%Y Cf. A073010 (s(3,1)), A121839 (1+s(3,3)), A222068 (s(4,1)), A244854 (2s(4,3)), A273959, A273984 (s(5,1)), A273985 (s(5,3)).

%K nonn,cons

%O 0,2

%A _Jean-François Alcover_, Jun 06 2016