cp's OEIS Frontend

A273985 Decimal expansion of the odd Bessel moment s(5,3) (see the referenced paper about the elliptic integral evaluations of Bessel moments).

%I A273985 #5 Jun 06 2016 05:42:43
%S A273985 0,8,5,9,3,7,2,9,0,6,9,1,7,6,8,4,5,2,4,2,3,8,4,1,7,4,5,7,8,7,6,4,6,9,
%T A273985 5,8,0,3,3,7,8,7,3,7,7,9,1,3,0,6,4,9,8,0,6,4,3,1,6,8,4,6,6,9,6,3,7,5,
%U A273985 7,9,0,7,5,2,2,9,7,2,3,0,2,5,5,5,6,5,1,6,0,0,9,8,3,3,8,1,9,3,1,2,4,6,7,7
%N A273985 Decimal expansion of the odd Bessel moment s(5,3) (see the referenced paper about the elliptic integral evaluations of Bessel moments).
%H A273985 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 A273985 s(5,3) = Integral_{0..inf} x^3*BesselI_0(x)*BesselK_0(x)^4 dx.
%F A273985 Equals Pi^2 (2/15)^2 (13 C - 1/(10 C)) (conjectural, where C is A273959).
%e A273985 0.0859372906917684524238417457876469580337873779130649806431684669637579...
%t A273985 s[5, 3] = NIntegrate[x^3*BesselI[0, x]*BesselK[0, x]^4, {x, 0, Infinity}, WorkingPrecision -> 103];
%t A273985 Join[{0}, RealDigits[s[5, 3]][[1]]]
%Y A273985 Cf. A073010 (s(3,1)), A121839 (1+s(3,3)), A222068 (s(4,1)), A244854 (2s(4,3)), A273959, A273984 (s(5,1)), A273986 (s(5,5)).
%K A273985 nonn,cons
%O A273985 0,2
%A A273985 _Jean-François Alcover_, Jun 06 2016