cp's OEIS Frontend

A273991 Decimal expansion of the odd Bessel moment t(5,5) (see the referenced paper about the elliptic integral evaluations of Bessel moments).

%I A273991 #9 Jun 06 2016 11:22:56
%S A273991 1,0,4,3,2,9,7,3,6,7,3,8,6,8,7,1,3,4,4,9,1,8,9,3,1,6,0,7,8,9,4,7,7,1,
%T A273991 2,2,1,7,5,6,6,1,6,3,3,1,2,2,6,9,1,5,5,7,8,8,6,8,8,3,2,5,5,8,9,8,6,6,
%U A273991 2,7,1,0,9,6,4,3,9,2,2,0,2,2,6,7,7,4,2,1,1,5,0,6,3,5,6,8,4,2,6,1,0,8,9
%N A273991 Decimal expansion of the odd Bessel moment t(5,5) (see the referenced paper about the elliptic integral evaluations of Bessel moments).
%H A273991 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, page 21.
%F A273991 Integral_{0..inf} x^5*BesselI_0(x)^2*BesselK_0(x)^3.
%F A273991 Conjecture: Equals 76/15 t(5,3) - 16/45 t(5,1).
%e A273991 1.0432973673868713449189316078947712217566163312269155788688325589866...
%t A273991 t[5, 5] = NIntegrate[x^5*BesselI[0, x]^2*BesselK[0, x]^3, {x, 0, Infinity}, WorkingPrecision -> 103];
%t A273991 RealDigits[t[5, 5]][[1]]
%Y A273991 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)), A273986 (s(5,5)), A273989 (t(5,1)), A273990 (t(5,3)).
%K A273991 nonn,cons
%O A273991 1,3
%A A273991 _Jean-François Alcover_, Jun 06 2016