cp's OEIS Frontend

A273990 Decimal expansion of the odd Bessel moment t(5,3) (see the referenced paper about the elliptic integral evaluations of Bessel moments).

%I A273990 #6 Jun 06 2016 11:24:17
%S A273990 2,5,2,2,5,3,9,4,4,8,9,7,8,4,1,9,6,5,9,9,4,5,0,9,6,1,2,5,5,5,0,9,0,4,
%T A273990 0,8,7,7,5,0,6,8,4,5,0,7,5,5,9,7,0,0,9,9,9,2,0,6,5,9,3,0,9,4,5,2,8,9,
%U A273990 7,1,0,2,0,7,4,1,9,8,6,0,5,9,0,8,1,5,6,3,5,4,9,5,9,6,5,1,7,4,1,1,9,2,7,9
%N A273990 Decimal expansion of the odd Bessel moment t(5,3) (see the referenced paper about the elliptic integral evaluations of Bessel moments).
%H A273990 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 A273990 Integral_{0..inf} x*BesselI_0(x)^2*BesselK_0(x)^3.
%e A273990 0.252253944897841965994509612555090408775068450755970099920659309452897...
%t A273990 t[5, 3] = NIntegrate[x^3*BesselI[0, x]^2*BesselK[0, x]^3, {x, 0, Infinity}, WorkingPrecision -> 104];
%t A273990 RealDigits[t[5, 3]][[1]]
%t A273990 (* or: *)
%t A273990 K[k_] := EllipticK[k^2/(-1+k^2)]/Sqrt[1-k^2];
%t A273990 D0[y_] := (4*y*K[Sqrt[((1-3*y)*(1+y)^3)/((1+3*y)*(1-y)^3)]])/Sqrt[(1+3*y)* (1-y)^3];
%t A273990 t[5, 3] = NIntegrate[4y^2*(1-2y^2+4y^4)*D0[y]/(1-4y^2)^(5/2), {y, 0, 1/3}, WorkingPrecision -> 104];
%t A273990 RealDigits[t[5, 3]][[1]]
%Y A273990 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)), A273991 (t(5,5)).
%K A273990 nonn,cons
%O A273990 0,1
%A A273990 _Jean-François Alcover_, Jun 06 2016