cp's OEIS Frontend

A273989 Decimal expansion of the odd Bessel moment t(5,1) (see the referenced paper about the elliptic integral evaluations of Bessel moments).

%I A273989 #14 Jan 06 2017 08:38:50
%S A273989 6,6,0,3,4,4,8,6,9,0,1,8,6,7,2,3,5,7,8,3,7,2,6,6,8,3,1,7,0,5,9,9,4,2,
%T A273989 6,3,8,5,4,2,4,1,9,9,1,6,9,6,8,7,3,8,5,8,3,0,0,8,0,3,5,8,7,5,5,3,8,9,
%U A273989 4,9,5,8,6,8,3,7,9,9,4,4,5,4,1,0,9,8,1,0,7,2,0,1,2,1,7,5,3,2,7,6,8,4,2,4,3
%N A273989 Decimal expansion of the odd Bessel moment t(5,1) (see the referenced paper about the elliptic integral evaluations of Bessel moments).
%H A273989 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 A273989 Integral_{0..inf} x*BesselI_0(x)^2*BesselK_0(x)^3.
%F A273989 Equals 4(7 - 4*sqrt(3)) EllipticK(1 - 32/(16 + 7*sqrt(3) - sqrt(15))) EllipticK(1 - 32/(16 + 7*sqrt(3) + sqrt(15))).
%e A273989 0.660344869018672357837266831705994263854241991696873858300803587553894...
%t A273989 t[5, 1] = NIntegrate[x*BesselI[0, x]^2*BesselK[0, x]^3, {x, 0, Infinity}, WorkingPrecision -> 105]; RealDigits[t[5, 1]][[1]]
%t A273989 (* or: *)
%t A273989 t[5, 1] = 4(7 - 4*Sqrt[3]) EllipticK[1 - 32/(16 + 7*Sqrt[3] - Sqrt[15])] EllipticK[1 - 32/(16 + 7*Sqrt[3] + Sqrt[15])]; RealDigits[t[5, 1], 10, 105][[1]]
%t A273989 RealDigits[EllipticK[(16 - 7 Sqrt[3] - Sqrt[15])/32] EllipticK[(16 - 7 Sqrt[3] + Sqrt[15])/32]/4, 10, 105][[1]] (* _Jan Mangaldan_, Jan 06 2017 *)
%Y A273989 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)), A273990 (t(5,3)), A273991 (t(5,5)).
%K A273989 cons,nonn
%O A273989 0,1
%A A273989 _Jean-François Alcover_, Jun 06 2016