A273984 - OEIS

%I #13 Oct 23 2023 09:34:12

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

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

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

%N Decimal expansion of the odd Bessel moment s(5,1) (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 [hep-th], 2008, page 21.

%F s(5,1) = Integral_{0..inf} x*BesselI_0(x)*BesselK_0(x)^4 dx.

%F Equals Pi^2 C (conjectural, where C is A273959).

%e 1.07128505542180765851871197803081716076317977716705621702469365995...

%t s[5, 1] = NIntegrate[x*BesselI[0, x]*BesselK[0, x]^4, {x, 0, Infinity}, WorkingPrecision -> 105];

%t RealDigits[s[5, 1]][[1]]

%o (PARI) intnumosc(x=0,x*besseli(0,x)*besselk(0,x)^4,Pi) \\ _Charles R Greathouse IV_, Oct 23 2023

%Y Cf. A073010 (s(3,1)), A121839 (1+s(3,3)), A222068 (s(4,1)), A244854 (2s(4,3)), A273959, A273985 (s(5,3)), A273986 (s(5,5)).

%K nonn,cons

%O 1,3

%A _Jean-François Alcover_, Jun 06 2016

%E Offset corrected by _Rick L. Shepherd_, Jun 07 2016