A273984 Decimal expansion of the odd Bessel moment s(5,1) (see the referenced paper about the elliptic integral evaluations of Bessel moments).

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, 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, 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

Offset: 1

Author

Jean-François Alcover, Jun 06 2016

Keywords

• nonn
• cons

Examples

			1.07128505542180765851871197803081716076317977716705621702469365995...
		

Links

• David H. Bailey, Jonathan M. Borwein, David Broadhurst and M. L. Glasser, Elliptic integral evaluations of Bessel moments, arXiv:0801.0891 [hep-th], 2008, page 21.

Crossrefs

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)).

Programs

Mathematica

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

PARI

intnumosc(x=0,x*besseli(0,x)*besselk(0,x)^4,Pi) \\ Charles R Greathouse IV, Oct 23 2023

Formula

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

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

Extensions

Offset corrected by Rick L. Shepherd, Jun 07 2016