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

1,3

Links

Table of n, a(n) for n=1..105.

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.

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).

Example

1.07128505542180765851871197803081716076317977716705621702469365995...

Mathematica

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

Prog

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

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)).

Sequence in context: A195409 A318353 A354639 * A119506 A304149 A305489

Adjacent sequences: A273981 A273982 A273983 * A273985 A273986 A273987

Keyword

nonn,cons

Author

Jean-François Alcover, Jun 06 2016

Extensions

Offset corrected by Rick L. Shepherd, Jun 07 2016

Status

approved