A273986 Decimal expansion of the odd Bessel moment s(5,5) (see the referenced paper about the elliptic integral evaluations of Bessel moments).

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

Offset

0,2

Links

Table of n, a(n) for n=0..103.

David H. Bailey, Jonathan M. Borwein, David Broadhurst and M. L. Glasser, Elliptic integral evaluations of Bessel moments, arXiv:0801.0891, page 21.

Formula

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

Equals Pi^2 (4/15)^3 (43 C - 19/(40 C)) (conjectural, where C is A273959).

Example

0.054514253132761880363033919802009596877614349544575913649940264634...

Mathematica

s[5, 5] = NIntegrate[x^5*BesselI[0, x]*BesselK[0, x]^4, {x, 0, Infinity}, WorkingPrecision -> 103];
Join[{0}, RealDigits[s[5, 5]][[1]]]

Crossrefs

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)).

Sequence in context: A019117 A204372 A279918 * A246729 A337029 A293557

Adjacent sequences: A273983 A273984 A273985 * A273987 A273988 A273989

Keyword

nonn,cons

Author

Jean-François Alcover, Jun 06 2016

Status

approved