A273985 Decimal expansion of the odd Bessel moment s(5,3) (see the referenced paper about the elliptic integral evaluations of Bessel moments).

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

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(5,3) = Integral_{0..inf} x^3*BesselI_0(x)*BesselK_0(x)^4 dx.

Equals Pi^2 (2/15)^2 (13 C - 1/(10 C)) (conjectural, where C is A273959).

Example

0.0859372906917684524238417457876469580337873779130649806431684669637579...

Mathematica

s[5, 3] = NIntegrate[x^3*BesselI[0, x]*BesselK[0, x]^4, {x, 0, Infinity}, WorkingPrecision -> 103];
Join[{0}, RealDigits[s[5, 3]][[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)), A273986 (s(5,5)).

Sequence in context: A335822 A233033 A244810 * A347195 A132036 A132717

Adjacent sequences: A273982 A273983 A273984 * A273986 A273987 A273988

Keyword

nonn,cons

Author

Jean-François Alcover, Jun 06 2016

Status

approved