A273991 Decimal expansion of the odd Bessel moment t(5,5) (see the referenced paper about the elliptic integral evaluations of Bessel moments).

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

Offset

1,3

Links

Table of n, a(n) for n=1..103.

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

Integral_{0..inf} x^5*BesselI_0(x)^2*BesselK_0(x)^3.

Conjecture: Equals 76/15 t(5,3) - 16/45 t(5,1).

Example

1.0432973673868713449189316078947712217566163312269155788688325589866...

Mathematica

t[5, 5] = NIntegrate[x^5*BesselI[0, x]^2*BesselK[0, x]^3, {x, 0, Infinity}, WorkingPrecision -> 103];
RealDigits[t[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)), A273986 (s(5,5)), A273989 (t(5,1)), A273990 (t(5,3)).

Sequence in context: A132668 A018866 A021235 * A292828 A020703 A084483

Adjacent sequences: A273988 A273989 A273990 * A273992 A273993 A273994

Keyword

nonn,cons

Author

Jean-François Alcover, Jun 06 2016

Status

approved