A273819 Decimal expansion the Bessel moment c(3,3) = Integral_{0..inf} x^3 K_0(x)^3 dx, where K_0 is the modified Bessel function of the second kind.

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

Offset

0,3

Links

Table of n, a(n) for n=0..101.

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

Formula

c(3, 3) = (1/9)*(PolyGamma(1, 1/3) - PolyGamma(1, 2/3)) - 2/3.

Example

0.1146357462298196302005207629574256896984676698786187535554333963...

Mathematica

c[3, 3] = (1/9)*(PolyGamma[1, 1/3] - PolyGamma[1, 2/3]) - 2/3;
RealDigits[c[3, 3], 10, 102][[1]]

Prog

(PARI) (zetahurwitz(2, 1/3)-zetahurwitz(2, 2/3)-6)/9 \\ Charles R Greathouse IV, Oct 23 2023

Crossrefs

Cf. A273816 (c(3,0)), A273817 (c(3,1)), A273818 (c(3,2)).

Sequence in context: A081709 A200640 A179453 * A276761 A073000 A198113

Adjacent sequences: A273816 A273817 A273818 * A273820 A273821 A273822

Keyword

nonn,cons

Author

Jean-François Alcover, May 31 2016

Status

approved