A273817 Decimal expansion the Bessel moment c(3,1) = Integral_{0..inf} x K_0(x)^3 dx, where K_0 is the modified Bessel function of the second kind.

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

Offset

0,1

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 [hep-th], 2008.

Formula

c(3, 1) = (1/12)*(PolyGamma(1, 1/3) - PolyGamma(1, 2/3)).

Example

0.585976809672364722650390572218069267273850752408964065166575...

Mathematica

c[3, 1] = (1/12)*(PolyGamma[1, 1/3] - PolyGamma[1, 2/3]);
RealDigits[c[3, 1], 10, 104][[1]]

Crossrefs

Cf. A273816 (c(3,0)), A273818 (c(3,2)), A273819 (c(3,3)).

Sequence in context: A213022 A198732 A202348 * A073212 A059742 A296486

Adjacent sequences: A273814 A273815 A273816 * A273818 A273819 A273820

Keyword

nonn,cons

Author

Jean-François Alcover, May 31 2016

Status

approved