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

Author

Jean-François Alcover, May 31 2016

Keywords

• nonn
• cons

Examples

			0.1146357462298196302005207629574256896984676698786187535554333963...
		

Links

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

Crossrefs

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

Programs

Mathematica

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

PARI

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

Formula

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