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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.
6
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
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 A377277
KEYWORD
nonn,cons
AUTHOR
STATUS
approved