cp's OEIS Frontend

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.

%I A273819 #10 Oct 23 2023 10:02:11
%S A273819 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,
%T A273819 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,
%U A273819 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
%N 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.
%H A273819 David H. Bailey, Jonathan M. Borwein, David Broadhurst and M. L. Glasser, <a href="http://arxiv.org/abs/0801.0891">Elliptic integral evaluations of Bessel moments</a>, arXiv:0801.0891 [hep-th], 2008.
%F A273819 c(3, 3) = (1/9)*(PolyGamma(1, 1/3) - PolyGamma(1, 2/3)) - 2/3.
%e A273819 0.1146357462298196302005207629574256896984676698786187535554333963...
%t A273819 c[3, 3] = (1/9)*(PolyGamma[1, 1/3] - PolyGamma[1, 2/3]) - 2/3;
%t A273819 RealDigits[c[3, 3], 10, 102][[1]]
%o A273819 (PARI) (zetahurwitz(2,1/3)-zetahurwitz(2,2/3)-6)/9 \\ _Charles R Greathouse IV_, Oct 23 2023
%Y A273819 Cf. A273816 (c(3,0)), A273817 (c(3,1)), A273818 (c(3,2)).
%K A273819 nonn,cons
%O A273819 0,3
%A A273819 _Jean-François Alcover_, May 31 2016