A273841 - OEIS

%I #9 Aug 18 2024 09:37:44

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

%T 8,5,4,7,9,8,4,0,7,5,1,4,4,9,4,8,4,1,3,0,3,9,2,0,5,9,4,0,2,7,3,1,0,2,

%U 7,1,0,7,5,1,5,7,5,5,9,8,8,4,7,8,2,8,7,2,2,2,3,5,2,0,4,2,0,8,7,7,1,9,4,8

%N Decimal expansion the Bessel moment c(4,3) = Integral_{0..inf} x^3 K_0(x)^4 dx, where K_0 is the modified Bessel function of the second kind.

%H 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.

%H R. J. Mathar, <a href="http://vixra.org/abs/1606.0141">Some definite intgrals over a power multiplied by four modified Bessel functions</a> vixra:1606.0141 (2016) eq. (64)

%F c(4,3) = (7/32)*zeta(3) - 3/16.

%e 0.075449947566161249931192722830629685479840751449484130392059402731...

%t c[4, 3] = (7/32)*Zeta[3] - 3/16;

%t RealDigits[c[4, 3], 10, 103][[1]]

%o (PARI) zeta(3)*7/32-3/16 \\ _Charles R Greathouse IV_, Oct 23 2023

%Y Cf. A273816 (c(3,0)), A273817 (c(3,1)), A273818 (c(3,2)), A273819 (c(3,3)), A273839 (c(4,0)), A233091 (c(4,1)), A273840 (c(4,2)).

%K nonn,cons

%O 0,2

%A _Jean-François Alcover_, Jun 01 2016