A273841 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.

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, 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, 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

Offset: 0

Author

Jean-François Alcover, Jun 01 2016

Keywords

• nonn
• cons

Examples

			0.075449947566161249931192722830629685479840751449484130392059402731...
		

Links

• David H. Bailey, Jonathan M. Borwein, David Broadhurst and M. L. Glasser, Elliptic integral evaluations of Bessel moments, arXiv:0801.0891.
• R. J. Mathar, Some definite intgrals over a power multiplied by four modified Bessel functions vixra:1606.0141 (2016) eq. (64)

Crossrefs

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)).

Programs

Mathematica

c[4, 3] = (7/32)*Zeta[3] - 3/16;
RealDigits[c[4, 3], 10, 103][[1]]

PARI

zeta(3)*7/32-3/16 \\ Charles R Greathouse IV, Oct 23 2023

Formula

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