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

0,2

Links

Table of n, a(n) for n=0..103.

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)

Formula

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

Example

0.075449947566161249931192722830629685479840751449484130392059402731...

Mathematica

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

Prog

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

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)).

Sequence in context: A334399 A066960 A061827 * A112407 A154195 A280870

Adjacent sequences: A273838 A273839 A273840 * A273842 A273843 A273844

Keyword

nonn,cons

Author

Jean-François Alcover, Jun 01 2016

Status

approved