A273840 Decimal expansion the Bessel moment c(4,2) = Integral_{0..inf} x^2 K_0(x)^4 dx, where K_0 is the modified Bessel function of the second kind.

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

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.

Formula

c(4,2) = (Pi^4/64)*(4 * 4F3(1/2, 1/2, 1/2, 1/2; 1, 1, 1; 1) - 3 * 4F3(1/2, 1/2, 1/2, 1/2; 2, 1, 1; 1)) - 3*Pi^2/16, where 4F3 is the generalized hypergeometric function.

Example

0.195770625247287917217458083275577237418827896966525028197933846...

Mathematica

c[4, 2] = (Pi^4/64)*(4*HypergeometricPFQ[{1/2, 1/2, 1/2, 1/2}, {1, 1, 1}, 1] - 3*HypergeometricPFQ[{1/2, 1/2, 1/2, 1/2}, {2, 1, 1}, 1]) - 3*Pi^2 / 16;
RealDigits[c[4, 2], 10, 104][[1]]

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)), A273841 (c(4,3)).

Sequence in context: A011259 A376330 A155754 * A117019 A155692 A011203

Adjacent sequences: A273837 A273838 A273839 * A273841 A273842 A273843

Keyword

nonn,cons

Author

Jean-François Alcover, Jun 01 2016

Status

approved