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
Examples
0.195770625247287917217458083275577237418827896966525028197933846...
Links
- David H. Bailey, Jonathan M. Borwein, David Broadhurst and M. L. Glasser, Elliptic integral evaluations of Bessel moments, arXiv:0801.0891.
Crossrefs
Programs
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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]]
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.