  In this paper we compute the asymptotic behavior of the recurrence
coefficients for polynomials orthogonal with respect to a logarithmic weight
$w(x){\rm d}x = \log \frac{2k}{1-x}{\rm d}x$ on $(-1,1)$, $k > 1$, and verify a
conjecture of A.&nbsp;Magnus for these coefficients. We use
Riemann-Hilbert/steepest-descent methods, but not in the standard way as there
is no known parametrix for the Riemann-Hilbert problem in a neighborhood of the
logarithmic singularity at $x=1$.
