Asymptotics of polynomials orthogonal with respect to a logarithmic weight

In this talk we show how to compute the asymptotic behavior of the recurrence coefficients for polynomials orthogonal with respect to a logarithmic weight w(x)dx = [log 2k/(1-x)] dx on (-1; 1), k > 1, and verify a conjecture of A. 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. This is joint work with Oliver Conway.Non UBCUnreviewedAuthor affiliation: New York UniversityFacult