  We provide a representation in terms of certain canonical functions for a
sequence of polynomials orthogonal with respect to a weight that is strictly
positive and analytic on the unit circle. These formulas yield a complete
asymptotic expansion for these polynomials, valid uniformly in the whole
complex plane. As a consequence, we obtain some results about the distribution
of zeros of these polynomials. The main technique is the steepest descent
analysis of Deift and Zhou, based on the matrix Riemann-Hilbert
characterization proposed by Fokas, Its and Kitaev.

Classical Analysis and ODEs;Complex Variables