Szeg\H{o} orthogonal polynomials with respect to an analytic weight:   canonical representation and strong asymptotics
  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. 
A. Martinez-Finkelshtein, K. T.-R. McLaughlin, and E. B. Saff