Yattselev, MaximBarhoumi, AhmadBleher, PavelIts, AlexanderTarasov, Vitaly2020-06-222020-06-222020-08https://hdl.handle.net/1805/23029http://dx.doi.org/10.7912/C2/2413Indiana University-Purdue University Indianapolis (IUPUI)We consider orthogonal polynomials P_n satisfying orthogonality relations where the measure of orthogonality is, in general, a complex-valued Borel measure supported on subsets of the complex plane. In our consideration we will focus on measures of the form d\mu(z) = \rho(z) dz where the function \rho may depend on other auxiliary parameters. Much of the asymptotic analysis is done via the Riemann-Hilbert problem and the Deift-Zhou nonlinear steepest descent method, and relies heavily on notions from logarithmic potential theory.en-USOrthogonal PolynomialsPadé ApproximantsRiemann–Hilbert ProblemThesis