Abstract
This is an introduction to the asymptotic analysis of orthogonal polynomials based on the steepest descent method for Riemann-Hilbert problems of Deift and Zhou. We consider in detail the polynomials that are orthogonal with respect to the modified Jacobi weight (1-x)α(1+x)β h(x) on [-1,1] where α, β > -1 and h is real analytic and positive on [-1,1]. These notes are based on joint work with Kenneth McLaughlin, Walter Van Assche and Maarten Vanlessen.
The author’s research was supported in part by FWO research project G.0176.02, INTAS project 2000-272, and by the Ministry of Science and Technology (MCYT) of Spain and the European Regional Development Fund (ERDF) through the grant BFM2001-3878-C02-02.
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Kuijlaars, A.B. (2003). Riemann-Hilbert Analysis for Orthogonal Polynomials. In: Koelink, E., Van Assche, W. (eds) Orthogonal Polynomials and Special Functions. Lecture Notes in Mathematics, vol 1817. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44945-0_5
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