arXiv:1608.04513 Abstract | arXiv Analytics

arXiv:1608.04513 [math.CA]Abstract References Reviews Resources

Asymptotics of orthogonal polynomials and the Painlevé transcendents

Published 2016-08-16Version 1

In this survey, we review asymptotic results of some orthogonal polynomials which are relate to the Painlev\'e transcendents. They are obtained by applying Deift-Zhou's nonlinear steepest descent method for Riemann-Hilbert problems. In the last part of this article, we list several open problems.

Comments: 22 pages, 2 figures

Categories: math.CA

Subjects: 33E17, 34M55, 41A60

Keywords: orthogonal polynomials, transcendents, deift-zhous nonlinear steepest descent method, applying deift-zhous nonlinear steepest descent, review asymptotic results

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