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Orthogonal Polynomials and Painlevé Equations

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Orthogonal Polynomials and Painlevé Equations Synopsis

There are a number of intriguing connections between Painlevé equations and orthogonal polynomials, and this book is one of the first to provide an introduction to these. Researchers in integrable systems and non-linear equations will find the many explicit examples where Painlevé equations appear in mathematical analysis very useful. Those interested in the asymptotic behavior of orthogonal polynomials will also find the description of Painlevé transcendants and their use for local analysis near certain critical points helpful to their work. Rational solutions and special function solutions of Painlevé equations are worked out in detail, with a survey of recent results and an outline of their close relationship with orthogonal polynomials. Exercises throughout the book help the reader to get to grips with the material. The author is a leading authority on orthogonal polynomials, giving this work a unique perspective on Painlevé equations.

About This Edition

ISBN: 9781108441940
Publication date: 28th December 2017
Author: Walter (Katholieke Universiteit Leuven, Belgium) Van Assche
Publisher: Cambridge University Press
Format: Paperback
Pagination: 190 pages
Series: Australian Mathematical Society Lecture Series
Genres: Calculus and mathematical analysis
Functional analysis and transforms
Number systems
Differential calculus and equations