Orthogonal Polynomials and Painleve Equations
Published on 28. December 2017
978-1-108-59907-8 (ISBN)
Description
There are a number of intriguing connections between Painleve 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 Painleve equations appear in mathematical analysis very useful. Those interested in the asymptotic behavior of orthogonal polynomials will also find the description of Painleve transcendants and their use for local analysis near certain critical points helpful to their work. Rational solutions and special function solutions of Painleve 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 Painleve equations.
More details
Series
Language
English
Place of publication
Cambridge
United Kingdom
Target group
Professional and scholarly
Illustrations
Worked examples or Exercises; 25 Line drawings, black and white
File size
2,24 MB
ISBN-13
978-1-108-59907-8 (9781108599078)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Classification
Other editions
Additional editions
Walter van Assche
Orthogonal Polynomials and Painleve Equations
Book
12/2017
Cambridge University Press
€54.20
Shipment within 15-20 days
Person
Walter Van Assche is a professor of mathematics at the Katholieke Universiteit Leuven, Belgium, and presently the Chair of the SIAM Activity Group on Orthogonal Polynomials and Special Functions (OPSF). He is an expert in orthogonal polynomials, special functions, asymptotics, approximation, and recurrence relations.
Content
1. Introduction; 2. Freud weights and discrete Painleve I; 3. Discrete Painleve II; 4. Ladder operators; 5. Other semi-classical orthogonal polynomials; 6. Special solutions of Painleve equations; 7. Asymptotic behavior of orthogonal polynomials near critical points; Appendix. Solutions to exercises; References; Index.
