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Orthogonal polynomials and Painlevé equations

Author: Walter Van Assche
Publisher: Cambridge : Cambridge University Press, 2018. ©2018
Series: Australian Mathematical Society lecture series, 27.
Edition/Format:   eBook : Document : EnglishView all editions and formats
Summary:
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  Read more...
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Genre/Form: Electronic books
Additional Physical Format: Print version:
Assche, Walter van, 1958-
Orthogonal polynomials and Painlevé equations.
Cambridge, United Kingdom ; New York, NY : Cambridge University Press, 2018
(DLC) 2017053332
(OCoLC)1004922287
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Walter Van Assche
ISBN: 9781108644860 1108644864
OCLC Number: 1019662820
Description: 1 online resource (xii, 179 pages).
Contents: Introduction --
Freud weights and discrete Painlevé I --
Discrete Painlevé II --
Ladder operators --
Other semi-classical orthogonal polynomials --
Special solutions of Painlevé equations --
Asymptotic behavior of orthogonal polynomials near critical points.
Series Title: Australian Mathematical Society lecture series, 27.
Responsibility: Walter van Assche, Katholieke Universiteit Leuven, Belgium.

Abstract:

The first detailed account of the relationships between Painleve equations and orthogonal polynomials. It gives clear examples as well as proofs, and there are exercises throughout to help the reader  Read more...

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