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Orthogonal Polynomials and Painlevé Equations Vital Source e-bog
Walter Van Assche
(2017)
Cambridge University Press
451,00 kr.
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Orthogonal Polynomials and Painlevé Equations
Walter Van Assche
(2017)
Sprog: Engelsk
Cambridge University Press
459,00 kr.
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Detaljer om varen
- Vital Source searchable e-book (Reflowable pages)
- Udgiver: Cambridge University Press (December 2017)
- ISBN: 9781108608978
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.
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Bookshelf online: 5 år fra købsdato.
Bookshelf appen: ubegrænset dage fra købsdato.
Udgiveren oplyser at følgende begrænsninger er gældende for dette produkt:
Print: -1 sider kan printes ad gangen
Copy: højest -1 sider i alt kan kopieres (copy/paste)
Detaljer om varen
- Paperback: 190 sider
- Udgiver: Cambridge University Press (December 2017)
- ISBN: 9781108441940
There are a number of intriguing connections between Painlev 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 Painlev equations appear in mathematical analysis very useful. Those interested in the asymptotic behavior of orthogonal polynomials will also find the description of Painlev transcendants and their use for local analysis near certain critical points helpful to their work. Rational solutions and special function solutions of Painlev 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 Painlev equations.
1. Introduction;
2. Freud weights and discrete Painlevé I;
3. Discrete Painlevé II;
4. Ladder operators;
5. Other semi-classical orthogonal polynomials;
6. Special solutions of Painlevé equations;
7. Asymptotic behavior of orthogonal polynomials near critical points; Appendix. Solutions to exercises; References; Index.
2. Freud weights and discrete Painlevé I;
3. Discrete Painlevé II;
4. Ladder operators;
5. Other semi-classical orthogonal polynomials;
6. Special solutions of Painlevé equations;
7. Asymptotic behavior of orthogonal polynomials near critical points; Appendix. Solutions to exercises; References; Index.
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