Orthogonal Polynomials and Painlevé Equations
eBook - PDF

Orthogonal Polynomials and Painlevé Equations

  1. English
  2. PDF
  3. Available on iOS & Android
eBook - PDF

Orthogonal Polynomials and Painlevé Equations

About this book

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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Yes, you can access Orthogonal Polynomials and Painlevé Equations by Walter Van Assche in PDF and/or ePUB format, as well as other popular books in Mathematics & Mathematical Analysis. We have over one million books available in our catalogue for you to explore.

Table of contents

  1. Cover
  2. Half-title page
  3. Series page
  4. Title page
  5. Copyright page
  6. Contents
  7. Preface
  8. 1 Introduction
  9. 2 Freud weights and discrete Painlevé I
  10. 3 Discrete Painlevé II
  11. 4 Ladder operators
  12. 5 Other semi-classical orthogonal polynomials
  13. 6 Special solutions of Painlevé equations
  14. 7 Asymptotic behavior of orthogonal polynomials near critical points
  15. Appendix Solutions to the exercises
  16. References
  17. Index