Skip to content
Register Sign in Wishlist

Orthogonal Polynomials and Painlevé Equations


Part of Australian Mathematical Society Lecture Series

  • Date Published: December 2017
  • availability: In stock
  • format: Paperback
  • isbn: 9781108441940

£ 32.99

Add to cart Add to wishlist

Other available formats:

Looking for an inspection copy?

This title is not currently available on inspection

Product filter button
About the Authors
  • 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.

    • Written by a leading expert in orthogonal polynomials
    • The first book to detail the interesting connections between Painlevé equations and orthogonal polynomials, an active area of research
    • Exercises throughout the book encourage the reader to get involved and get comfortable with the material
    Read more

    Customer reviews

    Not yet reviewed

    Be the first to review

    Review was not posted due to profanity


    , create a review

    (If you're not , sign out)

    Please enter the right captcha value
    Please enter a star rating.
    Your review must be a minimum of 12 words.

    How do you rate this item?


    Product details

    • Date Published: December 2017
    • format: Paperback
    • isbn: 9781108441940
    • length: 190 pages
    • dimensions: 228 x 152 x 12 mm
    • weight: 0.29kg
    • contains: 25 b/w illus.
    • availability: In stock
  • Table of Contents

    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

  • Author

    Walter Van Assche, Katholieke Universiteit Leuven, Belgium
    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.

Related Books

Sorry, this resource is locked

Please register or sign in to request access. If you are having problems accessing these resources please email

Register Sign in
Please note that this file is password protected. You will be asked to input your password on the next screen.

» Proceed

You are now leaving the Cambridge University Press website. Your eBook purchase and download will be completed by our partner Please see the permission section of the catalogue page for details of the print & copy limits on our eBooks.

Continue ×

Continue ×

Continue ×
warning icon

Turn stock notifications on?

You must be signed in to your Cambridge account to turn product stock notifications on or off.

Sign in Create a Cambridge account arrow icon

Find content that relates to you

Join us online

This site uses cookies to improve your experience. Read more Close

Are you sure you want to delete your account?

This cannot be undone.


Thank you for your feedback which will help us improve our service.

If you requested a response, we will make sure to get back to you shortly.

Please fill in the required fields in your feedback submission.