Skip to content
Register Sign in Wishlist

Orthogonal Polynomials and Continued Fractions
From Euler's Point of View

£103.00

Part of Encyclopedia of Mathematics and its Applications

  • Date Published: July 2008
  • availability: Available
  • format: Hardback
  • isbn: 9780521854191

£ 103.00
Hardback

Add to cart Add to wishlist

Other available formats:
eBook


Looking for an inspection copy?

This title is not currently available on inspection

Description
Product filter button
Description
Contents
Resources
Courses
About the Authors
  • Continued fractions, studied since Ancient Greece, only became a powerful tool in the eighteenth century, in the hands of the great mathematician Euler. This book tells how Euler introduced the idea of orthogonal polynomials and combined the two subjects, and how Brouncker's formula of 1655 can be derived from Euler's efforts in Special Functions and Orthogonal Polynomials. The most interesting applications of this work are discussed, including the great Markoff's Theorem on the Lagrange spectrum, Abel's Theorem on integration in finite terms, Chebyshev's Theory of Orthogonal Polynomials, and very recent advances in Orthogonal Polynomials on the unit circle. As continued fractions become more important again, in part due to their use in finding algorithms in approximation theory, this timely book revives the approach of Wallis, Brouncker and Euler and illustrates the continuing significance of their influence. A translation of Euler's famous paper 'Continued Fractions, Observation' is included as an Addendum.

    • Considers the modern state of continued fractions and orthogonal polynomials from Euler's point of view, giving a full account of his work on the subject
    • Outlines Brouncker's formula; Euler's discoveries of the Gamma and Beta functions; Markoff's Theorem on the Lagrange spectrum and its relation with Jean Bernoulli sequences; Brouncker's method as a solution to Fermat's question on Pell's equation
    • Contains the first English translation of Euler's 'Continued Fractions, Observation', 1739, with comments relating it to Brouncker's proof
    Read more

    Reviews & endorsements

    'The range of themes covered is very wide …' EMS Newsletter

    'The author has done an admirable job of putting together historical anecdotes and excerpts from original sources with some deep and modern mathematics. The book is a pleasure to read for people interested in either orthogonal polynomials and continued fractions or the history of mathematics, and I imagine that any reader will walk away with a deeper appreciation of both.' Mathematical Reviews

    See more reviews

    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: July 2008
    • format: Hardback
    • isbn: 9780521854191
    • length: 496 pages
    • dimensions: 241 x 163 x 31 mm
    • weight: 0.86kg
    • contains: 12 b/w illus. 180 exercises
    • availability: Available
  • Table of Contents

    Preface
    1. Continued fractions: real numbers
    2. Continued fractions: Algebra
    3. Continued fractions: Analysis
    4. Continued fractions: Euler
    5. Continued fractions: Euler's Influence
    6. P-fractions
    7. Orthogonal polynomials
    8. Orthogonal polynomials on the unite circle
    A1. Continued fractions, Observations
    Bibliography
    Index.

  • Author

    Sergey Khrushchev, Atilim University, Ankara
    Sergey Khrushchev is a Professor in the Department of Mathematics at Atilim University, Turkey.

Sign In

Please sign in to access your account

Cancel

Not already registered? Create an account now. ×

Sorry, this resource is locked

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

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 www.ebooks.com. Please see the permission section of the www.ebooks.com catalogue page for details of the print & copy limits on our eBooks.

Continue ×

Continue ×

Continue ×

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.

Cancel

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.
×