
Orthogonal Polynomials and Continued Fractions
From Euler's Point of View
Sergey Khrushchev(Author)
Cambridge University Press
Published on 24. July 2008
Book
Hardback
496 pages
978-0-521-85419-1 (ISBN)
Description
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.
Reviews / Votes
'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 ReviewsMore details
Series
Language
English
Place of publication
Cambridge
United Kingdom
Target group
Professional and scholarly
Illustrations
Worked examples or Exercises; 12 Line drawings, unspecified
Dimensions
Height: 240 mm
Width: 161 mm
Thickness: 31 mm
Weight
904 gr
ISBN-13
978-0-521-85419-1 (9780521854191)
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Schweitzer Classification
Other editions
Additional editions

E-Book
04/2011
1st Edition
Cambridge University Press
€121.99
Available for download
Person
Sergey Khrushchev is a Professor in the Department of Mathematics at Atilim University, Turkey.
Content
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.