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Orthogonal polynomials and continued fractions : from Euler's point of view

Author: S V Khrushchev
Publisher: Cambridge : Cambridge University Press, 2008.
Series: Encyclopedia of mathematics and its applications, 122.
Edition/Format:   Book : EnglishView all editions and formats
Database:WorldCat
Summary:
"This new and exciting historical book tells how Euler introduced the idea of orthogonal polynomials and how he combined them with continued fractions, as well as 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  Read more...
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Named Person: Leonhard Euler
Document Type: Book
All Authors / Contributors: S V Khrushchev
ISBN: 9780521854191 0521854199
OCLC Number: 213400529
Description: xvi, 478 p. : ill. ; 25 cm.
Contents: Continued fractions: real numbers --
Continued fractions: algebra --
Continued fractions: analysis --
Continued fractions: Euler --
Continued fractions: Euler's influence --
P-fractions --
Orthogonal polynomials --
Orthogonal polynomials on the unit circle --
Appendix. Continued fractions, observations L. Euler (1739).
Series Title: Encyclopedia of mathematics and its applications, 122.
Responsibility: Sergey Khrushchev.

Abstract:

Full account of Euler's work on continued fractions and orthogonal polynomials; illustrates the significance of his work on mathematics today.  Read more...

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'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 Read more...

 
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schema:description""This new and exciting historical book tells how Euler introduced the idea of orthogonal polynomials and how he combined them with continued fractions, as well as 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."--Publisher's description."
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