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

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ISBN-10: 0521854199

ISBN-13: 9780521854191

Edition: 2008

Authors: Sergey Khrushchev

List price: $170.00
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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.
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Book details

List price: $170.00
Copyright year: 2008
Publisher: Cambridge University Press
Publication date: 7/24/2008
Binding: Hardcover
Pages: 496
Size: 6.25" wide x 9.50" long x 1.25" tall
Weight: 1.870
Language: English

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

Preface
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 unite circle
Continued fractions, Observations
Bibliography
Index