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Encyclopedia of Mathematics and Its Applications Ser.: Orthogonal Polynomials and Continued Fractions : From Euler's Point of View by Sergey Khrushchev (2008, Hardcover)

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Orthogonal Polynomials and Continued Fractions : From Euler's Point of View, Hardcover by Khrushchev, Sergey, ISBN 0521854199, ISBN-13 9780521854191, Brand New, Free shipping in the US Full account of Euler's work on continued fractions and orthogonal polynomials; illustrates the significance of his work on mathematics today.

About this product

Product Identifiers

Publisher
Cambridge University Press
ISBN-10
0521854199
ISBN-13
9780521854191
eBay Product ID (ePID)
65857714

Product Key Features

Number of Pages
496 Pages
Language
English
Publication Name
Orthogonal Polynomials and Continued Fractions : from Euler's Point of View
Subject
Mathematical Analysis, Science & Technology
Publication Year
2008
Type
Textbook
Author
Sergey Khrushchev
Subject Area
Mathematics, Biography & Autobiography
Series
Encyclopedia of Mathematics and Its Applications Ser.
Format
Hardcover

Dimensions

Item Height
1.2 in
Item Weight
30.5 Oz
Item Length
9.5 in
Item Width
6.4 in

Additional Product Features

Intended Audience
Scholarly & Professional
Reviews
'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, "The resulting book is a pleasure to read for people interested in either the topic of orthogonal polynomials and continued fractions or for historians of mathematics, and I imagine that any reader will walk away with a deeper appreciation of both." Darren Glass, MAA Reviews, "The mathematics contained in this book is both beautiful and difficult. 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." Leonid B. Golinskii, Mathematical Reviews
Dewey Edition
22
Series Volume Number
Series Number 122
Illustrated
Yes
Dewey Decimal
515.55
Table Of 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.
Synopsis
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., This book tells how continued fractions, studied even in Ancient Greece, only became a powerful tool in the hands of Euler, how he introduced the idea of orthogonal polynomials and combined the two subjects. The approach of Wallis, Brouncker and Euler is revived to illustrate its continuing significance on mathematics today., 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.
LC Classification Number
QA404.5

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Encyclopedia of Mathematics and Its Applications Ser.: Orthogonal Polynomials and Continued Fractions : From Euler's Point of View by Sergey Khrushchev (2008, Hardcover)

About this product

Product Identifiers

Product Key Features

Dimensions

Additional Product Features

All listings for this product

item 1 New Race Politics in America: Understand..., Junn, Jane

item 2 Orthogonal Polynomials and Continued Fractions : From Euler's Point of View, ...

item 3 Orthogonal Polynomials and Continued Fractions : From Euler's Point of View, ...

item 4 Orthogonal Polynomials and Continued Fractions: From Euler's Point of View: New

item 5 Sergey Khrushch Orthogonal Polynomials and Continued Frac (Hardback) (UK IMPORT)

item 6 Orthogonal Polynomials and Continued Fractions: From Euler's Point of View by Se

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