Orthogonal Polynomials and Continued Fractions - From Euler's Point of View (Hardcover, New)

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.

General

Imprint:	Cambridge UniversityPress
Country of origin:	United Kingdom
Series:	Encyclopedia of Mathematics and its Applications
Release date:	July 2008
First published:	2008
Authors:	Sergey Khrushchev
Dimensions:	241 x 163 x 31mm (L x W x T)
Format:	Hardcover
Pages:	496
Edition:	New
ISBN-13:	978-0-521-85419-1
Categories:	Books > Science & Mathematics > Mathematics > Calculus & mathematical analysis > Vector & tensor analysis
LSN:	0-521-85419-9
Barcode:	9780521854191

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