Orthogonal Polynomials and Continued Fractions: From Euler's Point of View
(Book #122 in the Encyclopedia of Mathematics and its Applications Series)
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Book Overview
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.
Format:Hardcover
Language:English
ISBN:0521854199
ISBN13:9780521854191
Release Date:May 2008
Publisher:Cambridge University Press
Length:496 Pages
Weight:1.85 lbs.
Dimensions:1.4" x 6.1" x 9.2"
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