Orthogonal Polynomials and Continued Fractions 在线电子书 pdf 下载 txt下载 epub 下载 mobi 下载 2024

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Sergey Khrushchev 作者

Cambridge University Press

译者

2008-7-24 出版日期

496 页数

GBP 80.00 价格

Hardcover

丛书系列

9780521854191 图书编码

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Orthogonal Polynomials and Continued Fractions 在线电子书 epub 下载 mobi 下载 pdf 下载 txt 下载 2024

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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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