文件名称：Orthogonal Polynomials and Continued Fractions_ From Euler's Point of View
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正交多项式 连分数 连分式 欧拉 2008年
作者: Sergey Khrushchev 出版社: Cambridge University Press 副标题: From Euler's Point of View 出版年: 2008-7-24 页数: 496 定价: GBP 80.00 装帧: Hardcover ISBN: 9780521854191 内容简介 · · · · · · 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.