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- DescriptionContinued 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 polymials and combined the two subjects, and how Brouncker's formula of 1655 can be derived from Euler's efforts in Special Functions and Orthogonal Polymials. 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 Polymials, and very recent advances in Orthogonal Polymials 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.
- Author BiographySergey Khrushchev is a Professor in the Department of Mathematics at Atilim University, Turkey.
- Author(s)Sergey Khrushchev
- PublisherCambridge University Press
- Date of Publication24/07/2008
- Series TitleEncyclopedia of Mathematics and Its Applications
- Series Part/Volume NumberNo. 122
- Place of PublicationCambridge
- Country of PublicationUnited Kingdom
- ImprintCambridge University Press
- Content Note12 b/w illus. 180 exercises
- Weight870 g
- Width152 mm
- Height228 mm
- Spine27 mm
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