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Книга Orthogonal Polynomials and Continued Fractions Sergey Khrushchev

Orthogonal Polynomials and Continued Fractions

From Euler's Point of View

Автор: Sergey Khrushchev
Език: Английски език
Корици: С твърди корици
Издател: Cambridge University Press
Наличност: Външен склад
Изпращаме след 14-21 дни
194.80 € 381.00 лв
Continued fractions, studied since Ancient Greece, only became a powerful tool in the eighteenth cen...

Информация за книгата

Автор
Sergey Khrushchev
Език
Английски език
Корици
Книга - С твърди корици
Издадена
2008
страници
496
EAN
9780521854191
ISBN
0521854199
Enbook ID
02047230
Издател
Cambridge University Press
Теглоt
860
Размери
163 x 241 x 31

Пълно описание

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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