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Orthogonal polynomials and continued fractions : from Euler's point of view

Autor: S V Khrushchev
Editora: Cambridge : Cambridge University Press, 2008.
Séries: Encyclopedia of mathematics and its applications, 122.
Edição/Formato   Print book : InglêsVer todas as edições e formatos
Base de Dados:WorldCat
Resumo:
"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  Ler mais...
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Pessoa Denominada: Leonhard Euler; Leonhard Euler; Leonhard Euler
Tipo de Documento: Livro
Todos os Autores / Contribuintes: S V Khrushchev
ISBN: 9780521854191 0521854199
Número OCLC: 213400529
Descrição: xvi, 478 pages : illustrations ; 25 cm.
Conteúdos: Continued fractions: real numbers --
Continued fractions: algebra --
Continued fractions: analysis --
Continued fractions: Euler --
Continued fractions: Euler's influence --
P-fractions --
Orthogonal polynomials --
Orthogonal polynomials on the unit circle --
Appendix. Continued fractions, observations L. Euler (1739).
Título da Série: Encyclopedia of mathematics and its applications, 122.
Responsabilidade: Sergey Khrushchev.

Resumo:

Full account of Euler's work on continued fractions and orthogonal polynomials; illustrates the significance of his work on mathematics today.  Ler mais...

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'The range of themes covered is very wide ...' EMS Newsletter 'The author has done an admirable job of putting together historical anecdotes and excerpts from original sources with some deep and Ler mais...

 
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