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

Auteur : S V Khrushchev
Éditeur : Cambridge : Cambridge University Press, 2008.
Collection : Encyclopedia of mathematics and its applications, 122.
Édition/format :   Livre imprimé : EnglishVoir toutes les éditions et tous les formats
Base de données :WorldCat
Résumé :
"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  Lire la suite...
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Détails

Personne nommée : Leonhard Euler; Leonhard Euler; Leonhard Euler
Format : Book
Tous les auteurs / collaborateurs : S V Khrushchev
ISBN : 9780521854191 0521854199
Numéro OCLC : 213400529
Description : xvi, 478 pages : illustrations ; 25 cm.
Contenu : 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).
Titre de collection : Encyclopedia of mathematics and its applications, 122.
Responsabilité : Sergey Khrushchev.

Résumé :

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

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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 Lire la suite...

 
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