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Orthogonal polynomials and continued fractions : from Euler's point of view /
"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 m...
| Clasificación: | Libro Electrónico |
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| Autor principal: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Cambridge :
Cambridge University Press,
2008.
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| Colección: | Encyclopedia of mathematics and its applications ;
122. |
| Temas: | |
| Acceso en línea: | Texto completo |
| Sumario: | "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 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."--Publisher's description |
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| Descripción Física: | 1 online resource (xvi, 478 pages) : illustrations |
| Bibliografía: | Includes bibliographical references and index. |
| ISBN: | 9781107089679 1107089670 9780511721403 0511721404 1139883267 9781139883269 1107101581 9781107101586 1107104041 9781107104044 1107095980 9781107095984 1107092892 9781107092891 |