Special functions:
Special functions, natural generalizations of the elementary functions, have been studied for centuries. The greatest mathematicians, among them Euler, Gauss, Legendre, Eisenstein, Riemann, and Ramanujan, have laid the foundations for this beautiful and useful area of mathematics. This treatise pres...
Gespeichert in:
| Beteilige Person: | |
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| Weitere beteiligte Personen: | , |
| Format: | E-Book |
| Sprache: | Englisch |
| Veröffentlicht: |
Cambridge
Cambridge University Press
1999
|
| Schriftenreihe: | Encyclopedia of mathematics and its applications
volume 71 |
| Links: | https://doi.org/10.1017/CBO9781107325937 |
| Zusammenfassung: | Special functions, natural generalizations of the elementary functions, have been studied for centuries. The greatest mathematicians, among them Euler, Gauss, Legendre, Eisenstein, Riemann, and Ramanujan, have laid the foundations for this beautiful and useful area of mathematics. This treatise presents an overview of special functions, focusing primarily on hypergeometric functions and the associated hypergeometric series, including Bessel functions and classical orthogonal polynomials, using the basic building block of the gamma function. In addition to relatively new work on gamma and beta functions, such as Selberg's multidimensional integrals, many important but relatively unknown nineteenth century results are included. Other topics include q-extensions of beta integrals and of hypergeometric series, Bailey chains, spherical harmonics, and applications to combinatorial problems. The authors provide organizing ideas, motivation, and historical background for the study and application of some important special functions. This clearly expressed and readable work can serve as a learning tool and lasting reference for students and researchers in special functions, mathematical physics, differential equations, mathematical computing, number theory, and combinatorics. |
| Umfang: | 1 Online-Ressource (xvi, 664 Seiten) |
| ISBN: | 9781107325937 |
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| 100 | 1 | |a Andrews, George E. |d 1938- | |
| 245 | 1 | 0 | |a Special functions |c George E. Andrews, Richard Askey, Ranjan Roy |
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| 520 | |a Special functions, natural generalizations of the elementary functions, have been studied for centuries. The greatest mathematicians, among them Euler, Gauss, Legendre, Eisenstein, Riemann, and Ramanujan, have laid the foundations for this beautiful and useful area of mathematics. This treatise presents an overview of special functions, focusing primarily on hypergeometric functions and the associated hypergeometric series, including Bessel functions and classical orthogonal polynomials, using the basic building block of the gamma function. In addition to relatively new work on gamma and beta functions, such as Selberg's multidimensional integrals, many important but relatively unknown nineteenth century results are included. Other topics include q-extensions of beta integrals and of hypergeometric series, Bailey chains, spherical harmonics, and applications to combinatorial problems. The authors provide organizing ideas, motivation, and historical background for the study and application of some important special functions. This clearly expressed and readable work can serve as a learning tool and lasting reference for students and researchers in special functions, mathematical physics, differential equations, mathematical computing, number theory, and combinatorics. | ||
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| spelling | Andrews, George E. 1938- Special functions George E. Andrews, Richard Askey, Ranjan Roy Cambridge Cambridge University Press 1999 1 Online-Ressource (xvi, 664 Seiten) txt c cr Encyclopedia of mathematics and its applications volume 71 Special functions, natural generalizations of the elementary functions, have been studied for centuries. The greatest mathematicians, among them Euler, Gauss, Legendre, Eisenstein, Riemann, and Ramanujan, have laid the foundations for this beautiful and useful area of mathematics. This treatise presents an overview of special functions, focusing primarily on hypergeometric functions and the associated hypergeometric series, including Bessel functions and classical orthogonal polynomials, using the basic building block of the gamma function. In addition to relatively new work on gamma and beta functions, such as Selberg's multidimensional integrals, many important but relatively unknown nineteenth century results are included. Other topics include q-extensions of beta integrals and of hypergeometric series, Bailey chains, spherical harmonics, and applications to combinatorial problems. The authors provide organizing ideas, motivation, and historical background for the study and application of some important special functions. This clearly expressed and readable work can serve as a learning tool and lasting reference for students and researchers in special functions, mathematical physics, differential equations, mathematical computing, number theory, and combinatorics. Askey, Richard Roy, Ranjan 1948- Erscheint auch als Druck-Ausgabe 9780521623216 Erscheint auch als Druck-Ausgabe 9780521789882 |
| spellingShingle | Andrews, George E. 1938- Special functions |
| title | Special functions |
| title_auth | Special functions |
| title_exact_search | Special functions |
| title_full | Special functions George E. Andrews, Richard Askey, Ranjan Roy |
| title_fullStr | Special functions George E. Andrews, Richard Askey, Ranjan Roy |
| title_full_unstemmed | Special functions George E. Andrews, Richard Askey, Ranjan Roy |
| title_short | Special functions |
| title_sort | special functions |
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