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: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | Englisch |
| Veröffentlicht: |
Cambridge
Cambridge University Press
1999
|
| Schriftenreihe: | Encyclopedia of mathematics and its applications
volume 71 |
| Schlagwörter: | |
| Links: | https://doi.org/10.1017/CBO9781107325937 https://doi.org/10.1017/CBO9781107325937 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 |
| Beschreibung: | Title from publisher's bibliographic system (viewed on 05 Oct 2015) |
| Umfang: | 1 online resource (xvi, 664 pages) |
| ISBN: | 9781107325937 |
| DOI: | 10.1017/CBO9781107325937 |
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Datensatz im Suchindex
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| any_adam_object | |
| author | Andrews, George E. 1938- |
| author_facet | Andrews, George E. 1938- |
| author_role | aut |
| author_sort | Andrews, George E. 1938- |
| author_variant | g e a ge gea |
| building | Verbundindex |
| bvnumber | BV043940664 |
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| ctrlnum | (ZDB-20-CBO)CR9781107325937 (OCoLC)992905024 (DE-599)BVBBV043940664 |
| dewey-full | 515/.5 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515/.5 |
| dewey-search | 515/.5 |
| dewey-sort | 3515 15 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1017/CBO9781107325937 |
| format | Electronic eBook |
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| id | DE-604.BV043940664 |
| illustrated | Not Illustrated |
| indexdate | 2024-12-20T17:49:15Z |
| institution | BVB |
| isbn | 9781107325937 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-029349635 |
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| publishDate | 1999 |
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| series2 | Encyclopedia of mathematics and its applications |
| spelling | Andrews, George E. 1938- Verfasser aut Special functions George E. Andrews, Richard Askey, Ranjan Roy Cambridge Cambridge University Press 1999 1 online resource (xvi, 664 pages) txt rdacontent c rdamedia cr rdacarrier Encyclopedia of mathematics and its applications volume 71 Title from publisher's bibliographic system (viewed on 05 Oct 2015) 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 Functions, Special Orthogonale Polynome (DE-588)4172863-4 gnd rswk-swf Spezielle Funktion (DE-588)4182213-4 gnd rswk-swf Hypergeometrische Reihe (DE-588)4161061-1 gnd rswk-swf Gammafunktion (DE-588)4289118-8 gnd rswk-swf Bessel-Funktionen (DE-588)4069359-4 gnd rswk-swf Spezielle Funktion (DE-588)4182213-4 s 1\p DE-604 Hypergeometrische Reihe (DE-588)4161061-1 s DE-604 Bessel-Funktionen (DE-588)4069359-4 s Gammafunktion (DE-588)4289118-8 s Orthogonale Polynome (DE-588)4172863-4 s Askey, Richard Sonstige oth Roy, Ranjan 1948- Sonstige oth Erscheint auch als Druckausgabe 978-0-521-62321-6 Erscheint auch als Druckausgabe 978-0-521-78988-2 https://doi.org/10.1017/CBO9781107325937 Verlag URL des Erstveröffentlichers Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Andrews, George E. 1938- Special functions Functions, Special Orthogonale Polynome (DE-588)4172863-4 gnd Spezielle Funktion (DE-588)4182213-4 gnd Hypergeometrische Reihe (DE-588)4161061-1 gnd Gammafunktion (DE-588)4289118-8 gnd Bessel-Funktionen (DE-588)4069359-4 gnd |
| subject_GND | (DE-588)4172863-4 (DE-588)4182213-4 (DE-588)4161061-1 (DE-588)4289118-8 (DE-588)4069359-4 |
| 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 |
| topic | Functions, Special Orthogonale Polynome (DE-588)4172863-4 gnd Spezielle Funktion (DE-588)4182213-4 gnd Hypergeometrische Reihe (DE-588)4161061-1 gnd Gammafunktion (DE-588)4289118-8 gnd Bessel-Funktionen (DE-588)4069359-4 gnd |
| topic_facet | Functions, Special Orthogonale Polynome Spezielle Funktion Hypergeometrische Reihe Gammafunktion Bessel-Funktionen |
| url | https://doi.org/10.1017/CBO9781107325937 |
| work_keys_str_mv | AT andrewsgeorgee specialfunctions AT askeyrichard specialfunctions AT royranjan specialfunctions |