Basic Hypergeometric Functions as Limits of Elliptic Hypergeometric Functions
We describe a uniform way of obtaining basic hypergeometric functions as limits of the elliptic beta integral. This description gives rise to the construction of a polytope with a different basic hypergeometric function attached to each face of this polytope. We can subsequently obtain various relat...
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| Дата: | 2009 |
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| Автори: | , |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут математики НАН України
2009
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| Назва видання: | Symmetry, Integrability and Geometry: Methods and Applications |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/149119 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Basic Hypergeometric Functions as Limits of Elliptic Hypergeometric Functions / F.J. van de Bult, E.M. Rains // Symmetry, Integrability and Geometry: Methods and Applications. — 2009. — Т. 5. — Бібліогр.: 18 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
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irk-123456789-1491192019-02-20T01:27:44Z Basic Hypergeometric Functions as Limits of Elliptic Hypergeometric Functions van de Bult, F.J. Rains, E.M. We describe a uniform way of obtaining basic hypergeometric functions as limits of the elliptic beta integral. This description gives rise to the construction of a polytope with a different basic hypergeometric function attached to each face of this polytope. We can subsequently obtain various relations, such as transformations and three-term relations, of these functions by considering geometrical properties of this polytope. The most general functions we describe in this way are sums of two very-well-poised 10φ9's and their Nassrallah-Rahman type integral representation. 2009 Article Basic Hypergeometric Functions as Limits of Elliptic Hypergeometric Functions / F.J. van de Bult, E.M. Rains // Symmetry, Integrability and Geometry: Methods and Applications. — 2009. — Т. 5. — Бібліогр.: 18 назв. — англ. 1815-0659 2000 Mathematics Subject Classification: 33D15 http://dspace.nbuv.gov.ua/handle/123456789/149119 en Symmetry, Integrability and Geometry: Methods and Applications Інститут математики НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| description |
We describe a uniform way of obtaining basic hypergeometric functions as limits of the elliptic beta integral. This description gives rise to the construction of a polytope with a different basic hypergeometric function attached to each face of this polytope. We can subsequently obtain various relations, such as transformations and three-term relations, of these functions by considering geometrical properties of this polytope. The most general functions we describe in this way are sums of two very-well-poised 10φ9's and their Nassrallah-Rahman type integral representation. |
| format |
Article |
| author |
van de Bult, F.J. Rains, E.M. |
| spellingShingle |
van de Bult, F.J. Rains, E.M. Basic Hypergeometric Functions as Limits of Elliptic Hypergeometric Functions Symmetry, Integrability and Geometry: Methods and Applications |
| author_facet |
van de Bult, F.J. Rains, E.M. |
| author_sort |
van de Bult, F.J. |
| title |
Basic Hypergeometric Functions as Limits of Elliptic Hypergeometric Functions |
| title_short |
Basic Hypergeometric Functions as Limits of Elliptic Hypergeometric Functions |
| title_full |
Basic Hypergeometric Functions as Limits of Elliptic Hypergeometric Functions |
| title_fullStr |
Basic Hypergeometric Functions as Limits of Elliptic Hypergeometric Functions |
| title_full_unstemmed |
Basic Hypergeometric Functions as Limits of Elliptic Hypergeometric Functions |
| title_sort |
basic hypergeometric functions as limits of elliptic hypergeometric functions |
| publisher |
Інститут математики НАН України |
| publishDate |
2009 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/149119 |
| citation_txt |
Basic Hypergeometric Functions as Limits of Elliptic Hypergeometric Functions / F.J. van de Bult, E.M. Rains // Symmetry, Integrability and Geometry: Methods and Applications. — 2009. — Т. 5. — Бібліогр.: 18 назв. — англ. |
| series |
Symmetry, Integrability and Geometry: Methods and Applications |
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AT vandebultfj basichypergeometricfunctionsaslimitsofelliptichypergeometricfunctions AT rainsem basichypergeometricfunctionsaslimitsofelliptichypergeometricfunctions |
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2025-07-12T21:24:40Z |
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2025-07-12T21:24:40Z |
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1837477907134414848 |