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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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Date: | 2009 |
| Main Authors: | , |
| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2009
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/149119 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | 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. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862706487369924608 |
|---|---|
| author | van de Bult, F.J. Rains, E.M. |
| author_facet | van de Bult, F.J. Rains, E.M. |
| 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. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| 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.
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| first_indexed | 2025-12-07T17:00:19Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-149119 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-07T17:00:19Z |
| publishDate | 2009 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | van de Bult, F.J. Rains, E.M. 2019-02-19T17:30:57Z 2019-02-19T17:30:57Z 2009 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 https://nasplib.isofts.kiev.ua/handle/123456789/149119 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. This paper is a contribution to the Proceedings of the Workshop “Elliptic Integrable Systems, Isomonodromy Problems, and Hypergeometric Functions” (July 21–25, 2008, MPIM, Bonn, Germany). The second author was supported in part by NSF grant DMS-0833464. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Basic Hypergeometric Functions as Limits of Elliptic Hypergeometric Functions Article published earlier |
| spellingShingle | Basic Hypergeometric Functions as Limits of Elliptic Hypergeometric Functions van de Bult, F.J. Rains, E.M. |
| title | 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_short | Basic Hypergeometric Functions as Limits of Elliptic Hypergeometric Functions |
| title_sort | basic hypergeometric functions as limits of elliptic hypergeometric functions |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/149119 |
| work_keys_str_mv | AT vandebultfj basichypergeometricfunctionsaslimitsofelliptichypergeometricfunctions AT rainsem basichypergeometricfunctionsaslimitsofelliptichypergeometricfunctions |