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Basic Hypergeometric Functions as Limits of Elliptic Hypergeometric Functions
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- Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
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- Symmetry, Integrability and Geometry: Methods and Applications, 2009, том 5
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Basic Hypergeometric Functions as Limits of Elliptic Hypergeometric Functions
Інший ID:
2000 Mathematics Subject Classification: 33D15
Посилання:
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.
Підтримка:
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.
Дата:
2009
Переглядів:
502
Завантажень:
245
Анотація:
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.
