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ЖУРНАЛЫ // Symmetry, Integrability and Geometry: Methods and Applications // Архив

SIGMA, 2009, том 5, 059, 31 стр. (Mi sigma405)

Эта публикация цитируется в 7 статьях

Basic Hypergeometric Functions as Limits of Elliptic Hypergeometric Functions

Fokko J. van de Bult, Eric M. Rains

MC 253-37, California Institute of Technology, 91125, Pasadena, CA, USA

Аннотация: 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 ${}_{10}\phi_9$'s and their Nassrallah–Rahman type integral representation.

Ключевые слова: elliptic hypergeometric functions, basic hypergeometric functions, transformation formulas.

MSC: 33D15

Поступила: 1 февраля 2009 г.; опубликована 10 июня 2009 г.

Язык публикации: английский

DOI: 10.3842/SIGMA.2009.059



Реферативные базы данных:
ArXiv: 0902.0621


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