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This article is cited in 7 scientific papers (total in 7 papers)
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
Abstract:
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.
Keywords:
elliptic hypergeometric functions, basic hypergeometric functions, transformation formulas.
Received: February 1, 2009; Published online June 10, 2009
Citation:
Fokko J. van de Bult, Eric M. Rains, “Basic Hypergeometric Functions as Limits of Elliptic Hypergeometric Functions”, SIGMA, 5 (2009), 059, 31 pp.
Linking options:
https://www.mathnet.ru/eng/sigma405 https://www.mathnet.ru/eng/sigma/v5/p59
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Abstract page: | 248 | Full-text PDF : | 56 | References: | 34 |
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