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Symmetry, Integrability and Geometry: Methods and Applications, 2009, Volume 5, 059, 31 pp.
DOI: https://doi.org/10.3842/SIGMA.2009.059
(Mi sigma405)
 

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
Full-text PDF (406 kB) Citations (7)
References:
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
Bibliographic databases:
Document Type: Article
MSC: 33D15
Language: English
Citation: Fokko J. van de Bult, Eric M. Rains, “Basic Hypergeometric Functions as Limits of Elliptic Hypergeometric Functions”, SIGMA, 5 (2009), 059, 31 pp.
Citation in format AMSBIB
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\by Fokko J.~van de Bult, Eric M.~Rains
\paper Basic Hypergeometric Functions as Limits of Elliptic Hypergeometric Functions
\jour SIGMA
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  • This publication is cited in the following 7 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Symmetry, Integrability and Geometry: Methods and Applications
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