Published June 10, 2009
| Published
Journal Article
Open
Basic Hypergeometric Functions as Limits of Elliptic Hypergeometric Functions
- Creators
- van de Bult, Fokko J.
-
Rains, Eric M.
Chicago
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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 _10φ_9's and their Nassrallah-Rahman type integral representation.
Additional Information
The authors retain ownership of the copyright with respect to their papers published in SIGMA under the terms of the Creative Commons Attribution-NonCommercial-ShareAlike Licence. Received February 01, 2009; Published online June 10, 2009. 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 full collection is available at http://www.emis.de/journals/SIGMA/Elliptic-Integrable-Systems.html The second author was supported in part by NSF grant DMS-0833464.Attached Files
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Additional details
- Eprint ID
- 15634
- Resolver ID
- CaltechAUTHORS:20090904-142309890
- NSF
- DMS-0833464
- Created
-
2009-09-29Created from EPrint's datestamp field
- Updated
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2021-11-08Created from EPrint's last_modified field