Basic Hypergeometric Functions as Limits of Elliptic Hypergeometric Functions

Details Basic Hypergeometric Functions as Limits of Elliptic Hypergeometric Functions Basic Hypergeometric Functions as Limits of Elliptic Hypergeometric Functions

2009-02-03

arxiv.org/abs/0902.0621v2

SIGMA 5 (2009), 059, 31 pages

Mathematics

Classical Analysis and ODEs

3 figures

Scientific paper

10.3842/SIGMA.2009.059

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.

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