Basic Hypergeometric Functions as Limits of Elliptic Hypergeometric Functions

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van de Bult, Fokko
Rains, Eric
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Abstract
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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.
Comment: v3: Proposition 4.3 corrected
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Mathematics - Classical Analysis and ODEs
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