Basic Hypergeometric Functions as Limits of Elliptic Hypergeometric Functions - van de Bult, F.J.; Rains, E.M. (Symmetry, Integrability and Geometry: Methods and Applications, 2009)
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 10φ9's and their Nassrallah-Rahman type integral representation.