Hypergeometric and Basic Hypergeometric Series and Integrals Associated with Root Systems

摘要

We give an overview of some of the main results from the theories ofhypergeometric and basic hypergeometric series and integrals associated withroot systems. In particular, we list a number of summations, transformationsand explicit evaluations for such multiple series and integrals. We concentrateon such results which do not directly extend to the elliptic level. This textis a provisional version of a chapter on hypergeometric and basichypergeometric series and integrals associated with root systems for volume 2of the new Askey--Bateman project which deals with "Multivariable specialfunctions".