Michael J. Schlosser
Published 2017-05-25Version 1
We give an overview of some of the main results from the theories of hypergeometric and basic hypergeometric series and integrals associated with root systems. In particular, we list a number of summations, transformations and explicit evaluations for such multiple series and integrals. We concentrate on such results which do not directly extend to the elliptic level. This text is a provisional version of a chapter on hypergeometric and basic hypergeometric series and integrals associated with root systems for volume 2 of the new Askey--Bateman project which deals with "Multivariable special functions".
Comments: 38 pages; modulo minor edits this text will appear as a chapter in the book "Multivariable Special Functions" (edited by Tom Koornwinder and Jasper Stokman) which is part of the new Askey-Bateman project
Limits of Bessel functions for root systems as the rank tends to infinity
Expansion formulas for multiple basic hypergeometric series over root systems
Elliptic hypergeometric series on root systems
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