Hypergeometric and basic hypergeometric series and integrals associated with root systems

2017/05/25 by Schlosser, Michael J.
#33C67 #33D52 (Secondary) #33D67 (Primary) #Classical Analysis and ODEs (math.CA) #Combinatorics (math.CO) #FOS: Mathematics #Quantum Algebra (math.QA)

paper · doi:10.48550/arxiv.1705.09221

Abstract

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".

Related

• Elliptic hypergeometric series on root systems
• Expansion formulas for multiple basic hypergeometric series over root systems
• Factorization of Basic Hypergeometric Series
• Special values of the hypergeometric series
• Proof of a summation formula for an A_n basic hypergeometric series conjectured by Warnaar