# Hypergeometric and basic hypergeometric series and integrals associated with root systems

## TL;DR

This paper reviews key results in hypergeometric and basic hypergeometric series and integrals related to root systems, focusing on summations, transformations, and evaluations that do not extend to elliptic cases.

## Contribution

It compiles and discusses main results on hypergeometric series and integrals associated with root systems, serving as a chapter for the Askey–Bateman project.

## Key findings

- List of summations and transformations
- Explicit evaluations of multiple series and integrals
- Focus on results not extending to elliptic level

## 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".