Elliptic hypergeometric functions associated with root systems

Abstract

We give a survey of elliptic hypergeometric functions associated with root systems, comprised of three main parts. The first two form in essence an annotated table of the main evaluation and transformation formulas for elliptic hypergeometric integeral and series on root systems. The third and final part gives an introduction to Rains' elliptic Macdonald-Koornwinder theory (in part also developed by Coskun and Gustafson).

28 pages. Modulo minor edits this paper will appear as a chapter in the book "Multivariable Special Functions" (edited by Tom Koornwinder and Jasper Stokman) which is part of the Askey-Bateman project. This version: essential correction of equation (1.2.14) and some further minor corrections

References in corpus (3)

• Elliptic hypergeometric sum/integral transformations and supersymmetric lens index
• Theta Functions, Elliptic Hypergeometric Series, and Kawanaka's Macdonald Polynomial Conjecture
• Gustafson-Rakha-Type Elliptic Hypergeometric Series

Cited by in corpus (7)

• AFLT-type Selberg integrals
• Multidimensional Matrix Inversions and Elliptic Hypergeometric Series on Root Systems
• An Elliptic Hypergeometric Function Approach to Branching Rules
• Introduction to the theory of elliptic hypergeometric integrals
• The Hyperbolic Asymptotics of Elliptic Hypergeometric Integrals Arising in Supersymmetric Gauge Theory
• Further study on elliptic interpolation formulas for the elliptic Askey-Wilson polynomials and allied identities
• A duality formula between elliptic determinants