Elliptic hypergeometric functions associated with root systems
Classical Analysis and ODEs
2021-05-19 v3 Mathematical Physics
Combinatorics
math.MP
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).
Cite
@article{arxiv.1704.08406,
title = {Elliptic hypergeometric functions associated with root systems},
author = {Hjalmar Rosengren and S. Ole Warnaar},
journal= {arXiv preprint arXiv:1704.08406},
year = {2021}
}
Comments
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