The $q$-Dixon--Anderson integral and multi-dimensional $_1\psi_1$ summations
Complex Variables
2015-06-30 v2
Abstract
The Dixon--Anderson integral is a multi-dimensional integral evaluation fundamental to the theory of the Selberg integral. The summation is a bilateral generalization of the -binomial theorem. It is shown that a -generalization of the Dixon--Anderson integral, due to Evans, and multi-dimensional generalizations of the summation, due to Milne and Gustafson, can be viewed as having a common origin in the theory of -difference equations as expounded by Aomoto. Each is shown to be determined by a -difference equation of rank one, and a certain asymptotic behavior. In calculating the latter, essential use is made of the concepts of truncation, regularization and connection formulae.
Keywords
Cite
@article{arxiv.1308.6650,
title = {The $q$-Dixon--Anderson integral and multi-dimensional $_1\psi_1$ summations},
author = {Masahiko Ito and Peter J. Forrester},
journal= {arXiv preprint arXiv:1308.6650},
year = {2015}
}
Comments
36 pages. V2: minor corrections