A First Order $q$-Difference System for the $BC_1$-Type Jackson Integral and Its Applications
Classical Analysis and ODEs
2009-04-06 v1
Abstract
We present an explicit expression for the -difference system, which the -type Jackson integral (-series) satisfies, as first order simultaneous -difference equations with a concrete basis. As an application, we give a simple proof for the hypergeometric summation formula introduced by Gustafson and the product formula of the -integral introduced by Nassrallah-Rahman and Gustafson.
Keywords
Cite
@article{arxiv.0904.0561,
title = {A First Order $q$-Difference System for the $BC_1$-Type Jackson Integral and Its Applications},
author = {Masahiko Ito},
journal= {arXiv preprint arXiv:0904.0561},
year = {2009}
}