Study of $q$-Garnier system by Pad\'e method
Exactly Solvable and Integrable Systems
2016-08-24 v3 Mathematical Physics
Classical Analysis and ODEs
math.MP
Abstract
We give a simple form of the evolution equation and a scalar Lax pair for the -Garnier system. Some reductions to the -Painlev\'e equations and the autonomous case as a generalized QRT system are discussed. Using two kinds of Pad\'e problems on differential grid and -grid, we derive some special solutions of the -Garnier system in terms of the -Appell Lauricella function and the generalized -hypergeometric function.
Cite
@article{arxiv.1601.01099,
title = {Study of $q$-Garnier system by Pad\'e method},
author = {Hidehito Nagao and Yasuhiko Yamada},
journal= {arXiv preprint arXiv:1601.01099},
year = {2016}
}
Comments
21 pages