Analytic solutions of $q$-$P(A_1)$ near its critical points
Exactly Solvable and Integrable Systems
2016-11-23 v2
Abstract
For transcendental functions that solve non-linear -difference equations, the best descriptions available are the ones obtained by expansion near critical points at the origin and infinity. We describe such solutions of a -discrete Painlev\'e equation, with 7 parameters whose initial value space is a rational surface of type . The resultant expansions are shown to approach series expansions of the classical sixth Painlev\'e equation in the continuum limit.
Keywords
Cite
@article{arxiv.1510.07433,
title = {Analytic solutions of $q$-$P(A_1)$ near its critical points},
author = {Nalini Joshi and Pieter Roffelsen},
journal= {arXiv preprint arXiv:1510.07433},
year = {2016}
}