On Properties of meromorphic solutions of difference Painlevé I and II equation - Xue, Weimin; Teng, Yanmei (Global Journal of Mathematical Analysis, 2017)
In this paper, we investigate some properties of finite order transcendental meromorphic solutions of difference Painlev \(\)\acute{e}\) I and II equations, and obtain precise estimations of exponents of convergence of poles of difference \(\)Δ w(z)=w(z+1)-w(z)\) and divided difference \(\)\frac{Δ w(z)}{w(z)}\), and of fixed points of \(\)w(z+η)$ ($η\in \mathbb{C}\setminus\{0\}\)).