On properties of meromorphic solutions for difference Painlevé equations

摘要

In this paper, we mainly investigate properties of finite order transcendental meromorphic solutions of difference Painlevé equations. If f is a finite order transcendental meromorphic solution of difference Painlevé equations, then we get some estimates of the order and the exponent of convergence of poles of Δ f ( z ) $Delta f(z)$ , where Δ f ( z ) = f ( z + 1 ) − f ( z ) $Delta f(z)=f(z+1)-f(z)$ .