关键词: 正规族, 亚纯函数, 分担值, 微分多项式

Abstract:

Let F be a family of meromorphic function in a plane domain D, all of whose poles is of multiplicity k at least and zeros are of multiplicity s at least. Suppose that a and b are two complex numbers, a, b∈C, a≠0. If for every pair function f(z), g(z)∈F, f^(k)-af³ and g^(k)-ag³ share a value b, then F is normal in D, where s=3 as k=2, s=k as k≥3.

Key words: Normal family, Meromorphic function, Shared Value, Differential polynomial