与分担全纯函数相关的正规族

设F是在区域D内的一族亚纯函数,其零点重级至少为k,k是一个正整数,a(z)(≠0)在区域D内全纯.若对于任意的f∈F,有(1)f(z)与a(z)没有公共的零点;(2)f(z)=0f(k)(z)=a(z)■0|f~((k+1))(z)-a'(x)||a(z)|,则F在D内正规.

Normal Families and Shared Value of Holomorphic Function

Let $\F$ be a family of meromorphic functions in a domain $D$, all of whose zeros have multiplicity at least $k$ with $k$ being a positive integer, and $a(z)\ (\not\equiv 0)$ be a holomorphic function in $D$. If, for each $f \in \F$, (1) $f(z)$ and $a(z)$ have no common zeros; (2) $f(z) = 0 \Leftrightarrow f^{(k)}(z) = a(z) \Rightarrow 0 < |f^{(k+1)}(z) - a'(z)| < |a(z)|$, then $\F$ is normal in $D$.