与分担值相关的正规族

设F为区域D上的亚纯函数族,a和b都是不为零的两个有穷复数(a/b不是正整数),若每个f∈F,f(z)=a(?)f^((k))(z)=a,且f-a的零点重级至少为k,当f((k))(z)=a,且f-a的零点重级至少为k,当f^((k))(z)=b时有|f(z)-a|≥ε,其中ε为正数.则F在区域D内正规.

Normal families related to shared values

Let $\F$ be a family of meromorphic functions on a domain
$D$, $a$ and $b$ be two nonzero finite complex numbers($\frac{a}{b}$
not positive integer). If for every $f \in \F$, $f(z) = a
\Rightarrow f^{(k)}(z) = a$, and the zeros multiplicity of $f - a$
is at least $k$, and $|f(z) - a| \geq \varepsilon$ ($\varepsilon >
0)$ whenever $f^{(k)}(z) = b$, then $\F$ is normal on $D$.