与分担函数相关的亚纯函数的正规性

刘克笑

(怀化学院预科部,湖南怀化 418008)

与分担函数相关的亚纯函数的正规性

刘克笑

(怀化学院预科部,湖南怀化 418008)

设为定义在区域D内的一族亚纯函数,a(z)和b(z)为两个在D满足a(z)≠b(z)和a(z)≠b(k)(z)以及a(z)¢a′(z)的全纯函数,若对于任意的f∈,f(z)-a(z)的零点重级至少是k,f(z)和f(k)(z)分担a(z),且当f(z)=b(z)时,f(k)(z)=b(z),那么在D内正规.

亚纯函数; 正规族; 分担函数

1 引言及主要结论

3 定理的证明

这表明ξ0的个数是有限的即g(ξ)=0的零点是有限的,但从(9)可知g(ξ)=0有无限个零点1矛盾1

于是完成了定理的证明.

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Abstract:Letbe a familyof meromorphic functions on the plain domainD,a(z)andb(z)beholomorphic functions inD such thata(z)≠b(z)anda(z)≠b(k)(z)anda(z)¢a′(z)1If for everyf∈,the zeros off(z)-a(z)are of multiplicity at leastk,f(z)andf(k)(z)sharea(z),andf(z)=b(z)]f(k)(z)=b(z),thenis normal onD1

Key words:meromorphic function; normal family; shared function

Normal Families of Meromorphic Functions Concerning Shared Functions

LIU Ke-xiao
(Preparatory Department,Huaihua University,Huaihua,Hunan 418008)

O174152

A

1671-9743(2011)02-0011-05

2010-12-21

刘克笑(1973-),男,湖南辰溪人,怀化学院讲师,硕士,主要研究复分析1