與分擔函數(shù)相關的亞純函數(shù)的正規(guī)性

劉克笑

(懷化學院預科部,湖南懷化 418008)

與分擔函數(shù)相關的亞純函數(shù)的正規(guī)性

劉克笑

(懷化學院預科部,湖南懷化 418008)

設為定義在區(qū)域D內的一族亞純函數(shù),a(z)和b(z)為兩個在D滿足a(z)≠b(z)和a(z)≠b(k)(z)以及a(z)￠a′(z)的全純函數(shù),若對于任意的f∈,f(z)-a(z)的零點重級至少是k,f(z)和f(k)(z)分擔a(z),且當f(z)=b(z)時,f(k)(z)=b(z),那么在D內正規(guī).

亞純函數(shù); 正規(guī)族; 分擔函數(shù)

1 引言及主要結論

3 定理的證明

這表明ξ0的個數(shù)是有限的即g(ξ)=0的零點是有限的,但從(9)可知g(ξ)=0有無限個零點1矛盾1

于是完成了定理的證明.

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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

劉克笑(1973-),男,湖南辰溪人,懷化學院講師,碩士,主要研究復分析1