涉及一个微分多项式分担值的正规定则  

A Criterion for Meromorphic Functions Related to One of Its Differential Polynomials Sharing a Non-zero Value

作　　者：鲍文竹[1] 张兆迎[1] 

机构地区：[1]成都信息工程学院数学学院,四川成都610225

出　　处：《成都信息工程学院学报》2010年第2期210-212,共3页Journal of Chengdu University of Information Technology

摘　　要：应用正规族理论及Zalcman引理,推广了Yuntong Li和Yongxing Gu一个亚纯函数正规性的定理,得到了下面的定理,即:设F为复平面上一区域D上的亚纯函数族,k,n k+2为正整数,a为非零有穷复数,L(fn)的表达式为a0(fn)(k)+a1(fn)(k-1)+…+ak(fn),其中a0≠0,a1,…,ak为复数,对任意的f,g∈F,L(fn),L(gn)在D内分担a,则F在D上正规.In this paper, we mainly apply the theory of normal family and Zalcman＇s lemmas, and promote a theorem ＂on normal families of meromorphic functions＂, which promoted by Yuntong Li and Yongxing Gu. So we obtain the following result, that is： Let ~rbe a family of meromorphic functions defined on a domain D in the complex plane, k and n^k ＋ 2 be positive integers and a be a non-zero finite complex number. Denoting L （ff）＇s expression is a0 （f）（k） ＋ al （ff）（k- 1） ＋ ... ＋ ak （F）, where a0≠0,al ,＂＂ ,ak are finite complex numbers. Suppose that L （fn） and L（gn） share ＂a＂ on D for any f and g in：T, Then F is a normal family on D.

关 键 词：基础数学 函数论 亚纯函数 分担值 正规族 

分 类 号：O174.52[理学—数学]