涉及导函数与分担亚纯函数的正规定则  

Normal criteria concerning derivative functions and shared meromorphic functions

作　　者：陈巧玉 戚建明 童东兵[3] CHEN Qiao-yu;QI Jian-ming;TONG Dong-bing(School of Statistics and Mathematics,Shanghai Lixin University of Accounting and Finance,Shanghai 201620,China;College of Arts and Sciences,Shanghai Dianji University,Shanghai 201306,China;College of Electronic and Electrical Engineering,Shanghai University of Engineering Science,Shanghai 201620,China)

机构地区：[1]上海立信会计金融学院统计与数学学院,上海201620 [2]上海电机学院文理教学部,上海201306 [3]上海工程技术大学电子电气工程学院,上海201620

出　　处：《山东大学学报（理学版）》2019年第4期17-21,共5页Journal of Shandong University(Natural Science)

基　　金：国家自然科学基金资助项目(11501367;61673257);上海电机学院重点学科(16JCXK02)

摘　　要：针对涉及导函数与分担亚纯函数的正规定则,得到了如下结果:设Ω是区域D内的亚纯函数族,a(z)(≠0)是亚纯函数。若对于任意μ(z)∈Ω满足如下条件:(1)μ(z)≠0;(2)对μ(z)和a(z)的任意公共极点,其在μ(z)中的重级大于或等于在a(z)中的重级;(3)对任意函数对{μ(z),ν(z)}?Ω,μ^((m))(z)和ν^((m))(z)分担a(z),则Ω在D内正规。同时,给出了2个例子来说明条件(1)和(2)的必要性。Aiming at normal criteria concerning derivative functions and shared meromorphic functions,the result is show ed as follow s.Let Ω and a(z)(≠0)be a family of functions meromorphic and a meromorphic function in D,respectively.If every μ(z)∈Ω satisfies conditions as follows:(1)μ(z)≠0,(2)for each of the same poles of μ(z)and a(z),the multiplicities in μ(z)are greater than or equal to the multiplicities in a(z),(3)for every functions {μ(z),ν(z)}■Ω,μ^(m)(z)and ν^(m)(z)share a(z),then Ω is normal in D.And tw o examples are given to verify the necessity of conditions(1)and(2).

关 键 词：亚纯函数族 分担亚纯函数 正规定则 

分 类 号：O174.5[理学—数学]