亚纯函数涉及微分多项式的正规族  

A Normal Family of Meromorphic Functions Involving Differential Polynomials

作　　者：王皓然 杨祺[1] WANG Hao-ran;YANG Qi(School of Mathematical Sciences,Xinjiang Normal University,Urumqi 830017,China)

机构地区：[1]新疆师范大学数学科学学院,新疆乌鲁木齐830017

出　　处：《五邑大学学报（自然科学版）》2024年第2期9-13,26,共6页Journal of Wuyi University(Natural Science Edition)

基　　金：国家自然科学基金资助项目(11961068)。

摘　　要：本文研究了一类涉及微分多项式与分担值的正规定则.设n,k为2个正整数,令F是定义在复平面D上的一族亚纯函数,其零点重级至少k+1,a为一非零有穷复数,L (f)是关于f的微分多项式,且L(f)■0,若对■f,g∈F,都有f^(n)L(f)与g^(n)L(g)分担a,则F在D上正规.This paper studies a class of regular rules involving differential polynomials and shcned values.Let F be a family of meromorphic functions in DÌC such that L(f)■0 for f∈F,k,n be two positive integer and a be a finte non-zero complex number.If for each f∈F,the zeros of f have multiplicities at least k+1,and for each pair of functions f,g∈F,f^(n)L(f)and g^(n)L(g)share the value a,then F is normal in D.

关 键 词：正规族 亚纯函数 微分多项式 分担值 

分 类 号：O174.52[理学—数学]