Quasi-normal Family of Meromorphic Functions Whose Certain Type of Differential Polynomials Have No Zeros  

作　　者：Jian Ming CHANG 

机构地区：[1]School of Mathematics and Statistics,Changshu Institute of Technology,Changshu 215500,P.R.China [2]School of Mathematical Sciences,Qufu Normal University,Qufu 273165,P.R.China

出　　处：《Acta Mathematica Sinica,English Series》2021年第8期1267-1277,共11页数学学报（英文版）

基　　金：Supported by NSFC(Grant No.11471163)。

摘　　要：Define the differential operators φ_(n) for n∈N inductively by φ_(1)[f](z)=f(z)and φ_(n+1)[f](z)=f(z)φ_(n)[f](z)+d/daφ_(n)[f](z).For a positive integer k≥2 and a positive number δ,let F be the family of functions f meromorphic on domain D■C such that φ_(k)[f](z)≠0 and|Res(f,a)-j|≥δ for all j∈{0,1,...,k-1}and all simple poles α of f in D.Then F is quasi-normal on D of order 1.

关 键 词：Normal families quasi-normal families differential polynomials meromorphic functions 

分 类 号：O174.52[理学—数学]