整函数导数的幂次分担的唯一性  

Uniqueness of entire function for sharing condition of the power of derivative

作　　者：刘芝秀[1] 尚海涛[2] 邹娓[1] LIU Zhixiu;SHANG Haitao;ZOU Wei(School of Science,Nanchang Institute of Technology,Nanchang 330099,China;Institute of Technology,East China Jiaotong University,Nanchang 330100,China)

机构地区：[1]南昌工程学院理学院,江西南昌330099 [2]华东交通大学理工学院,江西南昌330100

出　　处：《南昌工程学院学报》2020年第3期106-109,共4页Journal of Nanchang Institute of Technology

基　　金：江西省教育厅科学技术研究项目(GJJ180944,GJJ190963,GJJ161561);江西省科技厅科技计划项目(20192BAB211006)。

摘　　要：证明了一个关于整函数导数幂次分担条件的唯一性结论,如果f(z)和g(z)是两个非常数整函数,c 1,c 2是两个有穷复数,n,k是两个正整数,且n≥3,若[f(k)(z)]n-c 1和[g(k)(z)]n-c 2在C上IM分担4个互不相同的有穷复数,那么,当c 1≠c 2时,f(z)和g(z)均为次数不超过k的多项式;当c 1=c 2时,f(z)=t ng(z)+p(z),其中t n=1,p(z)为次数不超过k-1的多项式。In this paper,we prove the uniqueness of sharing condition for the power of the derivative of entire functions.If f(z)and g(z)are two nonconstant entire functions,c1,c2 are two finite complex numbers,n,k are two positive integers and n≥3,suppose[f(k)(z)]n-c1and[g(k)(z)]n-c2 share four different finite complex numbers on by IM,then when c1≠c2,f(z)and g(z)are polynomials with degree no more than k;when c1=c2f(z)=tng(z)+p(z),where tn=1,p(z)is a polynomial with degree no more than k-1.

关 键 词：唯一性 整函数 分担值 

分 类 号：O174.52[理学—数学]