Uniqueness of Entire Functions Sharing Polynomials with Their Derivatives

被引:1
作者
Qi, Jianming [1 ]
Lue, Feng [2 ]
Chen, Ang [1 ]
机构
[1] Shandong Univ, Sch Math & Syst Sci, Jinan 250100, Shandong, Peoples R China
[2] China Univ Petr, Dept Math, Dongying 257061, Shandong, Peoples R China
关键词
MEROMORPHIC FUNCTIONS;
D O I
10.1155/2009/847690
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
We use the theory of normal families to prove the following. Let Q(1)(z) = a(1)z(p) + a(1),(p-1)z(p-1) + ... + a(1,0) and Q2(z) = a(2)z(p) + a(2,p- 1)z(p-1) + ... + a(2,0) be two polynomials such that deg Q(1) = deg Q(2) = p (where p is a nonnegative integer) and a(1), a(2)(a2 not equal 0) are two distinct complex numbers. Let f(z) be a transcendental entire function. If f(z) and f'(z) share the polynomial Q(1)(z)CM and if f(z) = Q2(z) whenever f'(z) = Q(2)(z), then f equivalent to f'. This result improves a result due to Li and Yi. Copyright (C) 2009 Jianming Qi et al.
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页数:9
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