| 亚纯函数及其导数分担小函数集的唯一性 |
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| 引用本文： | 赵小珍.亚纯函数及其导数分担小函数集的唯一性[J].江西师范大学学报(自然科学版),2012,36(2):141-146. |
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| 作者姓名： | 赵小珍 |
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| 作者单位： | 宁德师范学院数学系,福建宁德,352100 |
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| 基金项目： | 福建省教育厅A类科技(JK2010062);福建省高校科研(JA11276);宁德师范学院重点课题(2010003)资助项目 |
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| 摘 要： | 研究了亚纯函数及其k阶导数权分担小函数集的唯一性,得到了:设k,n为正整数,f,g为开平面上超越亚纯函数,以∞为IM公共值,E(S1,f)=E(S1,g)且E1(S2,f(k))=E1(S2,g(k)l(≥2)∈N如果2nδ2+k(an,fn)+(nk+4)Θ(∞,f)n(k+1)+4则f≡tg(tn=1)或f(k)n(akn)](gkn)(akn)]=]bn-(akn])2,并且文中还讨论了当l=0,1时的情形.这些定理推广和改进了先前的一些结果.
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| 关 键 词： | 亚纯函数 弱权分担 小函数 唯一性 |
The Uniqueness of Meromorphic Functions and Their Derivatives Weighted-Sharing the Sets of Small Functions |
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| ZHAO Xiao-zhen.The Uniqueness of Meromorphic Functions and Their Derivatives Weighted-Sharing the Sets of Small Functions[J].Journal of Jiangxi Normal University (Natural Sciences Edition),2012,36(2):141-146. |
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| Authors: | ZHAO Xiao-zhen |
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| Institution: | ZHAO Xiao-zhen(Department of Mathematics,Ningde Normal University,Ningde Fujian 352100,China) |
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| Abstract: | The uniqueness of meromorphic functions and their derivatives weakly weighted-sharing the sets of small functions is investigated,and the following theorem is obtained.Let k,n be two positive integers,f,g be nonconstant meromorphic functions in the complex plane C,f,g share ∞ IM,E(S1,f)=E(S1,g) and E1(S2,f(k))=E1(S2,g(k)l(≥2)∈N.If 2nδ2+k(an,fn)+(nk+4)Θ(∞,f)>n(k+1)+4 f≡tg(tn=1)= f(k)n(akn)](gkn)(akn)]=]bn-(akn])2.Some results about l = 0,1 in the above theorem are obtained in this paper.These theorems of this paper extend and improve the previous results. |
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| Keywords: | meromorphic function weakly weighted-sharing small function uniqueness |
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