| 亚纯函数及其n阶导数权分担两个值 |
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| 引用本文： | 徐洪焱,易才凤.亚纯函数及其n阶导数权分担两个值[J].纯粹数学与应用数学,2009,25(4):777-785. |
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| 作者姓名： | 徐洪焱 易才凤 |
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| 作者单位： | 1. 景德镇陶瓷学院信息学院,江西,景德镇,333403
2. 江西师范大学数信学院,江西,南昌,330027 |
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| 基金项目： | 国家自然科学基金，景德镇陶瓷学院科研项目 |
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| 摘 要： | 研究亚纯函数及其n阶导数权分担两个值的唯一性问题.得到了：如果两个非常数亚纯函数f,g分担（∞,∞）,f（n）与g（n）分担（1,0）,n（≥0）为一整数,且满足C0：=（4n＋6）λ＋δn＋1（0,f）＋δn＋1（0,g）＋δn＋2（0,f）＋δn＋2（0,g）＋δn（0,f）〉4n＋10,其中λ=max{min{Θ（∞,f）,Θ（0,f）},min{Θ（∞,g）,Θ（0,g）}},那么f（n）·g（n）≡1,或者f≡g.该结果改进了前人的有关定理.
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| 关 键 词： | 亚纯函数 权分担 唯一性 |
Mermorphic functions concerning their n-th derivative sharing two values with weight |
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| XU Hong-yan,YI Cai-feng.Mermorphic functions concerning their n-th derivative sharing two values with weight[J].Pure and Applied Mathematics,2009,25(4):777-785. |
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| Authors: | XU Hong-yan YI Cai-feng |
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| Institution: | XU Hong-yan 1,YI Cai-feng 2 (1.Department of Informatics , Engineering,Jingdezhen Ceramic Institute,Jingdezhen 333403,China,2.Institute of Mathematics , Informatics,Jiangxi Normal University,Nanchang 330027,China) |
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| Abstract: | In this paper,we deal with the uniqueness problem of meromorphic functions concerning their n-th derivative sharing two values with weight and obtain the following theorem: if two nonconstant meromorphic functions f,g share (∞,∞),f~n,g~n share (1,0),and satisfy Δco := (4n+6)λ+δ_(n+1)(0,f)+δ_(n+1)(0,g)+δ_(n+2)(0,f)+ δ_(n+2)(0,g) > 4n + 10,where λ = max{min{Θ(∞,f),Θ(0,f)},min{Θ(∞,g),Θ(0,g)}},then either f~((n))·g~((n)) ≡ 1 or f ≡ g,where n(> 0) is an integer. These results extend the former theorems. |
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| Keywords: | meromorphic function weighted sharing uniqueness |
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