| 涉及重级的亚纯函数族的正规定则 |
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| 引用本文： | 蒋艳,黄斌.涉及重级的亚纯函数族的正规定则[J].纺织高校基础科学学报,2011,24(1):88-91. |
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| 作者姓名： | 蒋艳 黄斌 |
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| 作者单位： | 长沙理工大学数学与计算机科学学院; |
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| 基金项目： | 湖南省教育厅资助项目(05C268); 国家自然科学基金资助项目(11071064) |
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| 摘 要： | 针对徐焱的定理给出了其逆命题成立的条件,进一步改进了Hayman猜想.并得到了新的正规定则:k∈N,设F是D内亚纯函数族,(V)f∈F在D内的零点之级≥k+2,极点之级≥2,h(z)≠0是D上的亚纯函数,若f(k)(z)≠h(z),z∈D,则F在D内正规.
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| 关 键 词： | 亚纯函数 正规族 重级 |
Normality criterion of families of meromorphic functions with multiple zeros and poles |
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| JIANG Yan,HUANG Bin.Normality criterion of families of meromorphic functions with multiple zeros and poles[J].Basic Sciences Journal of Textile Universities,2011,24(1):88-91. |
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| Authors: | JIANG Yan HUANG Bin |
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| Affiliation: | JIANG Yan,HUANG Bin (Department of Mathmatics,Changsha University of Science & Technology,Changsha 410114,China) |
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| Abstract: | The requirement of conversepro position on the basis of theorm given by Xu Yan was found,and the Hayman conjecture was further improved,then a new normal criterion was obtained:Let F be a family of meromorphic function in a complex domain D.Let k∈N,for f∈F,with multiple of zeros at least k+2 and poles at least 2,h(z)(■0) a meromorphic function in D,for z∈D,if f(k)(z)≠h(z),then F is a normal family in D. |
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| Keywords: | meromorphic functions normal families multiple order |
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