| 关于亚纯函数的k阶导函数和有理函数(英文) |
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| 引用本文： | 杨 拍,刘晓俊.关于亚纯函数的k阶导函数和有理函数(英文)[J].华东师范大学学报(自然科学版),2014,2014(4):8-17. |
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| 作者姓名： | 杨 拍 刘晓俊 |
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| 作者单位： | 1. College of Applied Mathematics, Chengdu University of Information Technology, Chengdu 610225, China;
2. Department of Mathematics, University of Shanghai for Science and Technology, Shanghai 200093, China |
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| 基金项目： | 国家自然科学基金(11001081);数学天元专项基金(11226095);成都信息工程学院科研基金(KYZ201403) |
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| 摘 要： | 设f是复平面C内的超越亚纯函数,R是一个有理函数且R(■)0,k是一个正整数.并假设f的零点重级至少为k+1,至多有限个零点例外.则f~((k))-R有无限多个零点.
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| 关 键 词： | 亚纯函数 Julia例外函数 拟正规族 |
| 收稿时间： | 2013-07-01 |
On the kth derivatives of meromorphic functions and rational functions |
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| YANG Pai,LIU Xiao-jun.On the kth derivatives of meromorphic functions and rational functions[J].Journal of East China Normal University(Natural Science),2014,2014(4):8-17. |
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| Authors: | YANG Pai LIU Xiao-jun |
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| Institution: | YANG Pai;LIU Xiao-jun;College of Applied Mathematics,Chengdu University of Information Technology;Department of Mathematics,University of Shanghai for Science and Technology; |
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| Abstract: | Let $f$ be a transcendental meromorphic function in
$\mathbb C$, $R\not\equiv0$
be a rational function,
and let $k$ be a positive integer.
Suppose that all zeros of $f$ have multiplicity at least $k+1$,
except possibly finite many.
Then $f^{(k)}-R$ has infinitely many zeros. |
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