| The Properties of Bianalytic Functions with Zero Arc at a Pole |
| Received:May 11, 2007 Revised:January 02, 2008 |
| Key Words:
bianalytic functions with zero arc pole convergence to a circle or line sufficient condition.
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| Fund Project:the National Natural Science Foundation of China (No.10601036). |
| Author Name | Affiliation | | WANG Fei | College of Mathematics and Physics, Xinjiang Agricultural University, Xinjiang 830052, China
College of Mathematics and Information Science, Guangxi University, Guangxi 530004, China | | HUANG Xin Min | College of Mathematics and Information Science, Guangxi University, Guangxi 530004, China | | LIU Hua | Department of Mathematics and Physics, Tianjin University of Technology and Education, Tianjin 300222, China |
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| Abstract: |
| In this paper, the properties of bianalytic functions $w(z)=\bar{z}\phi_1(z) \phi_2(z)$ with zero arc at the pole $z=0$ are discussed. Some conditions under which there exists an arc $\gamma$, an end of which is $z=0$, such that $w(z)=0$ for $\forall z\in\gamma\backslash\{0\}$ are given. Secondly, that the limit set of $w(z)$ is a circle or line as $z\to 0$ is proved in this case. Finally, two numerical examples are given to illustrate our results. |
| Citation: |
| DOI:10.3770/j.issn:1000-341X.2009.04.007 |
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