The Properties of Bianalytic Functions with Zero Arc at a Pole  

含零点弧的双解析函数在极点处的性质(英文)

作　　者：王飞 黄新民 刘华 

机构地区：[1]College of Mathematics and Physics,Xinjiang Agricultural University [2]College of Mathematics and Information Science,Guangxi University [3]Department of Mathematics and Physics,Tianjin University of Technology and Education

出　　处：《Journal of Mathematical Research and Exposition》2009年第4期623-628,共6页数学研究与评论（英文版）

基　　金：the National Natural Science Foundation of China(No.10601036)

摘　　要：In this paper, the properties of bianalytic functions w（z） = z^-Ф1（z） ＋Ф2（z） with zero arc at the pole z = 0 are discussed. Some conditions under which there exists an arc γ, an end of which is z = 0, such that w（z） =0 for arbitary z ∈γ／{0} are given. Secondly, that the limit set of w（z） is a circle or line as z → 0 is proved in this case. Finally, two numerical examples are given to illustrate our results.In this paper,the properties of bianalytic functions w(z)=zφ1(z)+φ2(z) with zero arc at the pole z=0 are discussed.Some conditions under which there exists an arc γ,an end of which is z=0,such that w(z)=0 for z∈γ\{0} are given.Secondly,that the limit set of w(z) is a circle or line as z→0 is proved in this case.Finally,two numerical examples are given to illustrate our results.

关 键 词：bianalytic functions with zero arc POLE convergence to a circle or line sufficient condition. 

分 类 号：O174.55[理学—数学] TM501.2[理学—基础数学]