有理分式函数的对称复极点的留数  

Residues at Symmetric Complex Poles of Rational Fractional Function

作　　者：丁明玲[1] 肖祥春 李薇[1] DING Mingling;XIAO Xiangchun;LI Wei(College of Computer and Information Sciences,Fujian Agriculture and Forestry University,Fuzhou 350002,China;School of Mathematics and Statistics,Xiamen University of Technology,Xiamen Fujian 361024,China)

机构地区：[1]福建农林大学计算机与信息学院,福州350002 [2]厦门理工学院数学与统计学院,福建厦门361024

出　　处：《大学数学》2024年第2期92-99,共8页College Mathematics

基　　金：福建省自然科学基金项目(2021J011192);福建省教育厅省级一流本科课程项目(117/111ZJ1926)。

摘　　要：在复平面上分别给出复系数有理分式函数关于坐标轴以及原点对称的对称极点的留数之间的关系.结合复变函数的奇偶性得到有理分式函数的对称极点的留数的简便计算方法,并应用于有理分式函数在闭合路径上的复积分的计算.We show the relationships of residues at some axial or central symmetric poles of rational fractional functions on the complex plane respectively.Based on these results,we provide the simple ways to calculate the residues at symmetric poles of rational functions by their parity,which are also used in the calculation of complex integral on a closed curve.

关 键 词：有理分式函数 极点 留数 对称 奇偶性 

分 类 号：O174.5[理学—数学]