复变函数在不同圆环域内洛朗展开的探究  

Research on Laurent series of complex functions in different annulus

作　　者：袁志杰[1] 张神星 YUAN Zhijie;ZHANG Shenxing(School of Mathematics,Hefei University of Technology,Hefei 230000,China)

机构地区：[1]合肥工业大学数学学院,安徽合肥230000

出　　处：《南阳师范学院学报》2024年第3期38-41,共4页Journal of Nanyang Normal University

基　　金：国家自然科学基金(12001510);中央高校基础科研业务费(JZ2023HGTB0217);安徽省教学改革项目(2022jyxm1232)。

摘　　要：针对解析函数在同圆心的不同圆环域内洛朗级数,给出了这些洛朗级数的系数之差与函数在两个圆环之间的极点的关系。特别地,由有理函数在某一圆环内的洛朗展开可以直接得到它在同圆心的任一圆环域内的洛朗级数。For the Laurent series of analytic functions in different circular domains with the same center,the rela-tionship between the difference of the coefficients of these Laurent series and the poles of the function between the two circular domains is given.In particular,the Laurent expansion of a rational function in a certain circular do-main can be directly obtained from its Laurent series in any circular domain with the same center.

关 键 词：解析函数 洛朗级数 有理函数 

分 类 号：O174.5[理学—数学]