摘要
文章给出了解析函数和级的定义,并讨论了级的定义的选择问题.通过两个定理分析可知,在|z|<1内的解析函数的级与|z|=1处奇点个数无关,而影响函数f(z)的级的关键在于奇点的类型.同时推广到在整个z平面上解析的整函数,给出了相应的级的定义,简介了它与|z|<1内的解析函数的级的相似性质.
In this paper,the definitions of analytic function and rank are presented,and the choice of the rank defintion is also discussed.Through two theorems,we conclude that analytic function rank in ｜z｜1has no relationship with the number of sigular point in ｜z｜=1,and the key factor influencing the rank of function f（z） is the types of sigular point.What′s more,the integral function analyzing inzplane is disscussed,the corresponding definition of the rank is given and the similar properities with the analytic function in ｜z｜1 are introduced.
出处
《太原师范学院学报（自然科学版）》
2010年第2期15-18,共4页
Journal of Taiyuan Normal University:Natural Science Edition
基金
湖北省教育厅(A类)重点项目(D20101304)
关键词
解析函数
解析函数级
整函数
奇点
analytic function
analytic function rank
integral function
integral point
