一种判定函数列非一致收敛的方法  

A judging method for non uniform convergence of function sequence

作　　者：王庆东[1] 王路桥 

机构地区：[1]商丘师范学院数学与信息科学学院,河南商丘476000 [2]太康县第一高级中学,河南太康475400

出　　处：《高师理科学刊》2016年第9期12-14,17,共4页Journal of Science of Teachers＇College and University

基　　金：国家级特色专业建设点项目(TS11575)

摘　　要：根据一致收敛与收敛的关系,得到一种判定函数列非一致收敛的方法.通过观察通项与极限函数之差中的不定式,若能找到参量关于自然数的函数,使得相应的数列发散或非无穷小量,那么函数列非一致收敛.该方法比定义法和柯西准则法简便,可优先试用.According to the relationship between uniform convergence and convergence, a judging method for non uniform convergence of function sequence is obtained. If some parameter is found to be the function of natural number by observing the infinitives in the difference between the general term and the limit function such that the corresponding series is divergent or non infinitesimal quantity, then the function sequence convergent non-uniformly. The method is easier than definition method and the Cauchy criterion and can be used as aprioroption.

关 键 词：函数列 非一致收敛 不定式 发散 

分 类 号：O172.2[理学—数学]