函数列非一致收敛的若干判别方法

Several Methods of Judging on the Non-uniform Convergence of Function Sequence

函数列非一致收敛性判别问题是数学分析中最重要的"非概念"之一,也是数学分析学习重难点之一,是后续函数项级数相关解析性质研究的基础.通过逆向思维,对数学分析教材内容进行剖析,总结了五种判别非一致收敛的方法,并给出了证明及应用实例.

Judging problem on the non - uniform convergence of function sequence is one of the most importantnon concept and difficult point in mathematical analysis, which is also research foundation for the follow -up func- tion series related analysis properties. Through reverse thinking, based on mathematical analysis teaching material content, the five methods of judging on the non - uniform convergence of function sequence are summarized. The proof and application example are given.