判定含参量反常积分非一致收敛的方法研究  

Study on the Methods of Determining Nonuniform Convergence of Improper Integral with Parameters

作　　者：王拥兵 WANG Yongbing(School of Mathematics and Physics,Anqing Normal University,Anqing 246133,China)

机构地区：[1]安庆师范大学数理学院,安徽安庆246133

出　　处：《安庆师范大学学报（自然科学版）》2022年第3期118-122,共5页Journal of Anqing Normal University(Natural Science Edition)

基　　金：安徽省大规模在线开放课程项目(2020mooc273);安徽省教学示范课程项目(20201509)。

摘　　要：关于“数学分析”课程中涉及含参量积分一致收敛性的判别法,一般比较熟悉的有Cauchy准则、魏尔斯特拉斯M判别法、狄利克雷判别法和阿贝尔判别法等,而含参量反常积分非一致收敛判别方法的情况相对复杂一些,也不太容易被学生所理解。为此,本文从“数学分析”课程中含参量反常积分一致收敛的概念和性质出发,给出了几种判定证明方法,并结合具体实例加以分析。The discriminant methods of uniform convergence of improper integral with parameters in the course of Math-ematical Analysis generally include Cauchy criterion,Weierstrass M discrimination,Dirichlet discrimination and Abel discrim-ination,etc.However,the discrimination of nonuniform convergence of improper integral with parameters is relatively com-plex,and it is not easy for students to understand.Combining with the concept and properties of uniform convergence of im-proper integral with parameters in the course of Mathematical Analysis,this paper presents several methods of proving the nonuniform convergence of improper integral with parameters,and analyzes with specific examples.

关 键 词：含参量反常积分 非一致收敛 连续 

分 类 号：O172.2[理学—数学]