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

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.