反常积分敛散性的一个新判别法  

A new criterion for convergence and divergence of improper integrals

作　　者：邓习军 敖和松 王成华 Deng Xijun;Ao Hesong;Wang Chenghua(School of Mathematics and Physics,Anqing Normal University,Anqing 246133,China;School of Mathematics and Computational Sciences,Huaihua University,Huaihua 418000,China;Honghu No.1 Middle School,Honghu 433200,China)

机构地区：[1]安庆师范大学数理学院,安徽安庆246133 [2]怀化学院数学与计算科学院,湖南怀化418000 [3]湖北省洪湖市第一中学,湖北洪湖433200

出　　处：《湖南文理学院学报（自然科学版）》2023年第4期20-24,共5页Journal of Hunan University of Arts and Science(Science and Technology)

基　　金：湖南省教育厅重点项目(21A0414)。

摘　　要：关于反常积分的敛散性判定问题的判别方法比较多,并且大部分都源于比较判别法,即要事先挑选出一个已知其敛散性的反常积分作为比较对象。然而,寻找到这样合适的比较对象却是很困难的。本文通过分析被积函数的自身性态,给出了关于反常积分敛散性的一种新的判别方法,并通过实例说明了其应用以及优越性。There are many methods to determine the convergence and divergence of improper integral,and most of them are derived from comparative discrimination,that is,to select an improper integral with known convergence and divergence as the comparison object.However,in the actual process,it is very difficult to find such a suitable comparison object.By analyzing the property of integrand function,in this paper we give a new discriminant method about the convergence and divergence of improper integrals,and illustrate its application and superiority by examples.

关 键 词：反常积分 敛散性 判别法 

分 类 号：O172.2[理学—数学]