一类非负函数无穷积分收敛性的刻画  

Characterizations on Convergence of Infinite Integrals of Nonnegative Functions

作　　者：焦圣华 韩成茂 JIAO Shen-hua;HAN Cheng-mao(School of Mathematics and Statistics,Linyi University,Linyi Shandong 276000,China;不详)

机构地区：[1]临沂大学数学与统计学院,山东临沂276000 [2]不详

出　　处：《大学数学》2020年第2期95-99,共5页College Mathematics

基　　金：国家社科基金项目(16XSS003)。

摘　　要：针对无穷积分教学的需要,在利用随机理论的重要概念——失效函数来刻画出非负函数的递减趋于坐标横轴程度的基础上,运用一般推理方法及无穷积分敛散性的比较判别法,得到了一类非负函数的无穷积分敛散性的较为简便而有效的判别方法.Aiming at the teaching of infinite integrals in the advanced mathematics,we describe the development trend to the axis of the non-negative function with the help of the important concept-the failure function of the stochastic theory.Used the general reasoning method and the comparison and convergence method of the infinite integrals,Many more effective and more simple convergence criterios of the infinite integralsare finally obtained.

关 键 词：反常积分 失效函数 收敛准则 

分 类 号：O172.2[理学—数学]