反常积分敛散性的新对数判别法  

New logarithmetic criteria of convergence of improper integrals

作　　者：赵建华[1] 

机构地区：[1]上海海事大学,上海200135

出　　处：《河北工程大学学报（自然科学版）》2012年第2期108-112,共5页Journal of Hebei University of Engineering:Natural Science Edition

摘　　要：在很多实际问题中,要突破积分区间的有穷性和被积函数的有界性,由此得到了定积分的两种形式的推广:无穷限反常积分和瑕积分。我们将这两种积分统称为反常积分。因为反常积分涉及到一个收敛问题,所以反常积分敛散性的判定就显得非常重要了。本文就讨论了一种判定反常积分敛散性的新的对数判别法,并证明了这种新的对数判别法比旧的对数判别法更加精细。In many practical problems, we must break through the finite interval of integral and the boundedness of integrand function, and consequently we get two forms of improper integrals： the im- proper integral in an infinite interval and the improper integral of an unbounded function. Because improper integrals are related to convergence, therefore, the determination of convergence and diver- gence of improper integrals are very important. This work discusses a new logarithmetic criterion for improper integrals, and proves that the new logarithmetic criterion is more precise than the old logarithetic criteria.

关 键 词：反常积分 敛散性 新判别法 

分 类 号：O172[理学—数学]