反常积分敛散性的新对数判别法

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 improper 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 divergence 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 logari-thetic criteria.