反常积分敛散性极限审敛法的等价定理

An equivalence theorem of criterion of convergence of abnormal integral

将无穷积分及无界函数积分的被积函数运用无穷小和无穷大比较的方法进行比较,得到了相应的反常积分敛散性极限审敛法的等价定理,并给予证明,从而可运用等价定理灵活的判断反常积分的敛散性.

This article compared the integrand of infinite integral and unbounded function integral by comparing the infinitesimal with the infinity, obtained the corresponding equivalence theorem of criterion of convergence of abnormal integral, and gave out the proof. Thus we can use the equivalence theorem to judge convergence of abnormal integral.