基于对数函数比值形式变化判别无穷积分的敛散性  

On the Ratio Form of Logarithmic Function to Distinguish the Convergence and Divergence of Infinite Integrals

作　　者：何鸿俊 黄晓芳 

机构地区：[1]广州大学数学与信息科学学院,广东 广州

出　　处：《理论数学》2024年第2期450-457,共8页Pure Mathematics

摘　　要：反常积分的基本问题就是探讨其敛散性的判别,这是求解无穷积分近似值的一个先决条件。本文根据定义在[1,+∞)上连续函数f(x)的对数形式与自变量x的对数形式的比值形式的变化,给出了一种新的判别无穷积分敛散性的判别方法。The basic problem of infinite integrals is to explore the judgement of their convergence and divergence, this is a prerequisite for solving the approximations of infinite integrals. In this paper, according to change of the ratio form between the logarithmic form of continuous function f(x) defined in [1,+∞) and the logarithmic form of the variable x, we give a new method for distinguishing the convergence and divergence of infinite integrals.

关 键 词：无穷积分 敛散性 比较判别法 

分 类 号：O17[理学—数学]