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

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。

Abstract: 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.