无穷积分收敛性反问题的若干探讨

Some discuss on the reverse problem of the convergence of infinite integral

有许多判别法讨论当f(x)满足某些条件时便可得到无穷积分∫a+∞f(x)dx的收敛性,讨论反问题,若∫a+∞f(x)dx收敛f(x)将有何种极限性质,重点讨论与极限limx→+∞f(x)=0的关系以及与级数情形的对比。

About the convergence of infinite integral , we have a lot of test methods. In this paper, we study the reverse problem. Under the condition of the convergence of, we study the limit properties of , especially the relations between the convergence of and . Some analogy with series are discussed also.