变限积分确定的函数的性质及其应用

上传者：网友
|

翻新时间：2023-03-07

收藏到账号

全屏

变限积分确定的函数的性质及其应用

摘要

由变限定积分和变限反常积分定义的1类函数，有重要的理论价值和应用价值。本文利用定积分和反常积分的性质以及复合函数的运算法则，从以下4个方面：

(1)由变限定积分确定的函数的性质；

(2)由变限定积分确定的复合函数的性质；

(3)由变限反常积分确定的函数的性质；

(4)由变限反常积分确定的复合函数的性质；

较系统地讨论了这类函数的性质,得到若干结果，并简要介绍了它们的几点应用。

关键词：变限积分，函数，可积，连续，收敛。

Abstract

It defines a sequence of function by variable limit integral and variable limit improper integral, those functions have important value in theory and application. This paper uses the nature of definite integral and improper integral and composite function’s operational method. Following four aspects:

（1）The nature of function is determined by variable limit definite integral.

（2）The nature of composite function is determined by variable limit definite integral.

（3）The nature of function is determined by variable limit improper integral.

（4）The nature of composite function is determined by variable limit improper integral.

We systematically discuss the nature of these functions. And have several consequences. And it simply introduces several applications of the consequences.

Key word: variable limit integral, function, integral, continuity, convergence.