變限積分確定的函數(shù)的性質(zhì)及其應用

變限積分確定的函數(shù)的性質(zhì)及其應用
 
摘要

由變限定積分和變限反常積分定義的1類函數(shù)，有重要的理論價值和應用價值。本文利用定積分和反常積分的性質(zhì)以及復合函數(shù)的運算法則，從以下4個方面：
(1)由變限定積分確定的函數(shù) 的性質(zhì)；
(2)由變限定積分確定的復合函數(shù) 的性質(zhì)；
(3)由變限反常積分確定的函數(shù) 的性質(zhì)；
(4)由變限反常積分確定的復合函數(shù) 的性質(zhì)；
較系統(tǒng)地討論了這類函數(shù)的性質(zhì),得到若干結(jié)果，并簡要介紹了它們的幾點應用。

關(guān)鍵詞：變限積分，函數(shù)，可積，連續(xù)，收斂。

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.

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