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變限積分確定的函數(shù)的性質(zhì)及其應(yīng)用
變限積分確定的函數(shù)的性質(zhì)及其應(yīng)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(jià)值和應(yīng)用價(jià)值。本文利用定積分和反常積分的性質(zhì)以及復(fù)合函數(shù)的運(yùn)算法則，從以下4個(gè)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(fù)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(fù)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(jiǎn)要介紹了它們的幾點(diǎn)應(yīng)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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