四種瑕積分的冪級數解

Power Series Forms of Four Types of Improper Integrals

本篇論文研究四種不同類型瑕積分的求解問題，我們利用高等微積分中兩個重要的方法－參數微分法和逐項積分法可以求出這四種瑕積分的羃級數解。同時我們舉出四個瑕積分的例子實際的來做計算，而這四個瑕積分的答案都是以無窮級數的型式呈現的。另一方面，我們利用數學軟體Maple計算這些瑕積分以及它們無窮級數解的近似值。

This paper studies the evaluating problem of four different types of improper integrals, and we can obtain the power series forms of these four types of improper integrals using two important methods in advanced calculus -differentiation with respect to a parameter and integration term by term. Simultaneously, we propose four improper integral examples to do calculation practically, and the answers of these four improper integrals are presented in infinite series forms. On the other hand, we employ the mathematical software Maple to calculate the approximations of these improper integrals and their infinite series forms.