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題名 | 分式型與指數型函數的微分問題=The Differential Problems of Fractional Type and Exponential Type of Functions |
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作者 | 余啟輝; | 書刊名 | 德霖學報 |
卷期 | 26 2013.04[民102.04] |
頁次 | 頁33-42 |
分類號 | 314.55 |
關鍵詞 | 二項級數定理; 逐項微分定理; 無窮級數解; Maple; Binomial series theorem; Differentiation term by term theorem; Infinite series forms; |
語文 | 中文(Chinese) |
中文摘要 | 本篇論文主要是研究分式型與指數型函數的微分問題。我們利用二項級數定理和逐項微分定理可以求出這兩種函數的任意階導函數,因此大大降低了求解它們高階微分值的困難度。此外,我們舉出兩個函數實際的求出它們的任意階導函數以及一些它們的高階微分值,而這些高階微分值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 計算出這些高階微分值以及它們無窮級數解的近似值。 |
英文摘要 | This paper mainly studies the differential problems of fractional type and exponential type of functions. We can obtain the derivative of any order of these two types of functions by using binomial series theorem and differentiation term by term theorem, and hence reducing the difficulty of evaluating their higher order derivative values greatly. In addition, we propose two functions to find their any order derivatives and some of their higher order derivative values practically, and the answers of these higher order derivative values are presented in infinite series forms. On the other hand, we employ the mathematical software Maple to calculate the approximations of these higher order derivative values and their infinite series forms. |
本系統之摘要資訊系依該期刊論文摘要之資訊為主。