利用微分方程将函数展开为幂级数

The Use of Differential Equation to Expand Function into Power Series

本文给出了利用微分方程展开幂级数的方法,对于导数中含有原来函数因式的某些函数,比如含有指数函数的函数,含有可变上限积分的函数,分式函数等等,本方法在使用上较为简便。

This paper gives the method of using differential equation for the expansion of the power series, which makes it simple to calculate some functions of the original function factor contained in derivative, such as function containing exponential function, function containing a variable upper limit integral function, fraction function and so on.