# 另外一种定义欧拉数$$e$$的方法

$$e=\lim_{n \to \infty} (1+\frac{1}{n})^n$$

$$f’=f$$                         ……（1）

$$f(x+a)=c*f(x)$$                     ……（2）

$$f(x+a)=f(a)*f(x)$$

$$f(1)=exp(1)=1+1+\frac{1}{2!}+\frac{1}{3!}+…+\frac{1}{n!}+…$$

$$\begin{gather*} \frac{d f(x)}{d x} = f(x)\\f(0)=1 \end{gather*}$$

$$\frac{d^2I}{dt^2}=-cI$$，其中$$c$$为大于零的常数。

$$k^2*e^{k*t}=-c*e^{k*t}$$，因此，

$$k^2=-c\\k=\pm\sqrt{c}*i$$

The reason this number e is considered the “natural” base of exponential functions is that this function is its own derivative.

This natural exponential function is identical with its derivative. This is really the source of all the properties of the exponential function, and the basic reason for its importance in applications…