自然对数：e

注：第三个是开n次方根，但是这里显示不支持！


\[级数形式：e=\sum_{k=0}^\infty \frac{1}{n!}，极限形式：e=\lim_{n \to \infty}(1+\frac{1}{n})^n，极限形式：e=\lim_{n \to \infty}\frac{n}{\sqrt{n!}}\]
\[\int_{0}^{+\infty} e^{-x}\, dx=1\]
\[\begin{alignat} {1} e^{ix} & =  1+ix+\frac{(ix)^2}{2!}+\frac{(ix)^3}{3!}+\frac{(ix)^4}{4!}+\frac{(ix)^5}{5!}+\frac{(ix)^6}{6!}+...\\  & =1+ix-\frac{x^2}{2!}-\frac{ix^3}{3!}+\frac{x^4}{4!}+\frac{ix^5}{5!}-\frac{x^6}{6!}...\\  & =1-\frac{x^2}{2!}+\frac{x^4}{4!}-\frac{x^6}{6!}+...+ix-\frac{ix^3}{3!}+\frac{ix^5}{5!}-...\\ & =\cos(x)+i\sin(x) \\ \end{alignat}\]

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欧拉积分:\[\Gamma(s)=\int_{0}^{+\infty} x^{s-1} e^{-x}\, dx,s >0,\Gamma(r)=(r-1)!\]

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傅里叶变换:\[f(t)=\int_{-\infty}^{+\infty} e^{itx} p(x)\, dx,称对p(x)做了傅里叶变换\]
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三角公式：\[\sin 2\theta=2 \sin \theta \cos \theta  ,  \cos 2 \theta=\cos^2 \theta-\sin^2 \theta\]
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反三角函数求导：\[(\acrtan x)^\prime=\frac{1}{1+x^2}\]