一些LaTeX语法和公式

[$\LaTeX$符号简览](http://www.mohu.org/info/symbols/symbols.htm)&[指令大全](https://katex.org/docs/supported.html) $\begin{vmatrix}a&c\\b&d\end{vmatrix}\cdot\begin{vmatrix}x\\y\end{vmatrix}=\begin{vmatrix}ax+cy\\bx+dy\end{vmatrix}$ $\displaystyle\sum_{n=1}^{x}\ln n=x\ln x-x+\frac{1}{2}\ln x+\ln\sqrt{2\pi}+o(1)$ $\displaystyle\int_{-\infty}^{+\infty}\frac{\sin x}{x}\mathrm{d}x=\pi$ $h=\lceil\log_2n\rceil+1$ $\displaystyle{n \choose m} = \frac{n-m+1}{m}{n \choose m-1}$ $\displaystyle{n \choose m}=(-1)^m{m-n-1 \choose m}$ $\arccos^2z+\text{arcosh}^2z=0$ $2H_2O_2\xlongequal{MnO_2}2H_2O+O_2\uparrow$ $2SO_2+O_2\xrightleftharpoons[\Delta]{V_2O_5}2SO_3$