显示latex格式的公式需要加美元号 $，例如 $\beta$显示的结果为 $\beta$，如果单独一行的公式可用双美元符号，例如 $$a+b=c$$会单独成行
$$a+b=c$$

0.常用公式

$x=\frac{-b\mp \sqrt{b^2-4ac}}{2a}$	x=\frac{-b\mp\sqrt{b^2-4ac}}{2a}
$x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$	x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}
$n!=1\times 2\times 3\cdots \times n$	n! = 1\times2\times3\cdots\times n
$\oint f(s)\mathrm{d}s$	\oint f(s)\mathrm{d}r
$\oint f(s)\mathrm{d}s$	\displaystyle\oint f(s)\mathrm{d}s
${\int }_{-1}^{+\infty }f(x)\mathrm{d}x$	\displaystyle\int_{-1}^{+\infty} f(x)\mathrm{d}x
$\iint f(\mathbf{x})\mathrm{d}\mathbf{x}$	\displaystyle\iint f(\bm x)\mathrm{d}\bm x
$\Vert {\sum }_{i=1}^{p+1}\Vert$	\left\|\sum_{i=1}^{p+1}\right\|
$\Vert \sum _{i=1}^{p+1}\Vert$	\left\|\displaystyle\sum_{i=1}^{p+1} \right\|
$\Vert \sum _{i=1}^{p+1}\Vert$	\Big\Vert\displaystyle\sum_{i=1}^{p+1}\bigg\Vert
$\nabla \cdot \nabla u=\Delta u$	\nabla\cdot\nabla u = \Delta u
$\left(\genfrac{}{}{0ex}{}{a+b}{a+b+c}\right)$	{a+b \choose a+b+c}
$\left({}_{a+b+c}^{a+b}\right)$	\left({}_{a+b+c}^{a+b}\right)
$\genfrac{}{}{0ex}{}{a+b}{a+b+c}$	{a+b \atop a+b+c}
$C_{a+b+c}^{a+b}$	C_{a+b+c}^{a+b}
$\stackrel{x\in \mathcal{R}}{\min }f(x)$	\min\limits^{x\in\mathcal{R}}f(x)
$\underset{x\in \mathcal{R}}{\max }f(x)$	\max\limits_{x\in\mathcal{R}}f(x)

$\frac{\mathrm{d}u}{\mathrm{d}t}=\frac{\partial u}{\partial x}\frac{\partial x}{\partial t}+\frac{\partial u}{\partial y}\frac{\partial y}{\partial t}$

\dfrac{\mathrm{d}u}{\mathrm{d}t}
=
\dfrac{\partial u}{\partial x}\dfrac{\partial x}{\partial t}
+
\dfrac{\partial u}{\partial y}\dfrac{\partial y}{\partial t}

1.希腊字母

$\alpha$	\alpha		$\theta$	\theta		$o$	o		$\tau$	\tau
$\beta$	\beta		$\vartheta$	\vartheta		$\pi$	\pi		$\upsilon$	\upsilon
$\gamma$	\gamma		$\iota$	\iota		$\varpi$	\varpi		$\varphi$	\phi
$\delta$	\delta		$\kappa$	\kappa		$\rho$	\rho		$\phi$	\varphi
$ϵ$	\epsilon		$\lambda$	\lambda		$\varrho$	\varrho		$\chi$	\chi
$\epsilon$	\varepsilon		$\mu$	\mu		$\sigma$	\sigma		$\psi$	\psi
$\zeta$	\zeta		$\nu$	\nu		$\varsigma$	\varsigma		$\omega$	\omega
$\eta$	\eta		$\zeta$	\zeta
$\Gamma$	\Gamma		$\Lambda$	\Lambda		$\Sigma$	\Sigma		$\Psi$	\Psi
$\Delta$	\Delta		$\Xi$	\Xi		${\rm Y}$	\Upsilon		$\Omega$	\Omega
$\Theta$	\Theta		$\Pi$	\Pi		$\Phi$	\Phi
$\aleph$	\aleph		$\beth$	\beth		$\daleth$	\daleth		$\gimel$	\gimel

2.数学相关

$\frac{abc}{xyz}$	\dfrac{abc}{xyz}		$\frac{abc}{xyz}$	\frac{abc}{xyz}		$\overline{abc}$	\overline{abc}
$\sqrt{abc}$	\sqrt{abc}		$\sqrt[n]{abc}$	\sqrt[n]{abc}		$\underline{abc}$	\underline{abc}
$\widehat{abc}$	\widehat{abc}		$\widetilde{abc}$	\widetilde{abc}		$\overrightarrow{abc}$	\overrightarrow{abc}
$\overleftarrow{abc}$	\overleftarrow{abc}		$\overbrace{abc}$	\overbrace{abc}		$\underbrace{abc}$	\underbrace{abc}
$\stackrel{⌢}{\mathrm{ab}}$	\overset{\frown}{ab}		$\overgroup{AB}$	\overparen{ab}

注：头顶的弧盖\overparen{ab}用于$\text{LATEX}$, $\overgroup{AB}$用于$\text{KATEX}$

3.分割符号

$|$	\vert		$⟨$	\langle		$\lfloor$	\lfoolr		$\lceil$	\lceil
$\Vert$	\Vert		$⟩$	\rangle		$\rfloor$	\rfloor		$\rceil$	\rceil
$\Uparrow$	\Uparrow		$\uparrow$	\uparrow		$\Downarrow$	\Downarrow		$\downarrow$	\downarrow
$└$	\llcorner		$┘$	\lrcorner		$┌$	\ulcorner		$┐$	\urcorner
$/$	/		$\backslash$	\backslash

4.可变公式

$\sum$	\sum		$\prod$	\prod		$\coprod$	\coprod
$\int$	\int		$\oint$	\ont		$\iint$	\iint
$⨄$	\biguplus		$\bigcap$	\bigcap		$\bigcup$	\bigcup
$⨁$	\bigoplus		$⨂$	\bigotimes		$⨀$	\bigodot
$\bigvee$	\bigvee		$\bigwedge$	\bigwedge		$⨆$	\bigsqcup

5.数学函数

只需要在常用数学函数前加上斜杠\即可
$\sin, \cos, \tan, \exp, \min, \max, \log, \ln, \lim, \cdots$
$\sin ,\cos ,\tan ,\exp ,\min ,\max ,\log ,\ln ,\lim ,\cdots$

6.运算符号

$+$	+		$-$	-		$\times$	\times		$÷$	\div
$\ast$	\ast		$\star$	\star		$\cdot$	\cdot		$\circ$	\circ
$\pm$	\pm		$\mp$	\mp		$\oplus$	\oplus		$\otimes$	\otimes
$\divideontimes$	\divideontimes		$\cdot$	\centerdot		$\odot$	\odot		$⊚$	\circledcirc
$\cap$	\cap		$\cup$	\cup		$\vee$	\vee		$\wedge$	\wedge
$\perp$	\bot		$\perp$	\perp		$\setminus$	\setminus		$\backslash$	\backslash
$\square$	\Box		$\square$	\square		$\wr$	\wr		$⊞$	\boxplus
$△$	\triangle		$▽$	\bigtriangledown		$\Delta$	\Delta		$\nabla$	\nabla
$\equiv$	\equiv		$\ne$	\neq		$\sim$	\sim		$\approx$	\approx
$\triangleq$	\triangleq		$\propto$	\varpropto		$\ll$	\ll		$⋘$	\lll
$\le$	\leq		$\ge$	\geq		$⩽$	\leqslant		$⩾$	\geqslant
$\in$	\in		$\notin$	\notin		$\prec$	\prec		$\succ$	\succ
$\subset$	\subset		$\subseteq$	\subseteq		$\supset$	\supset		$\supseteq$	\supseteq
$⫆$	\nsubseteq		$⫅$	\nsubseteqq		$⊈$	\nsubseteq		$$	\nsubseteqq
$⊊$	\nsubseteq		$⫋$	\nsubsetneqq		$⊋$	\nsupseteq		$⫌$	\nsupsetneqq
$\complement$	\complement

7.其它符号

$\because$	\because		$\therefore$	\therefore		$//$	//		$\perp$	\perp
$△$	\triangle		$\square$	\square		$\text{▱}$	\text{▱}		${}_{=}^{//}$	{}_{=}^{//}
$\infty$	\infty		$\angle$	\angle		$\measuredangle$	\measuredangle		$\sphericalangle$	\sphericalangle
$\forall$	\foall		$\exists$	\exist		$\varnothing$	\varnothing		$\varnothing$	\emptyset
$\partial$	\partial		$\prime$	\prime		$\hslash$	\hbar		$\surd$	\surd
$\cdots$	\cdots		$⋮$	\vdots		$\dots$	\ldots		$\ddots$	\ddots
$\Im$	\Im		$\Re$	\Re		$◊$	\lozenge		$\mho$	\mho
$♠$	\spadesuit		$♡$	\heartsuit		$♣$	\clubsuit		$♢$	\diamondsuit
$\text{c◯}$	\copyright		$Ⓢ$	\circledS		$\circledR$	\circledR		$\pounds$	\pounds
$	\$		$\%$	\%		$\#$	\#		~	\~{}
$ı$	\imath		$ȷ$	\jmath		$\ell$	\ell

注1：平行四边形符号▱并不是内置的latex符号而是特殊字符
注2：$//$与${}_{=}^{//}$是组合生成，并非内置

8.箭头合集

$\to$	\rightarrow	$⟶$	\longrightarrow	$\Rightarrow$	\Rightarrow
$⟹$	\Longrightarrow	$\leftarrow$	\leftarrow	$⟵$	\longleftarrow
$\Leftarrow$	\Leftarrow	$⟸$	\Longleftarrow	$\nearrow$	\nearrow
$\searrow$	\searrow	$\swarrow$	\swarrow	$\nwarrow$	\nwarrow
$\mapsto$	\mapsto	$⟼$	\longmapsto	$⇝$	\rightsquigarrow
$\rightrightarrows$	\rightrightarrows	$\leftrightarrow$	\leftrightarrow	$⟷$	\longleftrightarrow
$\iff$	\Leftrightarrow	$⟺$	\Longleftrightarrow	$\rightleftharpoons$	\rightleftharpoons
$\leftrightarrows$	\leftrightarrows	$\leftrightharpoons$	\leftrightharpoons	$\rightleftarrows$	\rightleftarrows
$\circlearrowleft$	\circlearrowleft	$\circlearrowright$	\circlearrowright	$\nLeftarrow$	\nLeftarrow
$\nRightarrow$	\nRightarrow	$\nLeftrightarrow$	\nLeftrightarrow	$\leftrightsquigarrow$	\leftrightsquigarrow
$⇢$	\dashrightarrow	$⇠$	\dashleftarrow

9.帽子标记

$\bar{a}$	\bar{a}		$\acute{a}$	\acute{a}		$\check{a}$	\check{a}		$\grave{a}$	\grave{a}
$\dot{a}$	\dot{a}		$\hat{a}$	\hat{a}		$\breve{a}$	\breve{a}		$\vec{a}$	\vec{a}
$\ddot{a}$	\ddot{a}		$\tilde{a}$	\tilde{a}

10.数学样式

\mathcal{A}
$\mathcal{A}\mathcal{B}\mathcal{C}\mathcal{D}\mathcal{E}\mathcal{F}\mathcal{G}\mathcal{H}\mathcal{I}\mathcal{J}\mathcal{K}\mathcal{L}\mathcal{M}\mathcal{N}\mathcal{O}\mathcal{P}\mathcal{Q}\mathcal{R}\mathcal{S}\mathcal{T}\mathcal{U}\mathcal{V}\mathcal{W}\mathcal{X}\mathcal{Y}\mathcal{Z}$

\mathbb{A}
$\mathbb{A}\mathbb{B}\mathbb{C}\mathbb{D}\mathbb{E}\mathbb{F}\mathbb{G}\mathbb{H}\mathbb{I}\mathbb{J}\mathbb{K}\mathbb{L}\mathbb{M}\mathbb{N}\mathbb{O}\mathbb{P}\mathbb{Q}\mathbb{R}\mathbb{S}\mathbb{T}\mathbb{U}\mathbb{V}\mathbb{W}\mathbb{X}\mathbb{Y}\mathbb{Z}$

\mathfrak{A}
$\mathfrak{A}\mathfrak{B}\mathfrak{C}\mathfrak{D}\mathfrak{E}\mathfrak{F}\mathfrak{G}\mathfrak{H}\mathfrak{I}\mathfrak{J}\mathfrak{K}\mathfrak{L}\mathfrak{M}\mathfrak{N}\mathfrak{O}\mathfrak{P}\mathfrak{Q}\mathfrak{R}\mathfrak{S}\mathfrak{T}\mathfrak{U}\mathfrak{V}\mathfrak{W}\mathfrak{X}\mathfrak{Y}\mathfrak{Z}$

\mathsf{A}
$\mathsf{A}\mathsf{B}\mathsf{C}\mathsf{D}\mathsf{E}\mathsf{F}\mathsf{G}\mathsf{H}\mathsf{I}\mathsf{J}\mathsf{K}\mathsf{L}\mathsf{M}\mathsf{N}\mathsf{O}\mathsf{P}\mathsf{Q}\mathsf{R}\mathsf{S}\mathsf{T}\mathsf{U}\mathsf{V}\mathsf{W}\mathsf{X}\mathsf{Y}\mathsf{Z}$

\mathscr{A}
$\mathcal{A}\mathcal{B}\mathcal{C}\mathcal{D}\mathcal{E}\mathcal{F}\mathcal{G}\mathcal{H}\mathcal{I}\mathcal{J}\mathcal{K}\mathcal{L}\mathcal{M}\mathcal{N}\mathcal{O}\mathcal{P}\mathcal{Q}\mathcal{R}\mathcal{S}\mathcal{T}\mathcal{U}\mathcal{V}\mathcal{W}\mathcal{X}\mathcal{Y}\mathcal{Z}$

\mathrm{A}
$\mathrm{A}\mathrm{B}\mathrm{C}\mathrm{D}\mathrm{E}\mathrm{F}\mathrm{G}\mathrm{H}\mathrm{I}\mathrm{J}\mathrm{K}\mathrm{L}\mathrm{M}\mathrm{N}\mathrm{O}\mathrm{P}\mathrm{Q}\mathrm{R}\mathrm{S}\mathrm{T}\mathrm{U}\mathrm{V}\mathrm{W}\mathrm{X}\mathrm{Y}\mathrm{Z}$

\mathit{A}
$ABCDEFGHIJKLMNOPQRSTUVWXYZ$

\mathnormal{A}
$ABCDEFGHIJKLMNOPQRSTUVWXYZ$

\mathbf{A}
$\mathbf{A}\mathbf{B}\mathbf{C}\mathbf{D}\mathbf{E}\mathbf{F}\mathbf{G}\mathbf{H}\mathbf{I}\mathbf{J}\mathbf{K}\mathbf{L}\mathbf{M}\mathbf{N}\mathbf{O}\mathbf{P}\mathbf{Q}\mathbf{R}\mathbf{S}\mathbf{T}\mathbf{U}\mathbf{V}\mathbf{W}\mathbf{X}\mathbf{Y}\mathbf{Z}$

\textbf{A} 文本样式粗体
$\text{ABCDEFGHIJKLMNOPQRSTUVWXYZ}$

\text{A} 文本样式
$\text{ABCDEFGHIJKLMNOPQRSTUVWXYZ}$

\bm{A}
$\mathbf{A}\mathbf{B}\mathbf{C}\mathbf{D}\mathbf{E}\mathbf{F}\mathbf{G}\mathbf{H}\mathbf{I}\mathbf{J}\mathbf{K}\mathbf{L}\mathbf{M}\mathbf{N}\mathbf{O}\mathbf{P}\mathbf{Q}\mathbf{R}\mathbf{S}\mathbf{T}\mathbf{U}\mathbf{V}\mathbf{W}\mathbf{X}\mathbf{Y}\mathbf{Z}$

\boldsymbol{A}
$\mathbf{A}\mathbf{B}\mathbf{C}\mathbf{D}\mathbf{E}\mathbf{F}\mathbf{G}\mathbf{H}\mathbf{I}\mathbf{J}\mathbf{K}\mathbf{L}\mathbf{M}\mathbf{N}\mathbf{O}\mathbf{P}\mathbf{Q}\mathbf{R}\mathbf{S}\mathbf{T}\mathbf{U}\mathbf{V}\mathbf{W}\mathbf{X}\mathbf{Y}\mathbf{Z}$

11.大小颜色

$123456789$	{\color{red}123} {\color{blue}456} {\color{green}789}
$abc$	\tiny{abc}
$abc$	\scriptsize{abc}
$abc$	\footnotesize{abc}
$abc$	\small{abc}
$abc$	\normalsize{abc}
$abc$	\large{abc}
$abc$	\Large{abc}
$abc$	\LARGE{abc}
$abc$	\huge{abc}
$abc$	\Huge{abc}
$\left[\left(\right([\right($	\left[ \Bigg( \bigg( \Big[ \big( \right.
$\left[\left\{\right\}\}\right]$	\left[ \bigg\{ \Big\}\big\} \right]

注：\left与\right成对出现，缺省可用.补充，它会自动设置大小

13.多行公式

多行公式常用的两环境有cases与aligned

$\{\begin{array}{l}x+y=1\\ x-y=1\end{array},\begin{array}{rl}& {\int }_{-\infty }^{+\infty }f(x)\mathrm{d}x\\ & \sum _{k=0}^{n}k\end{array}$

\begin{cases}
x+y=1\\
x-y=1
\end{cases},
\qquad % %后面是接注释，\qquaa表示空格
\begin{aligned}
&\int_{-\infty}^{+\infty}f(x)\mathrm{d}x\\[.5em]
&\sum_{k=0}^n k
\end{aligned}
% &字符号表示对齐，\\另起一行, \\[.5em]里面的.5表示行高

矩阵格式

$\left(\begin{array}{ccc}1& 2& 3\\ 4& 5& 6\\ 7& 8& 9\end{array}\right),\left|\begin{array}{cc}a& b\\ c& d\end{array}\right|,\begin{array}{cc}a& b\\ c& d\\ e& f\end{array}$

\left(\begin{matrix}
1&2&3\\
4&5&6\\
7&8&9
\end{matrix}\right)
,\qquad
\left|
\begin{matrix}
a&b\\
c&d
\end{matrix}\right|
,\qquad
\begin{matrix}
a&b\\
c&d \\
e&f
\end{matrix}

14.间距微调

间距紧凑：\!

$x+y$	x+y
$x+y$	x\!+y
$x+y$	x\!\!+y

间距拉开：\, \; \quad \qquad

$x+y$	x+y
$x+y$	x+\,y
$x+y$	x+\;y
$x+y$	x+\quad y
$x+y$	x+\qquad y

本文参考https://katex.org/docs/supported.html