Markdown 数学公式使用总结
1. 语法
1、行内公式
用 $...$ 表示行内公式，如 O_{1 - \left(\vert a \vert \over 2 \right)}：\(O_{1 - \left(\vert a \vert \over 2 \right)}\)
2、多行公式
用 $$...$$ 表示多行公式，如 \sum_{i=0}^\infty x^2 = x_1 + x_2 + x_3 + ... + x_n
\[\sum_{i=0}^\infty x^2 = x_1 + x_2 + x_3 + ... + x_n
\]
2. 上标、下标、分组
上标和下标
- 上标：
^，如x^y：\(x^y\) - 下标：
_，如a_i：\(a_i\)
分组
符号：{}，例：C_n^2 ：\(C_n^2\)、C_{n^2}：\(C_{n^2}\)
3. 希腊字母
| 公式 | 小写 | 公式 | 大写 |
|---|---|---|---|
\alpha |
\(\alpha\) | \Alpha |
\(\Alpha\) |
\beta |
\(\beta\) | \Beta |
\(\Beta\) |
\delta |
\(\delta\) | \Delta |
\(\Delta\) |
\epsilon |
\(\epsilon\) | \Epsilon |
\(\Epsilon\) |
\zeta |
\(\zeta\) | \Zeta |
\(\Zeta\) |
\eta |
\(\eta\) | \Eta |
\(\Eta\) |
\theta |
\(\theta\) | \Theta |
\(\Theta\) |
\iota |
\(\iota\) | \Iota |
\(\Iota\) |
\kappa |
\(\kappa\) | \Kappa |
\(\Kappa\) |
\lambda |
\(\lambda\) | \Lambda |
\(\Lambda\) |
\mu |
\(\mu\) | \Mu |
\(\Mu\) |
\nu |
\(\nu\) | \Nu |
\(\Nu\) |
\xi |
\(\xi\) | \Xi |
\(\Xi\) |
\pi |
\(\pi\) | \Pi |
\(\Pi\) |
\rho |
\(\rho\) | \Rho |
\(\Rho\) |
\sigma |
\(\sigma\) | \Sigma |
\(\Sigma\) |
\tau |
\(\kappa\) | \Tau |
\(\Tau\) |
\phi |
\(\phi\) | \Phi |
\(\Phi\) |
\psi |
\(\psi\) | \Psi |
\(\Psi\) |
\omega |
\(\omega\) | \omega |
\(\Omega\) |
\omicron |
\(\omicron\) | \Omicron |
\(\Omicron\) |
\gamma |
\(\gamma\) | \Gamma |
\(\Gamma\) |
斜体字母加上前缀 var，\varDelta：\(\varDelta\)
4. 算数运算
| 公式 | 符号 |
|---|---|
\times |
\(\times\) |
\div |
\(\div\) |
\cdot |
\(\cdot\) |
< |
\(<\) |
> |
\(>\) |
\ll |
\(\ll\) |
\gg |
\(\gg\) |
\lll |
\(\lll\) |
\pm |
\(\pm\) |
\le 、\leq |
\(\le\) 、\(\leq\) |
\ge 、\geq |
\(\ge\) 、\(\geq\) |
\mp |
\(\mp\) |
\leqq |
\(\leqq\) |
\geqq |
\(\geqq\) |
\neq |
\(\neq\) |
\leqslant |
\(\leqslant\) |
\geqslant |
\(\geqslant\) |
\approx |
\(\approx\) |
5. 集合
| 公式 | 符号 |
|---|---|
\complement |
\(\complement\) |
\in |
\(\in\) |
\notin |
\(\notin\) |
/subset |
\(\subset\) |
\subseteq |
\(\subseteq\) |
\subsetneq |
\(\subsetneq\) |
\cap |
\(\cap\) |
\cup |
\(\cup\) |
\varnothing |
\(\varnothing\) |
\emptyset |
\(\emptyset\) |
6. 逻辑运算
| 公式 | 符号 |
|---|---|
\land 、\wedge |
\(\land\) 、\(\wedge\) |
\lor 、\vee |
\(\lor\) 、\(\vee\) |
\lnot 、\neg |
\(\lnot\) 、\(\neg\) |
\forall |
\(\forall\) |
\exists |
\(\exists\) |
\bot |
\(\bot\) |
/top |
\(\top\) |
\vdash |
\(\vdash\) |
\Vdash |
\(\Vdash\) |
\vDash |
\(\vDash\) |
\models |
\(\models\) |
7.括号
| 公式 | 符号 |
|---|---|
(x) |
\((x)\) |
\Bigg(x \Bigg) |
\(\Bigg(x \Bigg)\) |
\bigg(x \bigg) |
\(\bigg(x \bigg)\) |
\Big(x \Big) |
\(\Big( x \Big)\) |
\big(x \big) |
\(\big(x \big)\) |
\{x \} 、\lbrace x \rbrace |
\(\{x \}\) 、\(\lbrace x \rbrace\) |
[x] |
\([x]\) |
\vert x \vert |
\(\vert x \vert\) |
\Vert x \Vert |
\(\Vert x \Vert\) |
\langle x \rangle |
\(\langle x \rangle\) |
\lceil x \rceil |
\(\lceil x \rceil\) |
\lfloor x \rfloor |
\(\lfloor x \rfloor\) |
二项式系数：\dbinom nr |
\(\dbinom nr\) |
\binom nr 、n \choose r |
\(\binom nr\) 、\(n \choose r\) |
8. 空格
| 公式 | 符号 |
|---|---|
无视空格：a b |
\(a b\) |
a \qquad b |
\(a \qquad b\) |
a \quad b |
\(a \quad b\) |
a \ b |
\(a \ b\) |
a \, b |
\(a \, b\) |
a \; b |
\(a \; b\) |
a \! b |
\(a \! b\) |
9. 求和、积分、微分
| 公式 | 符号 |
|---|---|
\sum_1^n |
\(\sum_1^n\) |
\sum_{i=0}^\infty x^2 |
\(\sum_{i=0}^\infty x^2\) |
\int |
\(\int\) |
\iint |
\(\iint\) |
\iiint |
\(\iiint\) |
\oint |
\(\oint\) |
\prod |
\(\prod\) |
\coprod |
\(\coprod\) |
\bigcap |
\(\bigcap\) |
\bigcup |
\(\bigcup\) |
\bigvee |
\(\bigvee\) |
\bigwedge |
\(\bigwedge\) |
\infty |
\(\infty\) |
\nabla |
\(\nabla\) |
\partial x |
\(\partial x\) |
\mathrm{d} x |
\(\mathrm{d} x\) |
\dot x |
\(\dot x\) |
\ddot x |
\(\ddot x\) |
10. 分式、根号、函数
| 公式 | 符号 |
|---|---|
\frac 12 |
\(\frac 12\) |
强制分式为显示模式：\dfrac 12 |
\(\dfrac 12\) |
强制分式为文本模式：\tfrac 12 |
\(\tfrac 12\) |
用于连续分式：\cfrac 12 |
\(\cfrac 12\) |
\frac {x^2}{1+x} |
\(\frac {x^2}{1+x}\) |
用于复杂分式：x^2 \over 1+x |
\(x^2 \over 1+x\) |
\sqrt {x^3} |
\(\sqrt {x^3}\) |
\sqrt[3] {\frac xy} |
\(\sqrt[3] {\frac xy}\) |
\sin x |
\(\sin x\) |
\lim_{x \to 0} |
\(\lim_{x \to 0}\) |
\varinjlim |
\(\varinjlim\) |
\varprojlim |
\(\varprojlim\) |
\varliminf |
\(\varliminf\) |
\varlimsup |
\(\varlimsup\) |
11. 箭头符号
| 公式 | 符号 |
|---|---|
\rightarrow |
\(\rightarrow\) |
\leftarrow |
\(\leftarrow\) |
\Rightarrow |
\(\Rightarrow\) |
\Leftarrow |
\(\Leftarrow\) |
\longrightarrow |
\(\longrightarrow\) |
\longleftarrow |
\(\longleftarrow\) |
\Leftrightarrow |
\(\Leftrightarrow\) |
\leftrightarrow |
\(\leftrightarrow\) |
\Longleftrightarrow |
\(\Longleftrightarrow\) |
\longleftrightarrow |
\(\longleftrightarrow\) |
\xrightarrow[y>0] {x+y} |
\(\xrightarrow[y>0] {x+y}\) |
a \to b |
\(a \to b\) |
a \gets b |
\(a \gets b\) |
a \implies b |
\(a \implies b\) |
a \impliedby b |
\(a \impliedby b\) |
\lim_{x \to 0} |
\(\lim_{x \to 0}\) |
\longmapsto |
\(\longmapsto\) |
\hookleftarrow |
\(\hookleftarrow\) |
12. 几何和向量
| 公式 | 符号 |
|---|---|
\triangle |
\(\triangle\) |
\Diamond |
\(\Diamond\) |
\Box |
\(\Box\) |
\odot |
\(\odot\) |
\angle ABC |
\(\angle ABC\) |
30^\circ |
\(30^\circ\) |
\perp |
\(\perp\) |
\sim |
\(\sim\) |
\cong |
\(\cong\) |
\\hat{a} |
\(\hat{a}\) |
\vec{a} |
\(\vec{a}\) |
\overrightarrow{AB} |
\(\overrightarrow{AB}\) |
\overleftarrow{AB} |
\(\overleftarrow{AB}\) |
\overleftrightarrow{AB} |
\(\overleftrightarrow{AB}\) |
\widehat{e f g} |
\(\widehat{e f g}\) |
13. 上、下划线和上、下括号
| 公式 | 符号 |
|---|---|
\overline{h i j} |
\(\overline{h i j}\) |
\underline{h i j} |
\(\underline{h i j}\) |
\underbrace{a+b+\cdots+z}_{10} |
\(\underbrace{a+b+\cdots+z}_{10}\) |
\overbrace{a+b+\cdots+z}_{10} |
\(\overbrace{a+b+\cdots+z}_{10}\) |
13. 特殊字符
| 公式 | 符号 |
|---|---|
\eth |
\(\eth\) |
\S |
\(\S\) |
\% |
\(\%\) |
/dagger |
\(\dagger\) |
\ddagger |
\(\ddagger\) |
\ast 、* |
\(\ast\) 、\(*\) |
\circ |
\(\circ\) |
\bullet |
\(\bullet\) |
\ldots |
\(\ldots\) |
\cdots |
\(\cdots\) |
\vdots |
\(\vdots\) |
\ddots |
\(\ddots\) |
\smile |
\(\smile\) |
\frown |
\(\frown\) |
\wr |
\(\wr\) |
\oplus |
\(\oplus\) |
\bigoplus |
\(\bigoplus\) |
\otimes |
\(\otimes\) |
\bigotimes |
\(\bigotimes\) |
\bigodot |
\(\bigodot\) |
\boxtimes |
\(\boxtimes\) |
\boxplus |
\(\boxplus\) |
\triangleleft |
\(\triangleleft\) |
\triangleright |
\(\triangleright\) |
\imath |
\(\imath\) |
\hbar |
\(\hbar\) |
\ell |
\(\ell\) |
\mho |
\(\mho\) |
\Finv |
\(\Finv\) |
\Re |
\(\Re\) |
\Im |
\(\Im\) |
\wp |
\(\wp\) |
\diamondsuit |
\(\diamondsuit\) |
\heartsuit |
\(\heartsuit\) |
\clubsuit |
\(\clubsuit\) |
\spadesuit |
\(\spadesuit\) |
\Game |
\(\Game\) |
\flat |
\(\flat\) |
\natural |
\(\natural\) |
\sharp |
\(\sharp\) |
14. 阵列、矩阵、等式对齐、分段函数、编号
1、阵列
语法： $$\begin{array} … \end{array}$$，r 右对齐，l 左对齐，c 居中，| 垂直线，\hline 横线，\\ 换行，元素之间以 & 间隔
$$
\begin{array} {c|lcr}
n & \text{Left} & \text{Center} & \text{Right} \\
\hline
1 & 0.24 & 1 & 125 \\
2 & -1 & 189 & -8 \\
3 & -20 & 2000 & 1+10i
\end{array}
$$
\[\begin{array} {c|lcr}
n & \text{Left} & \text{Center} & \text{Right} \\
\hline
1 & 0.24 & 1 & 125 \\
2 & -1 & 189 & -8 \\
3 & -20 & 2000 & 1+10i
\end{array}
\]
2、矩阵
语法： $$\begin{matrix} … \end{matrix}$$，每行以 \\ 结尾，元素之间以 & 间隔
$$
\begin{matrix}
1 & x & x^2 \\
1 & y & y^2 \\
1 & z & z^2 \\
\end{matrix}
$$
\[\begin{matrix}
1 & x & x^2 \\
1 & y & y^2 \\
1 & z & z^2 \\
\end{matrix}
\]
添加括号：
pmatrix：()bmatrix：[ ]Bmatrix：vmatrix：| |Vmatrix：‖ ‖
添加省略号：
$$
\begin{pmatrix}
1 & a_1^2 & a_1^2 & \cdots & a_1^2 \\
1 & a_2^2 & a_2^2 & \cdots & a_2^2 \\
\vdots & \vdots & \vdots & \ddots & \vdots \\
1 & a_n^2 & a_n^2 & \cdots & a_n^2 \\
\end{pmatrix}
$$
\[\begin{pmatrix}
1 & a_1^2 & a_1^2 & \cdots & a_1^2 \\
1 & a_2^2 & a_2^2 & \cdots & a_2^2 \\
\vdots & \vdots & \vdots & \ddots & \vdots \\
1 & a_n^2 & a_n^2 & \cdots & a_n^2 \\
\end{pmatrix}
\]
水平增广矩阵，使用阵列语法：
$$
\left[
\begin{array}{cc|c}
1&2&3\\
4&5&6
\end{array}
\right]
$$
\[\left[
\begin{array}{cc|c}
1&2&3\\
4&5&6
\end{array}
\right]
\]
垂直增广矩阵：
$$
\begin{pmatrix}
a & b\\
c & d\\
\hline
1 & 0\\
0 & 1
\end{pmatrix}
$$
\[\begin{pmatrix}
a & b\\
c & d\\
\hline
1 & 0\\
0 & 1
\end{pmatrix}
\]
3、等式对齐
语法： \begin{align} … \end{align}，每行以 \\ 结尾，元素之间以 & 间隔
$$
\begin{align}
\sqrt{37} & = \sqrt{\frac{73^2-1}{12^2}} \\
& = \sqrt{\frac{73^2}{12^2}\cdot\frac{73^2-1}{73^2}} \\
& = \sqrt{\frac{73^2}{12^2}}\sqrt{\frac{73^2-1}{73^2}} \\
& = \frac{73}{12}\sqrt{1 - \frac{1}{73^2}} \\
& \approx \frac{73}{12}\left(1 - \frac{1}{2\cdot73^2}\right)
\end{align}
$$
\[\begin{align}
\sqrt{37} & = \sqrt{\frac{73^2-1}{12^2}} \\
& = \sqrt{\frac{73^2}{12^2}\cdot\frac{73^2-1}{73^2}} \\
& = \sqrt{\frac{73^2}{12^2}}\sqrt{\frac{73^2-1}{73^2}} \\
& = \frac{73}{12}\sqrt{1 - \frac{1}{73^2}} \\
& \approx \frac{73}{12}\left(1 - \frac{1}{2\cdot73^2}\right)
\end{align}
\]
4、分段函数
语法： \begin{cases} … \end{cases}，每行以 \\ 结尾，元素之间以 & 间隔
$$
f(n) =
\begin{cases}
n/2, & \text{if $n$ is even} \\
3n+1, & \text{if $n$ is odd}
\end{cases}
$$
\[f(n) =
\begin{cases}
n/2, & \text{if $n$ is even} \\
3n+1, & \text{if $n$ is odd}
\end{cases}
\]
$$
\left.
\begin{array}{l}
\text{if $n$ is even:}&n/2\\
\text{if $n$ is odd:}&3n+1
\end{array}
\right\}
=f(n)
$$
\[\left.
\begin{array}{l}
\text{if $n$ is even:}&n/2\\
\text{if $n$ is odd:}&3n+1
\end{array}
\right\}
=f(n)
\]
5、编号
语法：\tag
$$
y=x^2 \tag{1.5a}
$$
\[y=x^2 \tag{1.5a}
\]
