数学公式

参考文档

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$x_i^2，{x^y}^z$

$\alpha，\beta，\omega，\Gamma，\Delta，\Omega$

$$\{ and \} (\frac12) \left(\frac12\right) ( and ) [ and ] \{ and \} |x| \langle and \rangle \lceil and \rceil \lfloor and \rfloor \left.\frac12\right\rbrace$$
$$\sum_1^n \sum_{i=0}^\infty i^2 \prod \int \bigcup \bigcap \iint$$
$$\frac ab \frac{a+1}{b+1} {a+1\over b+1}$$
$$\mathbb{CHNQTR}$$
$$\mathbf{CHNQTR}$$
$$\Bbb{CHNQTR}$$
$$\mathtt{CHNQTR}$$
$$\mathrm{CHNQTR}$$
$$\mathcal{CHNQTR}$$
$$\mathscr{CHNQTR}$$
$$\mathfrak{CHNQTR}$$
$${CHNQTR}$$

$$\sqrt{x^3} \sqrt[3]{\frac xy} \lim_{x\to 0}$$
$$\sin x \lt \gt \le \ge \neq \not\lt$$
$$\times \div \pm \mp \cdot$$
$$\cup \cap \setminus \subset \subseteq \subsetneq \supset \in \notin \emptyset \varnothing$$
$${n+1 \choose 2k} or \binom{n+1}{2k}$$
$$\to \rightarrow \leftarrow \Rightarrow \Leftarrow \mapsto$$
$$\land \lor \lnot \forall \exists \top \bot \vdash \vDash$$
$$\star \ast \oplus \circ \bullet$$
$$\approx \sim \simeq \cong \equiv \prec$$
$$\infty \aleph_0 ∞ℵ0 \nabla \partial$$
$$a\equiv b\pmod n$$
[\ldots] is the dots in {a1,a2,…,an}
[\cdots] is the dots in {a1+a2+⋯+an}
$$\epsilon \varepsilon \phi \varphi \ell$$
$$\text{DFGHH}$$
$$\hat{X} \widehat{X} \bar{x} \overline{xyz} \vec{x} \overrightarrow{xyz} \overleftrightarrow{xyz} \dot{x} \ddot{x} \$ \{ \_$$
$$\begin{matrix} 1 & x & x^2 \\ 1 & y & y^2 \\ 1 & z & z^2 \\ \end{matrix}$$
$$\begin{pmatrix} 1 & x & x^2 \\ 1 & y & y^2 \\ 1 & z & z^2 \\ \end{pmatrix}$$
$$\begin{bmatrix} 1 & x & x^2 \\ 1 & y & y^2 \\ 1 & z & z^2 \\ \end{bmatrix}$$
$$\begin{Bmatrix} 1 & x & x^2 \\ 1 & y & y^2 \\ 1 & z & z^2 \\ \end{Bmatrix}$$
$$\begin{vmatrix} 1 & x & x^2 \\ 1 & y & y^2 \\ 1 & z & z^2 \\ \end{vmatrix}$$
$$\begin{pmatrix} 1 & a_1 & a_1^2 & \cdots & a_1^n \\ 1 & a_2 & a_2^2 & \cdots & a_2^n \\ \vdots & \vdots & \vdots & \ddots & \vdots \\ 1 & a_m & a_m^2 & \cdots & a_m^n \\ \end{pmatrix}$$
$$\left[ \begin{array}{cc|c} 1&2&3\\ 4&5&6 \end{array} \right]$$
$$\bigl( \begin{smallmatrix} a & b \\ c & d \end{smallmatrix} \bigr)$$
$$\begin{align} \sqrt{37} & = \sqrt{\frac{73^2-1}{12^2}} \\ & = \sqrt{\frac{73^2}{12^2}\cdot\frac{73^2-1}{73^2}} \\ & = \sqrt{\frac{73^2}{12^2}}\sqrt{\frac{73^2-1}{73^2}} \\ & = \frac{73}{12}\sqrt{1 - \frac{1}{73^2}} \\ & \approx \frac{73}{12}\left(1 - \frac{1}{2\cdot73^2}\right) \end{align}$$
$$f(n) = \begin{cases} n/2, & \text{if $n$ is even} \\ 3n+1, & \text{if $n$ is odd} \end{cases} \\ \\ \left. \begin{array}{l} \text{if $n$ is even:}&n/2\\ \text{if $n$ is odd:}&3n+1 \end{array} \right\} =f(n)$$
$$f(n) = \begin{cases} \frac{n}{2}, & \text{if $n$ is even} \\[2ex] 3n+1, & \text{if $n$ is odd} \end{cases}$$
$$\begin{array}{c|lcr} n & \text{Left} & \text{Center} & \text{Right} \\ \hline 1 & 0.24 & 1 & 125 \\ 2 & -1 & 189 & -8 \\ 3 & -20 & 2000 & 1+10i \end{array}$$
$$\left\{x\middle | \frac{x^2}{2} \in \mathbb{z}\right\}$$
$$\color{red}{text}\\ \color{yellow}{text}\\ \color{blue}{text}\\ \color{green}{text}\\ \color{#000}{text}\\ $$
$$

$$\left\{ \begin{array}{c} a_1x+b_1y+c_1z=d_1 \\ a_2x+b_2y+c_2z=d_2 \\ a_3x+b_3y+c_3z=d_3 \end{array} \right.$$
$$\begin{cases} a_1x+b_1y+c_1z=d_1 \\ a_2x+b_2y+c_2z=d_2 \\ a_3x+b_3y+c_3z=d_3 \end{cases}$$
$$\left\{ \begin{aligned} a_1x+b_1y+c_1z &=d_1+e_1 \\ a_2x+b_2y&=d_2 \\ a_3x+b_3y+c_3z &=d_3 \end{aligned} \right.$$
$$\left\{ \begin{array}{ll} a_1x+b_1y+c_1z &=d_1+e_1 \\ a_2x+b_2y &=d_2 \\ a_3x+b_3y+c_3z &=d_3 \end{array} \right.$$
$$\begin{cases} a_1x+b_1y+c_1z=\frac{p_1}{q_1} \\[2ex] a_2x+b_2y+c_2z=\frac{p_2}{q_2} \\[2ex] a_3x+b_3y+c_3z=\frac{p_3}{q_3} \end{cases}$$
$$\left\{ \begin{array}{c} 0 = c_x-a_{x0}-d_{x0}\frac{(c_x-a_{x0})\cdot d_{x0}}{\|d_{x0}\|^2} + c_x-a_{x1}-d_{x1}\frac{(c_x-a_{x1})\cdot d_{x1}}{\|d_{x1}\|^2} \\ 0 = c_y-a_{y0}-d_{y0}\frac{(c_y-a_{y0})\cdot d_{y0}}{\|d_{y0}\|^2} + c_y-a_{y1}-d_{y1}\frac{(c_y-a_{y1})\cdot d_{y1}}{\|d_{y1}\|^2} \end{array} \right.$$
$$\underset{j=1}{\overset{\infty}{\LARGE\mathrm K}}\frac{a_j}{b_j}=\cfrac{a_1}{b_1+\cfrac{a_2}{b_2+\cfrac{a_3}{b_3+\ddots}}}$$
$$\mathop{\LARGE\mathrm K}_{i=1}^\infty \frac{a_i}{b_i}$$
$$f\left( \left[ \frac{ 1+\left\{x,y\right\} }{ \left( \frac{x}{y}+\frac{y}{x} \right) \left(u+1\right) }+a \right]^{3/2} \right)$$
$$\left\langle q \middle\| \frac{\frac{x}{y}}{\frac{u}{v}} \middle| p \right\rangle$$
$$\underbrace{a\cdot a\cdots a}_{b\text{ times}}\\ +y^3 \stackrel{\eqref{*}}= x^2\\ \lim\limits_{x \to 1} \frac{x^2-1}{x-1}\\ |x|, ||v|| \quad\longrightarrow\quad \lvert x\rvert, \lVert v\rVert\\ 90^\circ$$

$\require{AMScd}$

$$\begin{CD} A @>a>> B\\ @V b V V{\large\circlearrowleft} @VV c V\\ C @>>d> D \end{CD}$$

$$\begin{CD} A @>>> B @>{\text{very long label}}>> C \\ @. @AAA @| \\ D @= E @<<< F \end{CD}$$