# 수식 표현 안내

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## LaTeX 명령예

### cases

$$f(n) = \begin{cases} n/2, & \text{if n is even}\\ 3n+1, & \text{if n is odd} \\ \end{cases}$$

$$f(x)= \begin{cases} 0&x\in[-\pi,\pi]\\ 1&x\notin[-\pi,\pi] \end{cases}$$

#### atop

$$\tilde y=\left\{ {\ddot x\text{ if \vec x odd}\atop\hat{\,\bar x+1}\text{ if even}}\right.$$

### array

$$\left\{ \begin{array}{c} a_1x+b_1y+c_1z=d_1 \\ a_2x+b_2y+c_2z=d_2 \\ a_3x+b_3y+c_3z=d_3 \end{array} \right.$$ $$\begin{array}{c|lcr} n & \text{Left} & \text{Center} & \text{Right} \\ \hline 1 & 0.24 & 1 & 125 \\ 2 & -1 & 189 & -8 \\ 3 & -20 & 2000 & 1+10i \\ \end{array}$$

$A=\left( \begin{array}{c.cccc}&1&2&\cdots&n\\ 1&a_{11}&a_{12}&\cdots&a_{1n}\\ 2&a_{21}&a_{22}&\cdots&a_{2n}\\ \vdots&\vdots&\vdots&\ddots&\vdots\\ n&a_{n1}&a_{n2}&\cdots&a_{nn} \end{array} \right)$

### eqnarray

$$\left.\begin{eqnarray} x+y+z&=&3\\2y&=&x+z\\2x+y&=&z\end{eqnarray}\right\}$$

### align

\begin{align} & {} \quad \int Y_{l_1}^{m_1}(\theta,\varphi)Y_{l_2}^{m_2}(\theta,\varphi)Y_{l_3}^{m_3}(\theta,\varphi)\,\sin\theta\,\mathrm{d}\theta\,\mathrm{d}\varphi \\ & = \sqrt{\frac{(2l_1+1)(2l_2+1)(2l_3+1)}{4\pi}} \begin{pmatrix} l_1 & l_2 & l_3 \\[8pt] 0 & 0 & 0 \end{pmatrix} \begin{pmatrix} l_1 & l_2 & l_3\\ m_1 & m_2 & m_3 \end{pmatrix} \end{align}

\begin{align} \omega_{n} & =\int\cdots\int_{x_1^2+\cdots+x_n^2\leq\ 1} dx_{1}\cdots dx_{n} \\ & = \int_{-1}^{1}\left(\int\cdots \int_{x_1^2+\cdots +x_{n-1}^2\leq\ 1-x_{n}^2} dx_{1}\cdots dx_{n-1}\right)dx_{n} \end{align}

### overbrace/underbrace

$$\overbrace{ 1+2+\cdots+100 }^{5050}$$

$\underbrace{i \hbar \frac{\partial}{\partial t} |\varphi_\pm\rangle = \left( \frac{( \mathbf{p} -e \mathbf A)^2}{2 m} + e \phi \right) \hat 1 \mathbf |\varphi_\pm\rangle }_\mathrm{Schr\ddot{o}dinger~equation} - \underbrace{\frac{e \hbar}{2m}\mathbf{\sigma} \cdot \mathbf B \mathbf |\varphi_\pm\rangle }_\text{Stern Gerlach term}$ 파울리 방정식

### substack

$$\sum_{ \substack{ r,s,t\geq 0 \\ r+s=m,s+t=n}} \frac{q^{rt}}{(q)_r(q)_s(q)_t}=\frac{1}{(q)_{m}(q)_{n}}$$

### 크기

large

$$\large f^\prime(x)\ = \lim_{\Delta x\to0}\frac{f(x+\Delta x)-f(x)}{\Delta x}$$

Large

$$\Large f^\prime(x)\ = \lim_{\Delta x\to0}\frac{f(x+\Delta x)-f(x)}{\Delta x}$$

LARGE

$$\LARGE f^\prime(x)\ = \lim_{\Delta x\to0}\frac{f(x+\Delta x)-f(x)}{\Delta x}$$

### 그리스 문자

$$\alpha \beta \gamma \delta \epsilon (\varepsilon) \zeta \eta \theta (\vartheta) \iota \kappa \lambda \mu \nu \xi o \pi \rho \sigma \tau \upsilon \phi (\varphi) \chi \psi \omega$$

$$A B \Gamma \Delta E Z H \Theta I K \Lambda M N \Xi O \Pi P \Sigma T \Upsilon \Phi X \Psi \Omega$$

### 글꼴

$$\begin{array}{l|l} \text{mathcal }&\mathcal{ABCDEFGHIJKLMNOPQRSTUVWXYZ}\\ \text{mathcal }&\mathcal{abcdefghijklmnopqrstuvwxyz}\\ \text{mathscr }&\mathscr{ABCDEFGHIJKLMNOPQRSTUVWXYZ}\\ \text{mathscr }&\mathscr{abcdefghijklmnopqrstuvwxyz}\\ \text{mathsf }&\mathsf{ABCDEFGHIJKLMNOPQRSTUVWXYZ}\\ \text{mathsf }&\mathsf{abcdefghijklmnopqrstuvwxyz}\\ \text{mathbb }&\mathbb{ABCDEFGHIJKLMNOPQRSTUVWXYZ}\\ \text{mathbb }&\mathbb{abcdefghijklmnopqrstuvwxyz}\\ \text{mathbf }&\mathbf{ABCDEFGHIJKLMNOPQRSTUVWXYZ}\\ \text{mathbf }&\mathbf{abcdefghijklmnopqrstuvwxyz}\\ \text{mathfrak }&\mathfrak{ABCDEFGHIJKLMNOPQRSTUVWXYZ}\\ \text{mathfrak }&\mathfrak{abcdefghijklmnopqrstuvwxyz} \end{array}$$

### 기타

$$A \xleftarrow{n+\mu-1} B \xrightarrow[T]{n\pm i-1} C$$

$$\overset{\alpha}{\omega} \underset{\mu}{\nu} \overset{\beta}{\underset{\Delta}{\tau}} \stackrel{\zeta}{\eta}$$

\begin{align} \mathscr{I}_2 =&\color{red}{\cancelto{0}{\color{grey}{x\arctan^2{x}\ln{x}\Bigg{|}^1_0}}}-\int^1_0\arctan^2{x}\ {\rm d}x-\int^1_0\frac{2x\arctan{x}\ln{x}}{1+x^2}{\rm d}x\\ =&-\frac{\pi^2}{16}-\frac{\pi}{4}\ln{2}+\mathbf{G}+2\sum^\infty_{n=0}\frac{(-1)^nH_{2n+1}}{(2n+3)^2}-\sum^\infty_{n=0}\frac{(-1)^nH_{n}}{(2n+3)^2}\\ =&\frac{\pi^3}{16}-\frac{\pi^2}{16}-\frac{\pi}{4}\ln{2}+\mathbf{G}-2\sum^\infty_{n=0}\frac{(-1)^nH_{2n+1}}{(2n+1)^2}+\sum^\infty_{n=1}\frac{(-1)^{n}H_n}{(2n+1)^2} \end{align}

• $$\chi(t)=\left(\frac{t}{p}\right)$$
• $$\operatorname{Re} a > 0$$
• $$x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$$
• $$720\div12=60$$
• $\exists c \in (a,b) \quad \mathbf{s.t.} \quad f'(c)=\frac{f(b)-f(a)}{b-a}$
• $$\mathcal{H}om$$
• $$G\"odel$$ http://www.phil.cam.ac.uk/teaching_staff/Smith/LaTeX/other-macros/godelcorners.html
• $$\Large\begin{array}{rccclBCB} &f&\longr[75]^{\alpha:{\normalsize f\rightar~g}}&g\\ \large\gamma&\longd[50]&&\longd[50]&\large\gamma\\ &u&\longr[75]_\beta&v\end{array}$$
1. \Large\begin{array}{rccclBCB} &f&\longr[75]^{\alpha:{\normalsize f\rightar~g}}&g\\ \large\gamma&\longd[50]&&\longd[50]&\large\gamma\\ &u&\longr[75]_\beta&v\end{array}
• $$\Large\overbrace{a,...,a}^{\text{k a^,s}}, \underbrace{b,...,b}_{\text{l b^,s}}\hspace{10} \large\underbrace{\overbrace{a...a}^{\text{k a^,s}}, \overbrace{b...b}^{\text{l b^,s}}}_{\text{k+l elements}}$$
1. \Large\overbrace{a,...,a}^{\text{k a^,s}}, \underbrace{b,...,b}_{\text{l b^,s}}\hspace{10} \large\underbrace{\overbrace{a...a}^{\text{k a^,s}}, \overbrace{b...b}^{\text{l b^,s}}}_{\text{k+l elements}}