# $$\mu = \alpha + \beta_1 x_i + \beta_2 x_i^2 + \beta_3 x_i^3$$

#$$\frac{\sum (\bar{x} - x_i)^2}{n-1}$$

#$$
#begin{aligned}
#y &= \alpha + \beta x + \epsilon \\
#\epsilon &\in \text{Normal}(\mu, \sigma) 
#\end{aligned}
# $$

#$$
#\begin{split}
#a& =b+c-d\\
#& \quad +e-f\\
#& =g+h\\
#& =i
#\end{split}
#$$

#$$
#\begin{gather}
#a_1=b_1+c_1\\
#a_2=b_2+c_2-d_2+e_2
#\end{gather}
#$$

#$$
#\begin{align}
#{11}& =b_{11}&
#a_{12}& =b_{12}\\
#a_{21}& =b_{21}&
#a_{22}& =b_{22}+c_{22}
#\end{align}
#$$

用boldsymbol或pmb 命令加粗

#$$
#A_\infty + \pi A_0
#\sim \mathbf{A}_{\boldsymbol{\infty}} \boldsymbol{+}
#\boldsymbol{\pi} \mathbf{A}_{\boldsymbol{0}}
#\sim\pmb{A}_{\pmb{\infty}} \pmb{+}\pmb{\pi} \pmb{A}_{\pmb{0}}
#$$

\[ A_\infty + \pi A_0 \sim \mathbf{A}_{\boldsymbol{\infty}} \boldsymbol{+} \boldsymbol{\pi} \mathbf{A}_{\boldsymbol{0}} \sim\pmb{A}_{\pmb{\infty}} \pmb{+}\pmb{\pi} \pmb{A}_{\pmb{0}} \] # 各种分隔符

# $$
# \begin{pmatrix}
# \alpha& \beta^{*}\\
# \gamma^{*}& \delta
# \end{pmatrix}
# $$

\[ \begin{pmatrix} \alpha& \beta^{*}\\ \gamma^{*}& \delta \end{pmatrix} \]

# $$
# \begin{bmatrix}
# \alpha& \beta^{*}\\
# \gamma^{*}& \delta
# \end{bmatrix}
# $$

\[ \begin{bmatrix} \alpha& \beta^{*}\\ \gamma^{*}& \delta \end{bmatrix} \]

# $$
# \begin{vmatrix}
# \alpha& \beta^{*}\\
# \gamma^{*}& \delta
# \end{vmatrix}
# $$

\[ \begin{vmatrix} \alpha& \beta^{*}\\ \gamma^{*}& \delta \end{vmatrix} \] # 一个smallmatrix环境生成小矩阵，和文本一起

# $$
# \bigl( \begin{smallmatrix}
# a&b\\ c&d
# \end{smallmatrix} \bigr)
# $$

\[ \bigl( \begin{smallmatrix} a&b\\ c&d \end{smallmatrix} \bigr) \] # 用盒子boxed把他框柱

#$$\boxed{\eta \leq C(\delta(\eta) +\Lambda_M(0,\delta))}$$

\[\boxed{\eta \leq C(\delta(\eta) +\Lambda_M(0,\delta))}\] # frac 命令接受分子与分母，tfrac与dfrac来猜测大小（t = text style, d =display style）

# $$
# \begin{equation}
# \frac{1}{k}\log_2 c(f),\quad\dfrac{1}{k}\log_2 c(f),
# \quad\tfrac{1}{k}\log_2 c(f)
# \end{equation}
# $$

\[ \begin{equation} \frac{1}{k}\log_2 c(f),\quad\dfrac{1}{k}\log_2 c(f), \quad\tfrac{1}{k}\log_2 c(f) \end{equation} \]

# $$
# \begin{equation}
# \Re{z} =\frac{n\pi \dfrac{\theta +\psi}{2}}{
# \left(\dfrac{\theta +\psi}{2}\right)^2 + \left( \dfrac{1}{2}
# \log \left\lvert\dfrac{B}{A}\right\rvert\right)^2}.
# \end{equation}
# $$

\[ \begin{equation} \Re{z} =\frac{n\pi \dfrac{\theta +\psi}{2}}{ \left(\dfrac{\theta +\psi}{2}\right)^2 + \left( \dfrac{1}{2} \log \left\lvert\dfrac{B}{A}\right\rvert\right)^2}. \end{equation} \] # binom写二项表达式

#$$2^k-\binom{k}{1}2^{k-1}+\binom{k}{2}2^{k-2}$$

\[2^k-\binom{k}{1}2^{k-1}+\binom{k}{2}2^{k-2}\] # 写左括号与右括号

# $$
# \left((a_1 b_1) - (a_2 b_2)\right)
# \left((a_2 b_1) + (a_1 b_2)\right)
# \quad\text{versus}\quad
# \bigl((a_1 b_1) - (a_2 b_2)\bigr)
# \bigl((a_2 b_1) + (a_1 b_2)\bigr)
# $$

\[ \left((a_1 b_1) - (a_2 b_2)\right) \left((a_2 b_1) + (a_1 b_2)\right) \quad\text{versus}\quad \bigl((a_1 b_1) - (a_2 b_2)\bigr) \bigl((a_2 b_1) + (a_1 b_2)\bigr) \] # int_生成积分，但是为啥绝对值出错了

#$$\int_{\abs{x-x_z(t)}<X_0} ...$$

\[\int_{\abs{x-x_z(t)}<X_0} ...\]

I#$$\int\limits_{\abs{x-x_z(t)}<X_0} ...$$

## function (x) 
## {
##     structure(x, class = unique(c("AsIs", oldClass(x))))
## }
## <bytecode: 0x00000000152d5400>
## <environment: namespace:base>

\[\int\limits_{\abs{x-x_z(t)}<X_0} ...\] # substack 命令生成多行下标或上标

# $$
# \sum_{\substack{
# 0\le i\le m\\
# 0<j<n}}
# P(i,j)
# $$

\[ \sum_{\substack{ 0\le i\le m\\ 0<j<n}} P(i,j) \]

# $$
# \frac{\sum_{n > 0} z^n}
# {\prod_{1\leq k\leq n} (1-q^k)}
# $$

\[ \frac{\sum_{n > 0} z^n} {\prod_{1\leq k\leq n} (1-q^k)} \]

# $$
# \frac{{\displaystyle\sum\nolimits_{n> 0} z^n}}
# {{\displaystyle\prod\nolimits_{1\leq k\leq n} (1-q^k)}}
# $$

\[ \frac{{\displaystyle\sum\nolimits_{n> 0} z^n}} {{\displaystyle\prod\nolimits_{1\leq k\leq n} (1-q^k)}} \]

knitr::include_graphics("./img/latex.png")

knitr::include_graphics("./img/latex_2.png")

knitr::include_graphics("./img/latex_3.png")

knitr::include_graphics("./img/latex_4.png")