LaTeX插入数学公式

亦凉 2022-05-14 14:08 528阅读 0赞

form：[https://www.cnblogs.com/doodle777/p/4951096.html][https_www.cnblogs.com_doodle777_p_4951096.html]

# [LaTeX 中插入数学公式][https_www.cnblogs.com_doodle777_p_4951096.html] #

**一、常用的数学符号**

**1、小写希腊字母**

<table> 
 <tbody> 
  <tr> 
   <td style="vertical-align:top;"><img alt="\alpha" src="http://latex.codecogs.com/gif.latex?%5Calpha"></td> 
   <td style="vertical-align:top;">\alpha</td> 
   <td style="vertical-align:top;"><img alt="\nu" src="http://latex.codecogs.com/gif.latex?%5Cnu"></td> 
   <td style="vertical-align:top;">\nu</td> 
  </tr> 
  <tr> 
   <td style="vertical-align:top;"><img alt="\beta" src="http://latex.codecogs.com/gif.latex?%5Cbeta"></td> 
   <td style="vertical-align:top;">\beta</td> 
   <td style="vertical-align:top;"><img alt="\xi" src="http://latex.codecogs.com/gif.latex?%5Cxi"></td> 
   <td style="vertical-align:top;">\xi</td> 
  </tr> 
  <tr> 
   <td style="vertical-align:top;"><img alt="\gamma" src="http://latex.codecogs.com/gif.latex?%5Cgamma"></td> 
   <td style="vertical-align:top;">\gamma</td> 
   <td style="vertical-align:top;"><img alt="o" src="http://latex.codecogs.com/gif.latex?o"></td> 
   <td style="vertical-align:top;">o</td> 
  </tr> 
  <tr> 
   <td style="vertical-align:top;"><img alt="\delta" src="http://latex.codecogs.com/gif.latex?%5Cdelta%0A"></td> 
   <td style="vertical-align:top;">\delta</td> 
   <td style="vertical-align:top;"><img alt="\pi" src="http://latex.codecogs.com/gif.latex?%5Cpi"></td> 
   <td style="vertical-align:top;">\pi</td> 
  </tr> 
  <tr> 
   <td style="vertical-align:top;"><img alt="\epsilon" src="http://latex.codecogs.com/gif.latex?%5Cepsilon"></td> 
   <td style="vertical-align:top;">\epsilon</td> 
   <td style="vertical-align:top;"><img alt="\rho" src="http://latex.codecogs.com/gif.latex?%5Crho"></td> 
   <td style="vertical-align:top;">\rho</td> 
  </tr> 
  <tr> 
   <td style="vertical-align:top;"><img alt="\zeta" src="http://latex.codecogs.com/gif.latex?%5Czeta"></td> 
   <td style="vertical-align:top;">\zeta</td> 
   <td style="vertical-align:top;"><img alt="\sigma" src="http://latex.codecogs.com/gif.latex?%5Csigma"></td> 
   <td style="vertical-align:top;">\sigma</td> 
  </tr> 
  <tr> 
   <td style="vertical-align:top;"><img alt="\eta" src="http://latex.codecogs.com/gif.latex?%5Ceta"></td> 
   <td style="vertical-align:top;">\eta</td> 
   <td style="vertical-align:top;"><img alt="\tau" src="http://latex.codecogs.com/gif.latex?%5Ctau"></td> 
   <td style="vertical-align:top;">\tau</td> 
  </tr> 
  <tr> 
   <td style="vertical-align:top;"><img alt="\theta" src="http://latex.codecogs.com/gif.latex?%5Ctheta"></td> 
   <td style="vertical-align:top;">\theta</td> 
   <td style="vertical-align:top;"><img alt="\upsilon" src="http://latex.codecogs.com/gif.latex?%5Cupsilon"></td> 
   <td style="vertical-align:top;">\upsilon</td> 
  </tr> 
  <tr> 
   <td style="vertical-align:top;"><img alt="\iota" src="http://latex.codecogs.com/gif.latex?%5Ciota"></td> 
   <td style="vertical-align:top;">\iota</td> 
   <td style="vertical-align:top;"><img alt="\phi" src="http://latex.codecogs.com/gif.latex?%5Cphi"></td> 
   <td style="vertical-align:top;">\phi</td> 
  </tr> 
  <tr> 
   <td style="vertical-align:top;"><img alt="\kappa" src="http://latex.codecogs.com/gif.latex?%5Ckappa"></td> 
   <td style="vertical-align:top;">\kappa</td> 
   <td style="vertical-align:top;"><img alt="\chi" src="http://latex.codecogs.com/gif.latex?%5Cchi"></td> 
   <td style="vertical-align:top;">\chi</td> 
  </tr> 
  <tr> 
   <td style="vertical-align:top;"><img alt="\lambda" src="http://latex.codecogs.com/gif.latex?%5Clambda"></td> 
   <td style="vertical-align:top;">\lambda</td> 
   <td style="vertical-align:top;"><img alt="\psi" src="http://latex.codecogs.com/gif.latex?%5Cpsi"></td> 
   <td style="vertical-align:top;">\psi</td> 
  </tr> 
  <tr> 
   <td style="vertical-align:top;"><img alt="\mu" src="http://latex.codecogs.com/gif.latex?%5Cmu"></td> 
   <td style="vertical-align:top;">\mu</td> 
   <td style="vertical-align:top;"><img alt="\omega" src="http://latex.codecogs.com/gif.latex?%5Comega"></td> 
   <td style="vertical-align:top;">\omega</td> 
  </tr> 
 </tbody> 
</table>

**2、大写希腊字母**

大写希腊字母只需要将小写希腊字母的第一个英文字母大写即可。但是需要注意的是，有些小写希腊字母的大写可以直接通过键盘输入，也就是说和英文大写是相同的。

<table> 
 <tbody> 
  <tr> 
   <td style="vertical-align:top;"><img alt="\Gamma" src="http://latex.codecogs.com/gif.latex?%5CGamma"></td> 
   <td style="vertical-align:top;">\Gamma</td> 
   <td style="vertical-align:top;"><img alt="\Lambda" src="http://latex.codecogs.com/gif.latex?%5CLambda"></td> 
   <td style="vertical-align:top;">\Lambda</td> 
  </tr> 
  <tr> 
   <td style="vertical-align:top;"><img alt="\Sigma" src="http://latex.codecogs.com/gif.latex?%5CSigma"></td> 
   <td style="vertical-align:top;">\Sigma</td> 
   <td style="vertical-align:top;"><img alt="\Psi" src="http://latex.codecogs.com/gif.latex?%5CPsi"></td> 
   <td style="vertical-align:top;">\Psi</td> 
  </tr> 
  <tr> 
   <td style="vertical-align:top;"><img alt="\Delta" src="http://latex.codecogs.com/gif.latex?%5CDelta"></td> 
   <td style="vertical-align:top;">\Delta</td> 
   <td style="vertical-align:top;"><img alt="\Upsilon" src="http://latex.codecogs.com/gif.latex?%5CUpsilon"></td> 
   <td style="vertical-align:top;">\Upsilon</td> 
  </tr> 
  <tr> 
   <td style="vertical-align:top;"><img alt="\Omega" src="http://latex.codecogs.com/gif.latex?%5COmega"></td> 
   <td style="vertical-align:top;">\Omega</td> 
   <td style="vertical-align:top;"><img alt="\Theta" src="http://latex.codecogs.com/gif.latex?%5CTheta"></td> 
   <td style="vertical-align:top;">\Theta</td> 
  </tr> 
  <tr> 
   <td style="vertical-align:top;"><img alt="\Xi" src="http://latex.codecogs.com/gif.latex?%5CXi"></td> 
   <td style="vertical-align:top;">\Xi</td> 
   <td style="vertical-align:top;"><img alt="\Pi" src="http://latex.codecogs.com/gif.latex?%5CPi"></td> 
   <td style="vertical-align:top;">\Pi</td> 
  </tr> 
  <tr> 
   <td style="vertical-align:top;"><img alt="\Phi" src="http://latex.codecogs.com/gif.latex?%5CPhi"></td> 
   <td style="vertical-align:top;">\Phi</td> 
   <td style="vertical-align:top;">&nbsp;</td> 
   <td style="vertical-align:top;">&nbsp;</td> 
  </tr> 
 </tbody> 
</table>

**3、运算符**

对于加减除，对应键盘上便可打出来，但是对于乘法，键盘上没有这个符号，所以我们应该输入 \\times 来显示一个 ![\\times][times] 号。

普通字符在数学公式中含义一样，除了 \# $ % & ~ \_ ^ \\ \{ \} 若要在数学环境中表示这些符号\# $ % & \_ \{ \}，需要分别表示为\\\# \\$ \\% \\& \\\_ \\\{ \\\}，即在个字符前加上\\。

**二、简单格式**

**1、上下标**

上标：$ f(x) = x^2 $ 或者 $ f(x) = \{x\}^\{2\} $ 均可表示![f(x)=x^2][f_x_x_2]。

下标：$ f(x) = x\_2 $ 或者 $ f(x) = \{x\}\_\{2\} $ 均可表示![f(x)=x\_2][f_x_x_2 1]。

上下标可以级联：$ f(x) = x\_1^2 + \{x\}\_\{2\}^\{2\} $![f(x)=x\_1^2+\{x\}\_\{2\}^\{2\}][f_x_x_1_2_x_2_2]。

**2、加粗和倾斜**

加粗：$ f(x) = \\textbf\{x\}^2 $ ![f(x)=\\textbf\{x\}^2][f_x_textbf_x_2]。

文本：$ f(x) = x^2 \\mbox\{abcd\} $ ![f(x)=x^2\\mbox\{abcd\}][f_x_x_2_mbox_abcd]

倾斜：$ f(x) = x^2 \\mbox\{\\emph\{abcd\} defg\} $ ![f(x)=x^2\\mbox\{\\emph\{abcd\}defg\}][f_x_x_2_mbox_emph_abcd_defg]

**3、分数**

![f(x,y)=\\frac\{x^2\}\{y^3\}][f_x_y_frac_x_2_y_3]

**4、开根号**

![f(x,y)=\\sqrt\[n\]\{x^2y^3\}][f_x_y_sqrt_n_x_2y_3]

**5、省略号**

<table> 
 <tbody> 
  <tr> 
   <td> <p>1</p> </td> 
   <td> <p><code>$ f(x_1, x_2, \ldots, x_n) = x_1 + x_2 + \cdots + x_n $</code></p> </td> 
  </tr> 
 </tbody> 
</table>

![f(x\_1,x\_2,\\ldots,x\_n)=x\_1+x\_2+\\cdots+x\_n][f_x_1_x_2_ldots_x_n_x_1_x_2_cdots_x_n]

**6、括号和分隔符**

公式高度比较低的话直接从键盘输入括号即可，但是对于公式高度比较高的情形，需要特殊的运算。

![\{f\}'(x)=(\\frac\{df\}\{dx\})][f_x_frac_df_dx]

<table> 
 <tbody> 
  <tr> 
   <td> <p>1</p> </td> 
   <td> <p><code>$ {f}'(x) = \left( \frac{df}{dx} \right) $</code></p> </td> 
  </tr> 
 </tbody> 
</table>

![\{f\}'(x)=\\left(\\frac\{df\}\{dx\}\\right)][f_x_left_frac_df_dx_right]

可以看出，通过将 \\left( 和 \\right) 结合使用，可以将括号大小随着其内容变化。\[ \] 和 \{ \} 同理。

<table> 
 <tbody> 
  <tr> 
   <td> <p>1</p> </td> 
   <td> <p><code>$ {f}'(</code><code>0</code><code>) =&nbsp; \left. \frac{df}{dx} \right|_{x=</code><code>0</code><code>} $</code></p> </td> 
  </tr> 
 </tbody> 
</table>

![\{f\}'(0)=\\left.\\frac\{df\}\{dx\}\\right|\_\{x=0\}][f_0_left._frac_df_dx_right_x_0]

**三、矩阵和行列式**

<table> 
 <tbody> 
  <tr> 
   <td> <p>1</p> <p>2</p> <p>3</p> <p>4</p> </td> 
   <td> <p><code>$ A=\left[ \begin{matrix}</code></p> <p><code>&nbsp;&nbsp;&nbsp;</code><code>a &amp; b&nbsp; \\</code></p> <p><code>&nbsp;&nbsp;&nbsp;</code><code>c &amp; d&nbsp; \\</code></p> <p><code>\end{matrix} \right] $</code></p> </td> 
  </tr> 
 </tbody> 
</table>

![A=\\left\[\\begin\{matrix\} a&b\\\\ c&d\\\\ \\end\{matrix\}\\right\]][A_left_begin_matrix_ a_b_ c_d_ _end_matrix_right]

<table> 
 <tbody> 
  <tr> 
   <td> <p>1</p> <p>2</p> <p>3</p> <p>4</p> </td> 
   <td> <p><code>$ \chi (\lambda)=\left| \begin{matrix}</code></p> <p><code>&nbsp;&nbsp;&nbsp;</code><code>\lambda - a &amp; -b&nbsp; \\</code></p> <p><code>&nbsp;&nbsp;&nbsp;</code><code>-c &amp; \lambda - d&nbsp; \\</code></p> <p><code>\end{matrix} \right| $</code></p> </td> 
  </tr> 
 </tbody> 
</table>

![\\chi(\\lambda)=\\left|\\begin\{matrix\} \\lambda-a&-b\\\\ -c&\\lambda-d\\\\ \\end\{matrix\}\\right|][chi_lambda_left_begin_matrix_ _lambda-a_-b_ -c_lambda-d_ _end_matrix_right]

**四、求和与连乘**

![\\sum\_\{k=1\}^nk^2=\\frac\{1\}\{2\}n(n+1)][sum_k_1_nk_2_frac_1_2_n_n_1]

![\\prod\_\{k=1\}^nk=n!][prod_k_1_nk_n]

**五、导数、极限、积分**

**1、导数**

导数的表示用一对花括号将被导函数括起来，然后加上一个英文的引号即可。

![\{f\}'(x)=x^2+x][f_x_x_2_x]

**2、极限**

![\\lim\_\{x\\to0\}\\frac\{3x^2+7x^3\}\{x^2+5x^4\}=3][lim_x_to0_frac_3x_2_7x_3_x_2_5x_4_3]

**3、积分**

积分中，需要注意的是，在多重积分内 dx 和 dy 之间 使用一个斜杠加一个逗号 \\, 来增大稍许间距。同样，在两个积分号之间使用一个斜杠加一个感叹号 \\! 来减小稍许间距。使之更美观。

![\\int\_a^bf(x)\\,dx][int_a_bf_x_dx]

<table> 
 <tbody> 
  <tr> 
   <td> <p>1</p> </td> 
   <td> <p><code>$ \int_0^{+\infty} x^n e^{-x} \,dx = n! $</code></p> </td> 
  </tr> 
 </tbody> 
</table>

![\\int\_0^\{+\\infty\}x^ne^\{-x\}\\,dx=n!][int_0_infty_x_ne_-x_dx_n]

<table> 
 <tbody> 
  <tr> 
   <td> <p>1</p> </td> 
   <td> <p><code>$ \int_{x^</code><code>2</code>&nbsp;<code>+ y^</code><code>2</code>&nbsp;<code>\leq R^</code><code>2</code><code>} f(x,y)\,dx\,dy = \int_{\theta=</code><code>0</code><code>}^{ </code><code>2</code><code>\pi} \int_{r=</code><code>0</code><code>}^R f(r\cos\theta,r\sin\theta) r\,dr\,d\theta $</code></p> </td> 
  </tr> 
 </tbody> 
</table>

![\\int\_\{x^2 + y^2 \\leq R^2\} f(x,y)\\,dx\\,dy = \\int\_\{\\theta=0\}^\{2\\pi\} \\int\_\{r=0\}^R f(r\\cos\\theta,r\\sin\\theta) r\\,dr\\,d\\theta][int_x_2_y_2_leq_R_2_f_x_y_dx_dy_int_theta_0_2_pi_int_r_0_R_f_r_cos_theta_r_sin_theta_r_dr_d_theta]

![\\int \\!\\!\\! \\int\_D f(x,y)\\,dx\\,dy \\int \\int\_D f(x,y)\\,dx\\,dy][int_int_D_f_x_y_dx_dy _int_int_D_f_x_y_dx_dy]

在加入了 \\! 之后，距离的改变还是很明显的。

<table> 
 <tbody> 
  <tr> 
   <td> <p>1</p> </td> 
   <td> <p><code>$ i\hbar\frac{\partial \psi}{\partial {t}} = \frac{-\hbar^</code><code>2</code><code>}{2m} \left( \frac{\partial^</code><code>2</code><code>}{\partial x^</code><code>2</code><code>} + \frac{\partial^</code><code>2</code><code>}{\partial y^</code><code>2</code><code>} + \frac{\partial^</code><code>2</code><code>}{\partial z^</code><code>2</code><code>} \right) \psi + V \psi $</code></p> </td> 
  </tr> 
 </tbody> 
</table>

![i\\hbar\\frac\{\\partial \\psi\}\{\\partial \{t\}\} = \\frac\{-\\hbar^2\}\{2m\} \\left( \\frac\{\\partial^2\}\{\\partial x^2\} + \\frac\{\\partial^2\}\{\\partial y^2\} + \\frac\{\\partial^2\}\{\\partial z^2\} \\right) \\psi + V \\psi][i_hbar_frac_partial_psi_partial_t_frac_-_hbar_2_2m_left_frac_partial_2_partial_x_2_frac_partial_2_partial_y_2_frac_partial_2_partial_z_2_right_psi_V_psi]

<table> 
 <tbody> 
  <tr> 
   <td> <p>1</p> </td> 
   <td> <p><code>$ \frac{d}{dt} \</code><code>int</code>&nbsp;<code>\!\!\! \</code><code>int</code>&nbsp;<code>\!\!\! \int_{\textbf{R}^</code><code>3</code><code>} \left| \psi(\mathbf{r},t) \right|^</code><code>2</code><code>\,dx\,dy\,dz = </code><code>0</code>&nbsp;<code>$</code></p> </td> 
  </tr> 
 </tbody> 
</table>

![\\frac\{d\}\{dt\}\\int\\!\\!\\!\\int\\!\\!\\!\\int\_\{\\textbf\{R\}^3\}\\left|\\psi(\\mathbf\{r\},t)\\right|^2\\,dx\\,dy\\,dz=0][frac_d_dt_int_int_int_textbf_R_3_left_psi_mathbf_r_t_right_2_dx_dy_dz_0]

$ y^2 = x^2 + y^2 $
    $\gamma $
    $ \alpha \beta \gamma \delta \epsilon \varepsilon \zeta \eta \Gamma \Delta \Theta $
    $ \theta \vartheta \iota \kappa \lambda \mu \nu \xi \Lambda $
    #### 上下标 
    $x^2 +    x_i +\sqrt[n]{5} \dots \cdots $ 
    ####运算符
    $\pm \times \div \cdot \cap \cup \geq \leq \neq \approx \equiv ++++ \sum_1^n \int_1^n   lim_{x \to \infty} $
    
    ####分数
    
    $\frac{3}{8} $
    ####矩阵和行列式
    $$
    	\begin{matrix}
    	1 & x &x^2 \\
    	1&Y&Y^2 \\
    	1&Z&Z^2 \\
      \end{matrix}
     $$	
    ####行列式
    $$
    X = \left|
    	\begin{matrix}
    		x_{11} & x_{12} & \cdots & x_{1d} \\
    		x_{21} & x_{22} & \cdots & x_{2d}\\
            \vdots & \vdots & \ddots & \vdots\\
            x_{m1} & x_{m2} & \cdots & x_{md}\\
    	\end{matrix}
    \right|
    $$
    ####方程式
    \begin{equation}
    E=mc^2
    \end{equation}

--------------------

### 项目推荐： ###

**[2000多G的计算机各行业电子资源分享（持续更新）][2000_G]**

**[2020年微信小程序全栈项目之喵喵交友【附课件和源码】][2020]**

**[Spring Boot开发小而美的个人博客【附课件和源码】][Spring Boot]**

**[Java微服务实战296集大型视频-谷粒商城【附代码和课件】][Java_296_-]**

**[Java开发微服务畅购商城实战【全357集大项目】-附代码和课件][Java_357_-]**

**[最全最详细数据结构与算法视频-【附课件和源码】][-]**

![在这里插入图片描述][watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3FxXzQwNTg3NTc1_size_16_color_FFFFFF_t_70_pic_center]

\---------- done -------------

[https_www.cnblogs.com_doodle777_p_4951096.html]: https://www.cnblogs.com/doodle777/p/4951096.html
[times]: http://latex.codecogs.com/gif.latex?%5Ctimes
[f_x_x_2]: /images/20220504/90bc10c1d0284a2680895fc3ff403cbe.png
[f_x_x_2 1]: /images/20220504/d4b69ffeb6914a13a18592d118403c7e.png
[f_x_x_1_2_x_2_2]: /images/20220504/8ae9a6647a4f4bd9907f6c9e2cf0ae62.png
[f_x_textbf_x_2]: /images/20220504/cb048ce02fd84bcbb69874a46e841e58.png
[f_x_x_2_mbox_abcd]: /images/20220504/90bc10c1d0284a2680895fc3ff403cbe.png%5Cmbox%7Babcd%7D
[f_x_x_2_mbox_emph_abcd_defg]: /images/20220504/90bc10c1d0284a2680895fc3ff403cbe.png%5Cmbox%7B%5Cemph%7Babcd%7Ddefg%7D
[f_x_y_frac_x_2_y_3]: /images/20220504/cb6098d76f984d7b85327eec3bf9ae1c.png
[f_x_y_sqrt_n_x_2y_3]: /images/20220504/812c462104b84f4a925c4ba907fe335b.png
[f_x_1_x_2_ldots_x_n_x_1_x_2_cdots_x_n]: /images/20220504/e1caaceed7384bccb47de19b46219b5b.png
[f_x_frac_df_dx]: /images/20220504/22f6808192164a528c5591b9cb6d3d2c.png
[f_x_left_frac_df_dx_right]: /images/20220504/f79b733394dc470bbe5127bd03386180.png
[f_0_left._frac_df_dx_right_x_0]: /images/20220504/128676ac639b4bf29a492efee020b5b6.png
[A_left_begin_matrix_ a_b_ c_d_ _end_matrix_right]: /images/20220504/a6f98d08d822423b8261c227921f1f8b.png
[chi_lambda_left_begin_matrix_ _lambda-a_-b_ -c_lambda-d_ _end_matrix_right]: /images/20220504/1ae45b3f3ae14fbebf89223222a88af8.png
[sum_k_1_nk_2_frac_1_2_n_n_1]: /images/20220504/bab2ddc99b1c42acbf6ac81982671dd1.png
[prod_k_1_nk_n]: /images/20220504/fdfc87fe11d4493faf7e7cca8a2d1d25.png
[f_x_x_2_x]: /images/20220504/f67d58fe06894e28bd57d54feca8727e.png
[lim_x_to0_frac_3x_2_7x_3_x_2_5x_4_3]: /images/20220504/0f2495830d6c490e860caf7bf50811b4.png
[int_a_bf_x_dx]: /images/20220504/8dfbd24c1fe04bb5a574d44cee246ed3.png
[int_0_infty_x_ne_-x_dx_n]: /images/20220504/bf616ff815be4b859eeb25b931fd8983.png
[int_x_2_y_2_leq_R_2_f_x_y_dx_dy_int_theta_0_2_pi_int_r_0_R_f_r_cos_theta_r_sin_theta_r_dr_d_theta]: /images/20220504/1ca9abedc33e4bddaf993f6cfa063e07.png
[int_int_D_f_x_y_dx_dy _int_int_D_f_x_y_dx_dy]: /images/20220504/a7b77f1b0efa485891994f3702d18dca.png
[i_hbar_frac_partial_psi_partial_t_frac_-_hbar_2_2m_left_frac_partial_2_partial_x_2_frac_partial_2_partial_y_2_frac_partial_2_partial_z_2_right_psi_V_psi]: /images/20220504/8a6824b5872e48689dd919f3853c476a.png
[frac_d_dt_int_int_int_textbf_R_3_left_psi_mathbf_r_t_right_2_dx_dy_dz_0]: /images/20220504/2799d84a697e44e086e98be276fefc53.png
[2000_G]: https://mp.weixin.qq.com/s/sP4JgGWkCzpgwKr9sAV2_Q
[2020]: https://mp.weixin.qq.com/s?__biz=MzIyNTI3NDQ4NQ==&mid=2247487704&idx=1&sn=5f4b2127c4d49fd07ae072a0721424a2&chksm=e8036fc2df74e6d489c4aa9b06f917ef7cee6027f13e150fca53cf79d5d188d4ccc1af49e098&scene=21#wechat_redirect
[Spring Boot]: https://mp.weixin.qq.com/s?__biz=MzIyNTI3NDQ4NQ==&mid=2247487798&idx=2&sn=ac0293b996521b872a9dba5fbb3e65e6&chksm=e8036e2cdf74e73aba104a9a994a5b2e31483e8dcbe0f1d9936f6d5173b887e1560f59d2819c&scene=21#wechat_redirect
[Java_296_-]: https://mp.weixin.qq.com/s?__biz=MzIyNTI3NDQ4NQ==&mid=2247487674&idx=1&sn=7aff0bdf2bb727303f3d3618995aef21&chksm=e8036fa0df74e6b6d872c7e6ece179c524ed463a4a6b74c96875475c9a3d5ddb903427dd993b&scene=21#wechat_redirect
[Java_357_-]: https://mp.weixin.qq.com/s?__biz=MzIyNTI3NDQ4NQ==&mid=2247486376&idx=1&sn=d1fef270c463ea8ac663f6fbfedd70a0&chksm=e80374b2df74fda4d3bafba878a106a19e18c5fcda266008f4f37975847a21bc612ffcd5ff39&scene=21#wechat_redirect
[-]: https://mp.weixin.qq.com/s?__biz=MzIyNTI3NDQ4NQ==&mid=2247487750&idx=1&sn=747bccbb5f5ea6b58915198de40da777&chksm=e8036e1cdf74e70ae97a5e8e265b49d7236d904d291203309159d07ba1724033062c0e370843&scene=21#wechat_redirect
[watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3FxXzQwNTg3NTc1_size_16_color_FFFFFF_t_70_pic_center]: /images/20220504/d99abb3536b8440987e5ed92d45862c4.png