$$\begin{array}{c}\mathbf{\text{KaTeX 入门}}\text{fixed by 离散小波变换}\\ \boxed{{\displaystyle \begin{array}{rl}& \begin{array}{r}\\ & \text{先假设你有一个简单的公式。}\\ & f(x)=\{\begin{array}{ll}f(x-1)+f(x-2)& x\ge 3\\ 1& \text{Otherwise.}\end{array}\\ & \text{假设现在有人又给了一个公式。}\\ & g(x)=\{\begin{array}{ll}g(x-1)+f(x)& x\ge 2\\ f(1)& \text{Otherwise.}\end{array}\\ & \text{现在，看一看你所写的公式的码量。你会发现你的KaTeX技能提升了。}\\ & \text{也就是说，只要多写写公式你的水平自然会提升。}\\ \\ & \text{这就是公式的基本写法了。}\\ \\ & \text{那么，现在你已经对KaTeX的基本用法有了一定的了解，就让我们来看}\\ & \text{一看下面这个简单的例子，来把我们刚刚学到的东西运用到实践中吧。}\\ & \underset{―}{}\\ [-13pt]& \underset{―}{}\end{array}\\ & \boxed{{\displaystyle \stackrel{\mathbf{\text{试试看!}}}{\text{例题 1.8}}}}\\ & \begin{array}{c}\log \mathrm{\Pi }(N)=(N+{\displaystyle \frac{1}{2}})\log N-N+A-{\int }_N^{\mathrm{\infty }}{\displaystyle \frac{{\bar{B}}_1(x)\mathrm{d}x}{x}},A=1+{\int }_1^{\mathrm{\infty }}{\displaystyle \frac{{\bar{B}}_1(x)\mathrm{d}x}{x}}\\ \log \mathrm{\Pi }(s)=(s+{\displaystyle \frac{1}{2}})\log s-s+A-{\int }_0^{\mathrm{\infty }}{\displaystyle \frac{{\bar{B}}_1(t)\mathrm{d}t}{t+s}}\end{array}\\ & \begin{array}{rl}\log \mathrm{\Pi }(s)=& \underset{n\to \mathrm{\infty }}{lim}[s\log (N+1)+\sum _{n=1}^N\log n-\sum _{n=1}^N\log (s+n)]\\ =& \underset{n\to \mathrm{\infty }}{lim}[s\log (N+1)+{\int }_1^N\log x\mathrm{d}x-{\displaystyle \frac{1}{2}}\log N+{\int }_1^N{\displaystyle \frac{{\bar{B}}_1\mathrm{d}x}{x}}\\ & -{\int }_1^N\log (s+x)\mathrm{d}x-{\displaystyle \frac{1}{2}}[\log (s+1)+\log (s+N)]\\ & -{\int }_1^N{\displaystyle \frac{{\bar{B}}_1(x)\mathrm{d}x}{s+x}}]\\ =& \underset{n\to \mathrm{\infty }}{lim}[s\log (N+1)+N\log N-N+1+{\displaystyle \frac{1}{2}}\log N+{\int }_1^N{\displaystyle \frac{{\bar{B}}_1(x)\mathrm{d}x}{x}}\\ & -(s+N)\log (s+N)+(s+N)+(s+1)\log (s+1)\\ & -(s+1)-{\displaystyle \frac{1}{2}}\log (s+1)-{\displaystyle \frac{1}{2}}\log (s+N)-{\int }_1^N{\displaystyle \frac{{\bar{B}}_1(x)\mathrm{d}x}{s+x}}]\\ =& (s+{\displaystyle \frac{1}{2}})\log (s+1)+{\int }_1^{\mathrm{\infty }}{\displaystyle \frac{{\bar{B}}_1(x)\mathrm{d}x}{x}}-{\int }_1^N{\displaystyle \frac{{\bar{B}}_1(x)\mathrm{d}x}{s+x}}\\ & +\underset{n\to \mathrm{\infty }}{lim}[s\log (N+1)+(N{\displaystyle \frac{1}{2}})\log N\\ & -(s+N+{\displaystyle \frac{1}{2}})\log (s+N)]\\ =& (s+{\displaystyle \frac{1}{2}})\log (s+1)+(A-1)-{\int }_1^{\mathrm{\infty }}{\displaystyle \frac{{\bar{B}}_1(x)\mathrm{d}x}{s+x}}\\ & +lim[s\log {\displaystyle \frac{N+1}{2}}-(N+{\displaystyle \frac{1}{2}})\log (1+{\displaystyle \frac{s}{2}})]\end{array}\end{array}}}\\ \\ [-44pt]\stackrel{―}{}\\ [-7pt]\\ [-22pt]\mathbf{\text{假如让写KaTeX的那些人来出教程}}\end{array}$$

$\Large\fcolorbox{e00000}{e0efaf}{\textbf{入口地址}}$