$$ e^{ix}=\text{cos}x+i\text{sin}x $$

$$ \left(C_{n+1, t+1}-C_{n, t}\right)-\left(C_{n, t+1}-C_{n-1, t}\right)=\frac{2}{n+1} $$

$$ \begin{aligned} C_{n+1, t+1}-C_{n, t} &=\frac{2}{n+1}+\frac{2}{n}+\cdots+\frac{2}{t+2} +C_{t+1, t+1}-C_{t, t} \\ &=2\left(H_{n+1}-H_{t+1}\right)+2-2 /(t+1) \end{aligned} $$

\begin{aligned} 
C_{n+1, t+1}-C_{n, t} &=\frac{2}{n+1}+\frac{2}{n}+\cdots+\frac{2}{t+2}
+C_{t+1, t+1}-C_{t, t} \\\\ 
&=2\left(H_{n+1}-H_{t+1}\right)+2-2 /(t+1) 
\end{aligned}

换行需要使用\\\\

\begin{aligned}和\end{aligned}之间不能有空行

不支持\left[，\right)等

$$ \begin{cases}\begin{array}{l} \theta_{i}(t-j)^{\prime}=\frac{1}{3} \Sigma_{1}^{-1} \theta_{i}(t-j),\\ a_{i}(t-j)^{\prime}=\frac{1}{3} \sum_{1}^{-1} a_{i}(t-j), i=\{r h,l h, r k, l k\}\\w_{i}(t-j)^{\prime}=\frac{1}{3} \Sigma_{1}^{-1} w_{i}(t-j)\end{array}\end{cases} $$

\begin{cases}\begin{array}{l}
\theta_{i}(t-j)^{\prime}=\frac{13} \Sigma_{1}^{-1} \theta_{i}(t-j),\\\\ a_{i}(t-j)^{\prime}=\frac{1}{3} \sum_{1}^{-1} a_{i}(t-j), i=\\{r h,l h, r k, l k\\}\\\\w_{i}(t-j)^{\prime}=\frac{1}{3} \Sigma_{1}^{-1} w_{i}(t-j)\end{array}\end{cases}

\begin{array}和\end{array}之间不能换行😅

大括号只能用\begin{cases} \end{cases}实现了

花括号要这样\\}才能打出来$\}$