块级公式渲染：

$$ e=mc^2 $$

$$\underbrace{\overbrace{a+b}^6 \cdot \overbrace{c+d}^7}_\text{example of text} = 42\color{orange}{\prod_{\substack{p \leq x \\\text{p prime}}}} \left( 1 - \dfrac{1}{p} \right)$$

$$ \def\arraystretch{1.5} \begin{array}{c:c:c} a&b&c\\\hline d&e&f\\ \hdashline g&h&i \end{array} $$

$$ \begin{Vmatrix} a & b\\ c & d \end{Vmatrix} $$

$$ \Re\left(\frac{-2\mathrm{i}\kappa_{0}}{2\pi}\theta\right)=\frac{1}{\pi}\Im(\kappa_{0}\theta)~\mathrm{and}~\Re\left(\frac{(-2\mathrm{i}\kappa_{0})(-\omega^{2})}{2\pi(\mathrm{i}\kappa_{0})^{2}}\theta\right)=\frac{\omega^{2}}{\pi|\kappa_{0}|^{2}}\Im(\overline{\kappa_{0}}\theta) $$

$$ \begin{array}{rl}{S_{X}(f)}&{=\operatorname*{lim}_{T\rarr\infin}\frac{1}{T}E[|X_{T}(f)|^{2}]}\\ &{=\operatorname*{lim}_{T\rarr\infin}\frac{1}{T}E\left[\int_{-T/2}^{T/2}X(t_{1})e^{-j~2\pi ft_{1}}~\mathrm{d}t_{1}\int_{-T/2}^{T/2}X^{*}(t_{2})e^{j~2\pi ft_{2}}~\mathrm{d}t_{2}\right]}\\ &{=\operatorname*{lim}_{T\rarr\infin}\frac{1}{T}\int_{-T/2}^{T/2}\int_{-T/2}^{T/2}E[X(t_{1})X^{*}(t_{2})]e^{-j~2\pi f(t_{1}-t_{2})}~\mathrm{d}t_{2}~\mathrm{d}t_{1}}\\ &{=\operatorname*{lim}_{T\rarr\infin}\frac{1}{T}\int_{-T/2}^{T/2}\int_{-T/2}^{T/2}R_{X}(t_{1}-t_{2})e^{-j~2\pi f(t_{1}-t_{2})}~\mathrm{d}t_{2}~\mathrm{d}t_{1}.}\end{array} $$

行内公式渲染：
爱因斯坦质能方程：$E=mc^2$
平方和公式：$(a + b)^2 = a^2 + 2ab + b^2$
平方差公式：$(a - b)^2 = a^2 - 2ab + b^2$