在jupyter notebook使用latex编辑数学公式

上下标表示

使用下划线_表示下标，使用^表示上标

$$\a^5$$
$$\a_i$$

输出结果：$a^5\quad a_i$a5ai​

希腊字母表示

对相应希腊字母的音读前加上转义符 “\” 即可

$$ \alph  \beta $$

$\alpha \quad \beta$αβ

常用符号表示

微分与积分

微分：\partial{}
积分：\int_{}^{}

$$ \int_{\infty}^{+\infty}{(x^2+3)dx}$$
$$\left. \frac{\partial f(x, y)}{\partial x}\right|_{x=0}\qquad$$

$\int_{-\infty}^{+\infty}{\left(x^2+3\right)dx}$∫−∞+∞​(x2+3)dx
$\left. \frac{\partial f(x, y)}{\partial x}\right|_{x=0}\qquad$∂x∂f(x,y)​∣∣∣∣​x=0​

根号、求和、求积、分式

平方根：\sqrt
n次方根：\sqrt[n]{}
求和：\sum_{}^{}
求积：\prod_{}^{}
分式：\frac{分母}{分子}

矩阵

\begin{matrix\bmatrix\Bmatrix}
中间使用\\换行
\end{matrix\bmatrix\Bmatrix}

$$
\begin{bmatrix}1,2,3\\4,5,6\\,7,8,9\\\end{bmatrix}
\quad
\begin{Bmatrix}1,2,3\\4,5,6\\,7,8,9\\\end{Bmatrix}
$$

$\begin{bmatrix}1,2,3\\4,5,6\\,7,8,9\\\end{bmatrix}\quad \begin{Bmatrix}1,2,3\\4,5,6\\,7,8,9\\\end{Bmatrix}$⎣⎡​1,2,34,5,6,7,8,9​⎦⎤​⎩⎨⎧​1,2,34,5,6,7,8,9​⎭⎬⎫​
\begin{cases}\end{cases}可以配合&进行对齐,中间不使用{}包裹

$$
f(n)
\begin{cases}
n/2&if n=2
1&if n>2
\end{cases}
$$

$f(n) \begin{cases} n/2&if\; n=2\\ 1&if\; n>2\\ \end{cases}$f(n){n/21​ifn=2ifn>2​

更多示例

$$
x_{(22)}^{(n)}\qquad
\frac{1}{1+\frac{1}{2}}\qquad
\sqrt{1+\sqrt[^p]{1+a^2}}\qquad
\int_1^\infty\qquad
\sum_{k=1}^n\frac{1}{k}\qquad
\int_a^b f(x)dx\qquad
\frac{\partial E_w}{\partial w}\qquad
\lim_{1\to\infty}\qquad
\lt \gt \le \ge \neq \not\lt \neq\qquad
\times \div \pm \mp x \cdot y\qquad
\cup \cap \setminus \subset \subseteq \subsetneq \supset \in \notin \emptyset \varnothing\qquad
\to \rightarrow \leftarrow \Rightarrow \Leftarrow \mapsto\qquad
\land \lor \lnot \forall \exists \top \bot \vdash \vDash\qquad
\star \ast \oplus \circ \bullet\qquad
\approx \sim \cong \equiv \prec\qquad
\infty \aleph \nabla \partial\qquad
\epsilon \varepsilon\qquad
\phi \varphi\qquad
\left \lbrace \sum_{i=0}^n i^2 = \frac{(n^2+n)(2n+1)}{6} \right\rbrace \qquad
\left( \sum_{k=\frac{1}{2}}^{N^2}\frac{1}{k} \right)\qquad
\left. \frac{\partial f(x, y)}{\partial x}\right|_{x=0}\qquad
\left\lbrace\begin{aligned}a\\a\\a\\\end{aligned}\right\rbrace \qquad
\left\lbrace\begin{aligned}
a_1x+b_1y+c_1z &=d_1+e_1 \\\ 
a_2x+b_2y &=d_2 \\\ 
a_3x+b_3y+c_3z &=d_3
\end{aligned}\right\rbrace \qquad
$$

$x_{(22)}^{(n)}\qquad \frac{1}{1+\frac{1}{2}}\qquad \sqrt{1+\sqrt[^p]{1+a^2}}\qquad \int_1^\infty\qquad$x(22)(n)​1+21​1​1+p1+a2​​∫1∞​
$\sum_{k=1}^n\frac{1}{k}\qquad \int_a^b f(x)dx\qquad \frac{\partial E_w}{\partial w}\qquad \lim_{1\to\infty}\qquad$k=1∑n​k1​∫ab​f(x)dx∂w∂Ew​​1→∞lim​$\lt \gt \le \ge \neq \not\lt \neq\qquad \times \div \pm \mp x \cdot y\qquad$<>≤≥​=​<​=×÷±∓x⋅y
$\cup \cap \setminus \subset \subseteq \subsetneq \supset \in \notin \emptyset \varnothing\qquad$∪∩∖⊂⊆⊊⊃∈∈/​∅∅$\to \rightarrow \leftarrow \Rightarrow \Leftarrow \mapsto\qquad \land \lor \lnot \forall \exists \top \bot \vdash \vDash\qquad \star \ast \oplus \circ \bullet\qquad$→→←⇒⇐↦∧∨¬∀∃⊤⊥⊢⊨⋆∗⊕∘∙$\approx \sim \cong \equiv \prec\qquad \infty \aleph \nabla \partial\qquad \epsilon \varepsilon\qquad \phi \varphi\qquad$≈∼≅≡≺∞ℵ∇∂ϵεϕφ$\left \lbrace \sum_{i=0}^n i^2 = \frac{(n^2+n)(2n+1)}{6} \right\rbrace \qquad \left( \sum_{k=\frac{1}{2}}^{N^2}\frac{1}{k} \right)\qquad \left. \frac{\partial f(x, y)}{\partial x}\right|_{x=0}\qquad \left\lbrace\begin{aligned}a\\a\\a\\\end{aligned}\right\rbrace \qquad${i=0∑n​i2=6(n2+n)(2n+1)​}⎝⎛​k=21​∑N2​k1​⎠⎞​∂x∂f(x,y)​∣∣∣∣​x=0​⎩⎪⎨⎪⎧​aaa​⎭⎪⎬⎪⎫​$\left\lbrace\begin{aligned} a_1x+b_1y+c_1z &=d_1+e_1 \\\ a_2x+b_2y &=d_2 \\\ a_3x+b_3y+c_3z &=d_3 \end{aligned}\right\rbrace \qquad$⎩⎪⎨⎪⎧​a1​x+b1​y+c1​z a2​x+b2​y a3​x+b3​y+c3​z​=d1​+e1​=d2​=d3​​⎭⎪⎬⎪⎫​