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Markdown常用数学符号和公式
latex数学公式分为行内公式和行间公式两种，行内公式嵌入在一行内容之间，行间公式单独占用几行的空间，行内公式左右两侧各加一个美元符号，行间公式两侧各加两个美元符号
- 行内公式：
$数学公式$。例如$a\ge b$ - 行间公式：
$$数学公式$$。例如$$a\ge b$$
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文章目录
- 1 数学符号
- 2 字母
- 2.1 花体（数学）英文字母
- 2.2 二十四个希腊字母
- 3 复杂公式
- 3.1 矩阵
- 3.2 方程组
- 3.3 等式
1 数学符号
| 形式 | 表示 | |
|---|---|---|
| 1.求和 | y = ∑ n i = 1 x i \displaystyle y=\sum_{n}^{i=1}x_{i} y=n∑i=1xi | $\displaystyle y=\sum_{n}^{i=1}x_{i}$ |
| y = ∑ y → 0 x → ∞ x y y=\sum^{x \to \infty}_{y \to 0}{\frac{x}{y}} y=∑y→0x→∞yx | y=\sum^{x \to \infty}_{y \to 0}{\frac{x}{y}} | |
| 2.极限 | lim y → 0 x → ∞ x y \lim^{x \to \infty}_{y \to 0}{\frac{x}{y}} limy→0x→∞yx | \lim^{x \to \infty}_{y \to 0}{\frac{x}{y}} |
| lim y → 0 x → ∞ x y \displaystyle \lim^{x \to \infty}_{y \to 0}{\frac{x}{y}} y→0limx→∞yx | \displaystyle \lim^{x \to \infty}_{y \to 0}{\frac{x}{y}} | |
| 3.开方 | x \sqrt x x | \sqrt x |
| x + y 3 \sqrt[3]{x+y} 3x+y | \sqrt[3]{x+y} | |
| 4.微积分 | ∫ 0 ∞ x d x \int^{\infty}_{0}{xdx} ∫0∞xdx | \int^{\infty}_{0}{xdx} |
| ∬ \iint ∬ | \iint | |
| ∬ D z \iint \limits_{D_z} Dz∬ | \iint \limits_{D_z} | |
| ∭ \iiint ∭ | \iiint | |
| ∂ 2 f ∂ x 2 ∂ 2 f ∂ x ∂ y \dfrac{\partial^2 f}{\partial x^2} \dfrac{\partial^2 f}{\partial x \partial y} ∂x2∂2f∂x∂y∂2f | \dfrac{\partial^2 f}{\partial x^2} \dfrac{\partial^2 f}{\partial x \partial y} | |
| ∮ \oint ∮ | \oint | |
| ∂ x ∂ y \frac{\partial x}{\partial y} ∂y∂x | \frac{\partial x}{\partial y} | |
| ∂ f ( x , y ) ∂ x ∣ x = 0 \frac{\partial f(x,y)}{\partial x} \vert _{x=0} ∂x∂f(x,y)∣x=0 | \frac{\partial f(x,y)}{\partial x} \vert _{x=0} | |
| y ′ x y{\prime}x y′x | y{\prime}x | |
| ∇ \nabla ∇ | \nabla | |
| ∞ \infty ∞ | \infty | |
| 5.上下标 | x y x^y xy | x^y |
| x 9 x_9 x9 | x_9 | |
| y x \stackrel{x}{y} yx | \stackrel{x}{y} | |
| y z \overset{z}{y} yz | \overset{z}{y} | |
| y x \underset{x}{y} xy | \underset{x}{y} | |
| m i n ϕ l o g ( 1 − f ( x ) ) \mathop{min}\limits_{\phi}log(1-f(x)) ϕminlog(1−f(x)) | \mathop{min}\limits_{\phi} log(1-f(x)) | |
| 向量 | x y → \overrightarrow{xy} xy | \overrightarrow{xy} |
| 矢量 | x ⃗ \vec x x | \vec x |
| x y z ‾ \overline{xyz} xyz | \overline{xyz} | |
| x y z ‾ ‾ \overline{x\overline{yz}} xyz | \overline{x\overline{yz}} | |
| x y z ‾ \underline{xyz} xyz | \underline{xyz} | |
| 6.累乘 | ∏ n = 1 99 x n \prod_{n=1}^{99}{x_n} ∏n=199xn | \prod_{n=1}^{99}{x_n} |
| ∏ n = 1 99 x n \displaystyle \prod_{n=1}^{99}{x_n} n=1∏99xn | \displaystyle \prod_{n=1}^{99}{x_n} | |
| 7.箭头 | a ← b → c ↔ d ⇔ e ⇌ f a \leftarrow b \rightarrow c \leftrightarrow d \Leftrightarrow e \rightleftharpoons f a←b→c↔d⇔e⇌f | a \leftarrow b \rightarrow c \leftrightarrow d \Leftrightarrow e \rightleftharpoons f |
| a ⟵ b ⟶ c ⟺ d a \longleftarrow b \longrightarrow c \Longleftrightarrow d a⟵b⟶c⟺d | a \longleftarrow b \longrightarrow c \Longleftrightarrow d | |
| a ↗ b ↘ c ↖ d ↘ e a \nearrow b \searrow c \nwarrow d \searrow e a↗b↘c↖d↘e | a \nearrow b \searrow c \nwarrow d \searrow e | |
| a ↑ b ↓ c ⇑ d ⇓ e a \uparrow b \downarrow c \Uparrow d \Downarrow e a↑b↓c⇑d⇓e | a \uparrow b \downarrow c \Uparrow d \Downarrow e | |
| a ⇀ b ⇁ c ↼ d ↽ e a \rightharpoonup b \rightharpoondown c \leftharpoonup d \leftharpoondown e a⇀b⇁c↼d↽e | a \rightharpoonup b \rightharpoondown c \leftharpoonup d \leftharpoondown e | |
| 8.逻辑运算符 | ∀ a ∃ b \forall a \exists b ∀a∃b | \forall a \exists b |
| ¬ a ⋁ b ⋀ \lnot a \bigvee b \bigwedge ¬a⋁b⋀ | \lnot a \bigvee b \bigwedge | |
| ∵ a ∴ b \because a \therefore b ∵a∴b | \because a \therefore b | |
| 9.集合符号 | X ∪ Y ⋃ Z ∩ W X\cup Y \bigcup Z\cap W X∪Y⋃Z∩W | X\cup Y \bigcup Z\cap W |
| X ⊂ Y ⊄ Z ⊆ W ⊈ U X \subset Y \not\subset Z \subseteq W \not\subseteq U X⊂Y⊂Z⊆W⊆U | X \subset Y \not\subset Z \subseteq W \not\subseteq U | |
| c ∈ d ∉ e c \in d \notin e c∈d∈/e | c \in d \notin e | |
| ∅ \emptyset ∅ | \emptyset | |
| ∅ \varnothing ∅ | \varnothing | |
| 10.取整 | ⌈ x 2 ⌉ \lceil \frac{x}{2} \rceil ⌈2x⌉ | \lceil \frac{x}{2} \rceil |
| ⌊ x ⌋ \lfloor x \rfloor ⌊x⌋ | \lfloor x \rfloor | |
| 11.括号 | ( n k ) \tbinom{n}{k} (kn) | \tbinom{n}{k} |
| ( n k ) \binom{n}{k} (kn) | \binom{n}{k} | |
| ( n k ) \dbinom{n}{k} (kn) | \dbinom{n}{k} | |
| { n k } {n\brace k} {kn} | {n\brace k} | |
| ( n k ) {n\choose k} (kn) | {n\choose k} | |
| [ n k ] {n\brack k} [kn] | {n\brack k} | |
| 1 + 2 + ⋯ + 100 ⏞ \overbrace{1+2+\cdots+100} 1+2+⋯+100 | \overbrace{1+2+\cdots+100} | |
| 1 + 2 + ⋯ + 100 ⏟ \underbrace{1+2+\cdots+100} 1+2+⋯+100 | \underbrace{1+2+\cdots+100} | |
| 5050 1 + 2 + ⋯ + 100 ⏞ \begin{matrix} 5050 \\ \overbrace{ 1+2+\cdots+100 }\end{matrix} 50501+2+⋯+100 | \begin{matrix} 5050 \ \overbrace{ 1+2+\cdots+100 }\end{matrix} | |
| 12.运算符 | ≠ \neq = | \neq |
| ≤ \leq ≤ | \leq | |
| ≥ \geq ≥ | \geq | |
| ≈ \approx ≈ | \approx | |
| ≮ \not\lt < | \not\lt | |
| > \gt > | \gt | |
| < \lt < | \lt | |
| ≫ \gg ≫ | \gg | |
| ⋘ \lll ⋘ | \lll | |
| ± \pm ± | \pm | |
| × \times × | \times | |
| ÷ \div ÷ | \div | |
| ∣ \mid ∣ | \mid | |
| ∗ \ast ∗ | \ast | |
| ⊗ a n d ⨂ \otimes and \bigotimes ⊗and⨂ | \odot and\bigodot | |
| ⊗ a n d ⨂ \otimes and \bigotimes ⊗and⨂ | \otimes and \bigotimes | |
| ⋈ \bowtie ⋈ | \bowtie | |
| ∠ \angle ∠ | \angle | |
| ⊥ \bot ⊥ | \bot | |
| ∼ \sim ∼ | \sim | |
| 13.三角函数 | sin 3 0 ∘ \sin 30^\circ sin30∘ | \sin 30^\circ |
| cos \cos cos | \cos | |
| tan \tan tan | \tan | |
| 14.对数 | ln 2 \ln 2 ln2 | \ln 2 |
| log 2 8 \log_2 8 log28 | \log_2 8 | |
| lg 10 \lg 10 lg10 | \lg 10 |
2 字母
2.1 花体（数学）英文字母
| 例子 | 表示 |
|---|---|
| A B C H T Z \mathcal{ABCHTZ} ABCHTZ | \mathcal{ABCHTZ} |
| A B C H T Z \mathbb{ABCHTZ} ABCHTZ | \mathbb{ABCHTZ} |
| A B C H T Z \mathscr{ABCHTZ} ABCHTZ | \mathcal{ABCHTZ} |
| A B C H T Z \mathfrak{ABCHTZ} ABCHTZ | \mathfrak{ABCHTZ} |
2.2 二十四个希腊字母
| 序号 | 小写 | 表示 | 大写 | 表示 |
|---|---|---|---|---|
| 1 | α \alpha α | \alpha | A \Alpha A | \Alpha |
| 2 | β \beta β | \beta | B \Beta B | \Beta |
| 3 | γ \gamma γ | \gamma | Γ \Gamma Γ | \Gamma |
| 4 | δ \delta δ | \delta | Δ \Delta Δ | \Delta |
| 5 | ϵ \epsilon ϵ | \epsilon | E \Epsilon E | \Epsilon |
| ε \varepsilon ε | \varepsilon | |||
| 6 | ζ \zeta ζ | \zeta | Z \Zeta Z | \Zeta |
| 7 | η \eta η | \eta | H \Eta H | \Eta |
| 8 | θ \theta θ | \theta | Θ \Theta Θ | \Theta |
| 9 | ι \iota ι | \iota | I \Iota I | \Iota |
| 10 | κ \kappa κ | \kappa | K \Kappa K | \Kappa |
| 11 | λ \lambda λ | \lambda | Λ \Lambda Λ | \Lambda |
| 12 | μ \mu μ | \mu | M \Mu M | \Mu |
| 13 | ν \nu ν | \nu | N \Nu N | \Nu |
| 14 | ξ \xi ξ | \xi | Ξ \Xi Ξ | \Xi |
| 15 | ο \omicron ο | \omicron | O \Omicron O | \Omicron |
| 16 | π \pi π | \pi | Π \Pi Π | \Pi |
| 17 | ρ \rho ρ | \rho | P \Rho P | \Rho |
| 18 | σ \sigma σ | \sigma | Σ \Sigma Σ | \Sigma |
| 19 | τ \tau τ | \tau | T \Tau T | \Tau |
| 20 | υ \upsilon υ | \upsilon | Υ \Upsilon Υ | \Upsilon |
| 21 | ϕ \phi ϕ | \phi | Φ \Phi Φ | \Phi |
| φ \varphi φ | \varphi | |||
| 22 | χ \chi χ | \chi | X \Chi X | \Chi |
| 23 | ψ \psi ψ | \psi | Ψ \Psi Ψ | \Psi |
| 24 | ω \omega ω | \omega | Ω \Omega Ω | \Omega |
3 复杂公式
3.1 矩阵
| 符号 | 表示 |
|---|---|
| 0 1 3 4 \begin{matrix} 0 & 1 \\ 3 & 4 \\ \end{matrix} 0314 | $$\begin{matrix} 0 & 1 \\ 3 & 4 \\ \end{matrix}$$ |
| ( 0 1 3 4 ) \begin{pmatrix} 0 & 1 \\ 3 & 4 \\ \end{pmatrix} (0314) | \begin{pmatrix} 0 & 1 \\ 3 & 4 \\ \end{pmatrix} |
| ∣ 0 1 3 4 ∣ \begin{vmatrix} 0 & 1 \\ 3 & 4 \\ \end{vmatrix} 0314 | \begin{vmatrix} 0 & 1 \\ 3 & 4 \\ \end{vmatrix} |
| ∥ 0 1 3 4 ∥ \begin{Vmatrix} 0 & 1 \\ 3 & 4 \\ \end{Vmatrix} 0314 | \begin{Vmatrix} 0 & 1 \\ 3 & 4 \\ \end{Vmatrix} |
| [ 0 1 3 4 ] \begin{bmatrix} 0 & 1 \\ 3 & 4 \\ \end{bmatrix} [0314] | \begin{bmatrix} 0 & 1 \\ 3 & 4 \\ \end{bmatrix} |
| { 0 1 3 4 } \begin{Bmatrix} 0 & 1 \\ 3 & 4 \\ \end{Bmatrix} {0314} | \begin{Bmatrix} 0 & 1 \\ 3 & 4 \\ \end{Bmatrix} |
% 可将 [] 换成 () 或 ||...$$
\left[
\begin{array}{ccc|c}\psi(x) & g(x) & \cdots & a_{1n} \\\hlinea_{21} & a_{22} & \dots & a_{2n} \\\vdots & \vdots & \ddots & \vdots \\a_{n1} & a_{n2} & ... & a_{nn}
\end{array}
\right]
$$
[ ψ ( x ) g ( x ) ⋯ a 1 n a 21 a 22 … a 2 n ⋮ ⋮ ⋱ ⋮ a n 1 a n 2 . . . a n n ] \left[ \begin{array}{ccc|c} \psi(x) & g(x) & \cdots & a_{1n} \\ \hline a_{21} & a_{22} & \dots & a_{2n} \\ \vdots & \vdots & \ddots & \vdots \\ a_{n1} & a_{n2} & ... & a_{nn} \end{array} \right] ψ(x)a21⋮an1g(x)a22⋮an2⋯…⋱...a1na2n⋮ann
$$
\begin{bmatrix}1 & x_{0} &... & x_{0}^{n} \\1 & x_{1} &... & x_{1}^{n} \\& & \cdots & \\1 & x_{n} & \dots & x_{n}^{n}
\end{bmatrix}
\begin{bmatrix}a_{0}\\ a_{1}\\ ...\\ a_{n}
\end{bmatrix}=
\begin{bmatrix}y_{0}\\ y_{1}\\ ...\\ y_{n}
\end{bmatrix}
$$
[ 1 x 0 . . . x 0 n 1 x 1 . . . x 1 n ⋯ 1 x n … x n n ] [ a 0 a 1 . . . a n ] = [ y 0 y 1 . . . y n ] \begin{bmatrix} 1 & x_{0} &... & x_{0}^{n} \\ 1 & x_{1} &... & x_{1}^{n} \\ & & \cdots & \\ 1 & x_{n} & \dots & x_{n}^{n} \end{bmatrix} \begin{bmatrix} a_{0}\\ a_{1}\\ ...\\ a_{n} \end{bmatrix}= \begin{bmatrix} y_{0}\\ y_{1}\\ ...\\ y_{n} \end{bmatrix} 111x0x1xn......⋯…x0nx1nxnn a0a1...an = y0y1...yn
3.2 方程组
$$
\begin{cases}a_{0}+a_{1}x_{0}+...+a_{n}x_{0}^{n}=y_{0} \\a_{0}+a_{1}x_{1}+...+a_{n}x_{1}^{n}=y_{1} \\\cdots\\a_{0}+a_{1}x_{n}+...+a_{n}x_{n}^{n}=y_{n}
\end{cases}
$$
{ a 0 + a 1 x 0 + . . . + a n x 0 n = y 0 a 0 + a 1 x 1 + . . . + a n x 1 n = y 1 ⋯ a 0 + a 1 x n + . . . + a n x n n = y n \begin{cases} a_{0}+a_{1}x_{0}+...+a_{n}x_{0}^{n}=y_{0} \\ a_{0}+a_{1}x_{1}+...+a_{n}x_{1}^{n}=y_{1} \\ \cdots\\ a_{0}+a_{1}x_{n}+...+a_{n}x_{n}^{n}=y_{n} \end{cases} ⎩ ⎨ ⎧a0+a1x0+...+anx0n=y0a0+a1x1+...+anx1n=y1⋯a0+a1xn+...+anxnn=yn
3.3 等式
% 使用 \& 使 = 左对齐$$
\begin{aligned}(f,K^{'}_{x}y+K^{''}_{x}y)_{F}&=(f^{'}+f^{''},K^{'}_{x}y+K^{''}_{x}y)_{F}\\&=(f^{'},K^{'}_{x}y)_{F}+(f^{''},K^{''}_{x}y)_{F}+(f^{'},K^{''}_{x}y)_{F}+(f^{''},K^{'}_{x}y)_{F}\\&=(f^{'},K^{'}_{x}y)_{F}+(f^{''},K^{''}_{x}y)_{F}\\&=(f^{'}(x),y)_{Y}+(f^{''}(x),y)_{Y}\\&=(f^{'}(x)+f^{''}(x),y)_{Y}\\&=(f(x),y)_{Y}\\&=(f,K_{x}y)_{F}
\end{aligned}
$$
( f , K x ′ y + K x ′ ′ y ) F = ( f ′ + f ′ ′ , K x ′ y + K x ′ ′ y ) F = ( f ′ , K x ′ y ) F + ( f ′ ′ , K x ′ ′ y ) F + ( f ′ , K x ′ ′ y ) F + ( f ′ ′ , K x ′ y ) F = ( f ′ , K x ′ y ) F + ( f ′ ′ , K x ′ ′ y ) F = ( f ′ ( x ) , y ) Y + ( f ′ ′ ( x ) , y ) Y = ( f ′ ( x ) + f ′ ′ ( x ) , y ) Y = ( f ( x ) , y ) Y \begin{aligned} (f,K^{'}_{x}y+K^{''}_{x}y)_{F} &=(f^{'}+f^{''},K^{'}_{x}y+K^{''}_{x}y)_{F}\\ &=(f^{'},K^{'}_{x}y)_{F}+(f^{''},K^{''}_{x}y)_{F}+(f^{'},K^{''}_{x}y)_{F}+(f^{''},K^{'}_{x}y)_{F}\\ &=(f^{'},K^{'}_{x}y)_{F}+(f^{''},K^{''}_{x}y)_{F}\\ &=(f^{'}(x),y)_{Y}+(f^{''}(x),y)_{Y}\\ &=(f^{'}(x)+f^{''}(x),y)_{Y}\\ &=(f(x),y)_{Y}\\ \end{aligned} (f,Kx′y+Kx′′y)F=(f′+f′′,Kx′y+Kx′′y)F=(f′,Kx′y)F+(f′′,Kx′′y)F+(f′,Kx′′y)F+(f′′,Kx′y)F=(f′,Kx′y)F+(f′′,Kx′′y)F=(f′(x),y)Y+(f′′(x),y)Y=(f′(x)+f′′(x),y)Y=(f(x),y)Y
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Markdown常用数学符号和公式
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