markdown中数学符号公式和字母表示

一. 常用数学符号markdown表示

乘号，正负号，：$\times$ $\pm$: ×\times× ±\pm±
除号，竖线：$\div$ $\mid$: ÷\div÷ ∣\mid∣
点： $\cdot$ : ⋅\cdot⋅
圆 $\circ$ : ∘\circ∘
克罗内克积 $\bigotimes$ : ⨂\bigotimes⨂
异或 $\bigoplus$ : ⨁\bigoplus⨁
小于等于，大于等于不等于$\leq$ $\geq$ $\neq$: ≤\leq≤ ≥\geq≥ ≠\neq=
约等于 $\approx$ : ≈\approx≈
积分，双重积分，曲线积分$\int$ $\iint$ $\oint$: ∫\int∫ ∬\iint∬ ∮\oint∮
无穷 $\infty$ : ∞\infty∞
梯度 $\nabla$ : ∇\nabla∇
因为，所以$\because$ 和 $\therefore$ ∵\because∵ 和 ∴\therefore∴
任意和存在$\forall$ 和 $\exists$: ∀\forall∀ 和 ∃\exists∃
属于和不属于$\in$ 和 $\notin$: ∈\in∈ 和 ∉\notin∈/
子集，真子集，空集$\subset$，$\subseteq$，$\emptyset$: ⊂\subset⊂，⊆\subseteq⊆，∅\emptyset∅
交集和并集$\bigcap$ 和 $\bigcup$:⋂\bigcap⋂ 和 ⋃\bigcup⋃
逻辑或和逻辑与$\bigvee$ 和 $\bigwedge$: ⋁\bigvee⋁ 和 ⋀\bigwedge⋀
期望值 $\hat{y}$ : y^\hat{y}y^
平均值 $\overline{a+b+c+d}$ : a+b+c+d‾\overline{a+b+c+d}a+b+c+d

二. 数学符号markdown表示的案例

三角函数：$$\sin$$: sin⁡\sinsin

分数:

$\dfrac{2}{3}$，$\tfrac{2}{3}$: 23\dfrac{2}{3}32，23\tfrac{2}{3}32
$$\frac{7x+5}{2+y^2}$$ 效果为：7x+52+y2\frac{7x+5}{2+y^2}2+y27x+5
$$x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$$: x=−b±b2−4ac2ax=\frac{-b\pm\sqrt{b^2-4ac}}{2a}x=2a−b±b2−4ac

对数函数： $$\ln15, \log_2 10 , \lg7$$: ln⁡15,log⁡210,lg⁡7\ln15, \log_2 10 , \lg7ln15,log210,lg7

关系运算符: $$\pm \times \div \sum \prod \neq \leq \geq$$: ±×÷∑∏≠≤≥\pm \times \div \sum \prod \neq \leq \geq±×÷∑∏=≤≥

上标：

$A^2$、$A^{上标}$ : A2A^2A2、A上标A^{上标}A上标
$$A^2 \; A^{上标} \; \mathop{A}\limits^2$$ A2A上标A2A^2 \; A^{上标} \; \mathop{A}\limits^2A2A上标A2

下标:

$A_2$、$A_{下标}$ A2A_2A2、A下标A_{下标}A下标
$$A_2 \; A_{下标}\; \mathop{A}\limits_2$$: A2A下标A2A_2 \; A_{下标}\; \mathop{A}\limits_2A2A下标2A
$$z=z_l$$: z=zlz=z_lz=zl

开根号:

$\sqrt[开方数]{参数}$ : 参数开方数\sqrt[开方数]{参数}开方数参数
$$\sqrt[开方数]{参数}$$: 参数开方数\sqrt[开方数]{参数}开方数参数
$$\sqrt{2};\sqrt[n]{3}$$: 2;3n\sqrt{2};\sqrt[n]{3}2;n3
$$ \sqrt x * \sqrt[3] x * \sqrt[-1] x $$: x∗x3∗x−1\sqrt x * \sqrt[3] x * \sqrt[-1] x x∗3x∗−1x

求和:

$\sum$ : ∑\sum∑
求和上下标： $\sum_{i=0}^n$ : ∑i=0n\sum_{i=0}^n∑i=0n
$$\sum ^2_3\;\sum \nolimits^2_3$$ : ∑32∑32\sum ^2_3\;\sum \nolimits^2_33∑2∑32

积分:

$\int$ : ∫\int∫
$$\int ^2_3\;\int \limits^2_3$$: ∫32∫32\int ^2_3\;\int \limits^2_3∫323∫2
$$\int ^2_3 x^2 {\rm d}x$$: ∫32x2dx\int ^2_3 x^2 {\rm d}x∫32x2dx
$$\iint$$: ∬\iint∬

极限：

$$\lim_{n\rightarrow+\infty} n$$: lim⁡n→+∞n\lim_{n\rightarrow+\infty} nn→+∞limn
$$\begin{aligned} \lim_{a\to \infty} \tfrac{1}{a} \end{aligned}$$: lim⁡a→∞1a\begin{aligned} \lim_{a\to \infty} \tfrac{1}{a} \end{aligned}a→∞lima1

累加：$$\sum \frac{1}{i^2}$$: ∑1i2\sum \frac{1}{i^2}∑i21
累乘：

$$\prod \frac{1}{i^2}$$: ∏1i2\prod \frac{1}{i^2}∏i21
$$ \prod_{{ \begin{gathered} 1\le i \le n\\ 1\le j \le m \end{gathered} }} M_{i,j} $$:
∏1≤i≤n1≤j≤mMi,j\prod_{{ \begin{gathered} 1\le i \le n\\ 1\le j \le m \end{gathered} }} M_{i,j} 1≤i≤n1≤j≤m∏Mi,j

矢量：$$\vec{a} \cdot \vec{b}=0$$: $$a⃗⋅b⃗=0\vec{a} \cdot \vec{b}=0a⋅b=0

三. 希腊字符

$$\alpha \beta \gamma \delta \epsilon $$: αβγδϵ\alpha \beta \gamma \delta \epsilon αβγδϵ
$$ \zeta \eta \theta \vartheta \iota $$: ζηθϑι\zeta \eta \theta \vartheta \iota ζηθϑι
$$ \kappa \lambda \mu \nu \xi $$: κλμνξ\kappa \lambda \mu \nu \xi κλμνξ
$$o \pi \varpi \rho \varrho $$: oπϖρϱo \pi \varpi \rho \varrho oπϖρϱ
$$ \sigma \varsigma \tau \upsilon \phi $$: σςτυϕ\sigma \varsigma \tau \upsilon \phi σςτυϕ
$$ \varphi \chi \psi \omega A $$: φχψωA\varphi \chi \psi \omega A φχψωA
$$ B \Gamma \varGamma \Delta \varDelta $$: BΓΓΔΔB \Gamma \varGamma \Delta \varDelta BΓΓΔΔ
$$ E Z H \Theta \varTheta $$: EZHΘΘE Z H \Theta \varTheta EZHΘΘ
$$ I K \Lambda \varLambda M $$: IKΛΛMI K \Lambda \varLambda M IKΛΛM
$$ N \Xi \varXi O \Pi $$: NΞΞOΠN \Xi \varXi O \Pi NΞΞOΠ
$$ \varPi P \Sigma \Upsilon \varUpsilon $$: ΠPΣΥΥ\varPi P \Sigma \Upsilon \varUpsilon ΠPΣΥΥ
$$ \Phi \varPhi X \varPsi \Omega \varOmega$$: ΦΦXΨΩΩ\Phi \varPhi X \varPsi \Omega \varOmega ΦΦXΨΩΩ

四. 一些公式

矩阵：
$$ \left[ \begin{matrix} 1 & 2 & 3 \\ 4 & 5 & 6 \\ 7 & 8 & 9 \end{matrix} \right]\tag{2}$$
[123456789](2)\left[ \begin{matrix} 1 & 2 & 3 \\ 4 & 5 & 6 \\ 7 & 8 & 9 \end{matrix} \right]\tag{2} ⎣⎡147258369⎦⎤(2)

分段函数：

$$
f(x) = \left\{\begin{array}{lr}x^2 & : x < 0\\x^3 & : x \ge 0\end{array}
\right.
$$$$
u(x) = \begin{cases} \exp{x} & \text{if } x \geq 0 \\1       & \text{if } x < 0\end{cases}
$$

f(x)={x2:x<0x3:x≥0f(x) = \left\{ \begin{array}{lr} x^2 & : x < 0\\ x^3 & : x \ge 0 \end{array} \right. f(x)={x2x3:x<0:x≥0

u(x)={exp⁡xif x≥01if x<0u(x) = \begin{cases} \exp{x} & \text{if } x \geq 0 \\ 1 & \text{if } x < 0 \end{cases} u(x)={expx1if x≥0if x<0
方程组：

$$
\left\{
\begin{array}{c}a_1x+b_1y+c_1z=d_1 \\ a_2x+b_2y+c_2z=d_2 \\ a_3x+b_3y+c_3z=d_3
\end{array}
\right.
$$

{a1x+b1y+c1z=d1a2x+b2y+c2z=d2a3x+b3y+c3z=d3\left\{ \begin{array}{c} a_1x+b_1y+c_1z=d_1 \\ a_2x+b_2y+c_2z=d_2 \\ a_3x+b_3y+c_3z=d_3 \end{array} \right. ⎩⎨⎧a1x+b1y+c1z=d1a2x+b2y+c2z=d2a3x+b3y+c3z=d3

线性模型：

$$
h(\theta) = \sum_{j = 0} ^n \theta_j x_j
$$

h(θ)=∑j=0nθjxjh(\theta) = \sum_{j = 0} ^n \theta_j x_j h(θ)=j=0∑nθjxj

均方误差：

$$
J(\theta) = \frac{1}{2m}\sum_{i = 0} ^m(y^i - h_\theta (x^i))^2
$$

J(θ)=12m∑i=0m(yi−hθ(xi))2J(\theta) = \frac{1}{2m}\sum_{i = 0} ^m(y^i - h_\theta (x^i))^2 J(θ)=2m1i=0∑m(yi−hθ(xi))2

批量梯度下降：

$$
\frac{\partial J(\theta)}{\partial\theta_j}=-\frac1m\sum_{i=0}^m(y^i-h_\theta(x^i))x^i_j
$$

∂J(θ)∂θj=−1m∑i=0m(yi−hθ(xi))xji\frac{\partial J(\theta)}{\partial\theta_j}=-\frac1m\sum_{i=0}^m(y^i-h_\theta(x^i))x^i_j ∂θj∂J(θ)=−m1i=0∑m(yi−hθ(xi))xji

五. 关系符号和箭头符号

3.1 关系符号

$$
\bowtie    \Join    \propto    \varpropto    \multimap    \pitchfork  \therefore    \because    =    \neq    \equiv    \approx    \sim    \simeq    \backsimeq    \approxeq    \cong    \ncong        \smile    \frown    \asymp    \smallfrown    \smallsmile    \between    \prec    \succ    \nprec    \nsucc    \preceq    \succeq    \npreceq    \nsucceq    \preccurlyeq    \succcurlyeq    \curlyeqprec    \curlyeqsucc    \precsim    \succsim    \precnsim    \succnsim    \precapprox    \succapprox    \precnapprox    \succnapprox    \perp    \vdash    \dashv    \nvdash    \Vdash    \Vvdash    \models    \vDash    \nvDash    \nVDash    \mid    \nmid    \parallel    \nparallel    \shortmid    \nshortmid    \shortparallel    \nshortparallel    <    >    \nless    \ngtr    \lessdot    \gtrdot    \ll    \gg    \lll    \ggg    \leq    \geq    \lneq    \gneq    \nleq    \ngeq    \leqq    \geqq    \lneqq    \gneqq    \lvertneqq    \gvertneqq    \nleqq    \ngeqq    \leqslant    \geqslant    \nleqslant    \ngeqslant    \eqslantless    \eqslantgtr    \lessgtr    \gtrless    \lesseqgtr    \gtreqless    \lesseqqgtr    \gtreqqless    \lesssim    \gtrsim    \lnsim    \gnsim    \lessapprox    \gtrapprox    \lnapprox    \gnapprox    \vartriangleleft    \vartriangleright    \ntriangleleft    \ntriangleright    \trianglelefteq    \trianglerighteq    \ntrianglelefteq    \ntrianglerighteq    \blacktriangleleft    \blacktriangleright    \subset    \supset    \subseteq    \supseteq    \subsetneq    \supsetneq    \varsubsetneq    \varsupsetneq    \nsubseteq    \nsupseteq    \subseteqq    \supseteqq    \subsetneqq    \supsetneqq    \nsubseteqq    \nsupseteqq    \backepsilon    \Subset    \Supset    \sqsubset    \sqsupset    \sqsubseteq    \sqsupseteq
$$

⋈⋈∝∝⊸⋔∴∵=≠≡≈∼≃⋍≊≅≆⌣⌢≍⌢⌣≬≺≻⊀⊁⪯⪰⋠⋡≼≽⋞⋟≾≿⋨⋩⪷⪸⪹⪺⊥⊢⊣⊬⊩⊪⊨⊨⊭⊯∣∤∥∦∣∤∥∦<>≮≯⋖⋗≪≫⋘⋙≤≥⪇⪈≰≱≦≧≨≩≨≩≰≱⩽⩾≰≱⪕⪖≶≷⋚⋛⪋⪌≲≳⋦⋧⪅⪆⪉⪊⊲⊳⋪⋫⊴⊵⋬⋭◀▶⊂⊃⊆⊇⊊⊋⊊⊋⊈⊉⫅⫆⫋⫌⊈⊉∍⋐⋑⊏⊐⊑⊒\bowtie \Join \propto \varpropto \multimap \pitchfork \therefore \because = \neq \equiv \approx \sim \simeq \backsimeq \approxeq \cong \ncong \smile \frown \asymp \smallfrown \smallsmile \between \prec \succ \nprec \nsucc \preceq \succeq \npreceq \nsucceq \preccurlyeq \succcurlyeq \curlyeqprec \curlyeqsucc \precsim \succsim \precnsim \succnsim \precapprox \succapprox \precnapprox \succnapprox \perp \vdash \dashv \nvdash \Vdash \Vvdash \models \vDash \nvDash \nVDash \mid \nmid \parallel \nparallel \shortmid \nshortmid \shortparallel \nshortparallel < > \nless \ngtr \lessdot \gtrdot \ll \gg \lll \ggg \leq \geq \lneq \gneq \nleq \ngeq \leqq \geqq \lneqq \gneqq \lvertneqq \gvertneqq \nleqq \ngeqq \leqslant \geqslant \nleqslant \ngeqslant \eqslantless \eqslantgtr \lessgtr \gtrless \lesseqgtr \gtreqless \lesseqqgtr \gtreqqless \lesssim \gtrsim \lnsim \gnsim \lessapprox \gtrapprox \lnapprox \gnapprox \vartriangleleft \vartriangleright \ntriangleleft \ntriangleright \trianglelefteq \trianglerighteq \ntrianglelefteq \ntrianglerighteq \blacktriangleleft \blacktriangleright \subset \supset \subseteq \supseteq \subsetneq \supsetneq \varsubsetneq \varsupsetneq \nsubseteq \nsupseteq \subseteqq \supseteqq \subsetneqq \supsetneqq \nsubseteqq \nsupseteqq \backepsilon \Subset \Supset \sqsubset \sqsupset \sqsubseteq \sqsupseteq ⋈⋈∝∝⊸⋔∴∵==≡≈∼≃⋍≊≅≆⌣⌢≍⌢⌣≬≺≻⊀⊁⪯⪰⋠⋡≼≽⋞⋟≾≿⋨⋩⪷⪸⪹⪺⊥⊢⊣⊬⊩⊪⊨⊨⊭⊯∣∤∥∦∣∥<>≮≯⋖⋗≪≫⋘⋙≤≥⪇⪈≰≱≦≧≨≩⩽⩾⪕⪖≶≷⋚⋛⪋⪌≲≳⋦⋧⪅⪆⪉⪊⊲⊳⋪⋫⊴⊵⋬⋭◀▶⊂⊃⊆⊇⊊⊋⊈⊉⫅⫆⫋⫌∍⋐⋑⊏⊐⊑⊒

3.2 箭头符号

$$
\leftarrow    \leftrightarrow    \rightarrow    \mapsto    \longleftarrow        \longleftrightarrow    \longrightarrow    \longmapsto    \downarrow    \updownarrow    \uparrow    \nwarrow        \searrow    \nearrow    \swarrow        \nleftarrow            \nleftrightarrow        \nrightarrow        \hookleftarrow        \hookrightarrow        \twoheadleftarrow        \twoheadrightarrow        \leftarrowtail        \rightarrowtail        \Leftarrow        \Leftrightarrow        \Rightarrow        \Longleftarrow        \Longleftrightarrow        \Longrightarrow            \Updownarrow        \Uparrow        \Downarrow        \nLeftarrow        \nLeftrightarrow    \nRightarrow        \leftleftarrows        \leftrightarrows        \rightleftarrows        \rightrightarrows        \downdownarrows        \upuparrows        \circlearrowleft        \circlearrowright        \curvearrowleft        \curvearrowright        \Lsh        \Rsh        \looparrowleft        \looparrowright        \dashleftarrow        \dashrightarrow        \leftrightsquigarrow        \rightsquigarrow        \Lleftarrow        \leftharpoondown        \rightharpoondown        \leftharpoonup        \rightharpoonup        \rightleftharpoons        \leftrightharpoons        \downharpoonleft        \upharpoonleft        \downharpoonright            \upharpoonright
$$

←↔→↦⟵⟷⟶⟼↓↕↑↖↘↗↙↚↮↛↩↪↞↠↢↣⇐⇔⇒⟸⟺⟹⇕⇑⇓⇍⇎⇏⇇⇆⇄⇉⇊⇈↺↻↶↷↰↱↫↬⇠⇢↭⇝⇚↽⇁↼⇀⇌⇋⇃↿⇂↾\leftarrow \leftrightarrow \rightarrow \mapsto \longleftarrow \longleftrightarrow \longrightarrow \longmapsto \downarrow \updownarrow \uparrow \nwarrow \searrow \nearrow \swarrow \nleftarrow \nleftrightarrow \nrightarrow \hookleftarrow \hookrightarrow \twoheadleftarrow \twoheadrightarrow \leftarrowtail \rightarrowtail \Leftarrow \Leftrightarrow \Rightarrow \Longleftarrow \Longleftrightarrow \Longrightarrow \Updownarrow \Uparrow \Downarrow \nLeftarrow \nLeftrightarrow \nRightarrow \leftleftarrows \leftrightarrows \rightleftarrows \rightrightarrows \downdownarrows \upuparrows \circlearrowleft \circlearrowright \curvearrowleft \curvearrowright \Lsh \Rsh \looparrowleft \looparrowright \dashleftarrow \dashrightarrow \leftrightsquigarrow \rightsquigarrow \Lleftarrow \leftharpoondown \rightharpoondown \leftharpoonup \rightharpoonup \rightleftharpoons \leftrightharpoons \downharpoonleft \upharpoonleft \downharpoonright \upharpoonright ←↔→↦⟵⟷⟶⟼↓↕↑↖↘↗↙↚↮↛↩↪↞↠↢↣⇐⇔⇒⟸⟺⟹⇕⇑⇓⇍⇎⇏⇇⇆⇄⇉⇊⇈↺↻↶↷↰↱↫↬⇠⇢↭⇝⇚↽⇁↼⇀⇌⇋⇃↿⇂↾

六. 其它

行间公式：$$\frac{d}{dx}e^{ax}=ae^{ax}\quad \sum_{i=1}^{n}{(X_i - \overline{X})^2}$$: ddxeax=aeax∑i=1n(Xi−X‾)2\frac{d}{dx}e^{ax}=ae^{ax}\quad \sum_{i=1}^{n}{(X_i - \overline{X})^2}dxdeax=aeaxi=1∑n(Xi−X)2

省略号：

$$\cdots 和 \ldots$$: ⋯和…\cdots 和 \ldots⋯和…
$$ {1+2+3+\ldots+n} $$: 1+2+3+…+n{1+2+3+\ldots+n} 1+2+3+…+n

行内公式: $R^s_r(t_r,t_e)=(t_r-t_e)c$ : Rrs(tr,te)=(tr−te)cR^s_r(t_r,t_e)=(t_r-t_e)cRrs(tr,te)=(tr−te)c

显示公式: $$R^s_r(t_r,t_e)=(t_r-t_e)c$$: Rrs(tr,te)=(tr−te)cR^s_r(t_r,t_e)=(t_r-t_e)cRrs(tr,te)=(tr−te)c

$$\frac{\partial f(x,y)}{\partial x}$$: ∂f(x,y)∂x\frac{\partial f(x,y)}{\partial x}∂x∂f(x,y)