MarkDown数学公式的详解

MarkDown数学公式的详解

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例子：$\sum_{i=0}^n i^2 = \frac{(n^2+n)(2n+1)}{6}$

求和公式（1）：$\sum_{i=0}^n$

求和公式（2）：

$$\sum_{i=0}^n i^2$$

使一对或者两对$号，可以用不同方式显示

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大写	表达式	小写	表达式
A	A	α	\alpha
B	B	β	\beta
Γ	\Gamma	γ	\gamma
Δ	\Delta	δ	\delta
E	E	ϵ	\epsilon
		ε	\varepsilon
Z	Z	ζ	\zeta
H	H	η	\eta
Θ	\Theta	θ	\theta
I	I	ι	\iota
K	K	κ	\kappa
Λ	\Lambda	λ	\lambda
M	M	μ	\mu
N	N	ν	\nu
Ξ	\Xi	ξ	\xi
O	O	ο	\omicron
Π	\Pi	π	\pi
P	P	ρ	\rho
Σ	\Sigma	σ	\sigma
T	T	τ	\tau
Υ	\Upsilon	υ	\upsilon
Φ	\Phi	ϕ	\phi
		φ φ	\varphi
X	X	χ	\chi
Ψ	\Psi	ψ	\psi
Ω	\Omega	ω	\omega
$\ell$	\ell
$\mathcal{E}$	\mathcal{E}
$\varepsilon{E}$	\varepsilon{E}

---

表达式	代码
$\frac{7x+5}{1+y^2}$	\frac{7x+5}{1+y^2}
$z=z_1$	z=z_l
$\cdots$	\cdots
$\sqrt{2};\sqrt[n]{3}$	\sqrt{2};\sqrt[n]{3}
$\vec{a} \cdot \vec{b}=0$	\vec{a} \cdot \vec{b}=0
$\int ^2_3 x^2 {\rm d}x$	\int ^2_3 x^2 {\rm d}x
$\lim_{n\rightarrow+\infty} n$	\lim_{n\rightarrow+\infty} n
$$\lim_{n\rightarrow+\infty} n$$	加双$$
$\sum \frac{1}{i^2}$	\sum \frac{1}{i^2}
$\prod \frac{1}{i^2}$	\prod \frac{1}{i^2}
$\sin$	\sin
$\cos$	\cos
$\tan$	\tan
$\ln15$	\ln15
$\log_2 10$	\log_2 10
$\lg7$	\lg7
$\pm$	\pm
$\mp$	\mp
$\times$	\times
$\div$	\div
$\sum$	\sum
$\int$	\int
$\iint$	\iint
$\prod$	\prod
$\neq$	\neq
$\leq$	\leq
$\geq$	\geq
$\lt$	\lt
$\gt$	\gt
$\not \lt$	\not \lt
$\star$	\star
$\ast$	\ast
$\oplus$	\oplus
$\circ$	\circ
$\bullet$	\bullet
$\bigcup$	\bigcup
$\bigcap$	\bigcap

表达式	代码
$\sum_{i=0}^n i^2 = \frac{(n^2+n)(2n+1)}{6}$	\sum_{i=0}^n i^2 = \frac{(n^2+n)(2n+1)}{6}
${x^y}^z$	{x^y}^z
$x^{y^z}$	x^{y^z}
$x_i^2$	x_i^2
$x_{i^2}$	x_{i^2}
$\frac ab$	\frac ab
$()[]$	()[]
$\{ and \}$	\{ and \}
$\frac{\sqrt x}{y^3}$	\frac{\sqrt x}{y^3}
$\left (\frac{\sqrt x}{y^3} \right)$	\left (\frac{\sqrt x}{y^3} \right)
$\Biggl(\biggl(\Bigl(\bigl((x)\bigr)\Bigr)\biggr)\Biggr)$	\Biggl(\biggl(\Bigl(\bigl((x)\bigr)\Bigr)\biggr)\Biggr)
$\vert \vert$	\vert
$\sum_{i=0}^\infty i^2$	\sum_{i=0}^\infty i^2
${a+1\over b+1}$	{a+1\over b+1}
$\mathbb$	\mathbb
$\Bbb$	\Bbb
$\mathbf$	\mathbf,\mathcal,\mathtt,\mathscr,\mathfrak
${...}^{1/2}$	{…}^{1/2}
$$\lim_{x\to 0}$$	\lim_{x\to 0}
${n+1 \choose 2k}$	{n+1 \choose 2k},\binom{n+1}{2k}

集合论

表达式	代码
$\cup$	\cup
$\cap$	\cap
$\setminus$	\setminus
$\subset$	\subset
$\subseteq$	\subseteq
$\subsetneq$	\subsetneq
$\supset$	\supset
$\in$	\in
$\notin$	\notin
$\emptyset$	\emptyset
$\varnothing$	\varnothing

其他符号

表达式	代码
$\to$	\to
$\rightarrow$	\rightarrow
$\leftarrow$	\leftarrow
$\Rightarrow$	\Rightarrow
$\Leftarrow$	\Leftarrow
$\mapsto$	\mapsto
$\land$	\land
$\lor$	\lor
$\lnot$	\lnot
$\forall$	\forall
$\exists$	\exists
$\top$	\top
$\bot$	\bot
$\vdash$	\vdash
$\vDash$	\vDash
$\approx$	\approx
$\sim$	\sim
$\simeq$	\simeq
$\cong$	\cong
$\equiv$	\equiv
$\prec$	\prec
$\lhd$	\lhd
$\aleph_0$	\infty \aleph_0
$\infty$	\infty
$\nabla$	\nabla
$\partial$	\partial
$\Im$	\Im
$\Re$	\Re
$a\equiv b\pmod n$	a\equiv b\pmod n
$\hat{d}$	\hat{d}
$\widehat{x}$	\widehat{x}
$\bar{x}$	\bar{x}
$\overline{xy}$	\overline{xy}
$\vec{x}$	\vec{x}
$\overrightarrow{xyz}$	\overrightarrow{xyz}
$\overleftrightarrow{xy}$	\overleftrightarrow{xy}
$\mathrm{B}$	\mathrm{B}
$\operatorname{Spec}$	\operatorname{Spec}
$_5C_3$	_5C_3

矩阵

$$\begin{matrix} 1 & x & x^2 \\ 1 & y & y^2 \\ 1 & z & z^2 \\ \end{matrix}$$

$$
    \begin{matrix}
    1 & x & x^2 \\
    1 & y & y^2 \\
    1 & z & z^2 \\
    \end{matrix}
$$

---

$$\begin{pmatrix} 1 & x & x^2 \\ 1 & y & y^2 \\ 1 & z & z^2 \\ \end{pmatrix}$$

$$
    \begin{pmatrix}
    1 & x & x^2 \\
    1 & y & y^2 \\
    1 & z & z^2 \\
    \end{pmatrix}
$$

---

$$\begin{bmatrix} 1 & x & x^2 \\ 1 & y & y^2 \\ 1 & z & z^2 \\ \end{bmatrix}$$

$$
    \begin{bmatrix}
    1 & x & x^2 \\
    1 & y & y^2 \\
    1 & z & z^2 \\
    \end{bmatrix}
$$

---

$$\begin{Bmatrix} 1 & x & x^2 \\ 1 & y & y^2 \\ 1 & z & z^2 \\ \end{Bmatrix}$$

$$
    \begin{Bmatrix}
    1 & x & x^2 \\
    1 & y & y^2 \\
    1 & z & z^2 \\
    \end{Bmatrix}
$$

---

$$\begin{vmatrix} \cdots & x & x^2 \\ \ddots & y & y^2 \\ 1 & \vdots & z^2 \\ \end{vmatrix}$$

$$
    \begin{vmatrix}
    \cdots & x & x^2 \\
    \ddots & y & y^2 \\
    1 & \vdots & z^2 \\
    \end{vmatrix}
$$ 

---

$$\begin{Vmatrix} 1 & x & x^2 \\ 1 & y & y^2 \\ 1 & z & z^2 \\ \end{Vmatrix}$$

$$
    \begin{Vmatrix}
    1 & x & x^2 \\
    1 & y & y^2 \\
    1 & z & z^2 \\
    \end{Vmatrix}
$$

---

$$\begin{array}{cc|c} 1&2&3\\ 4&5&6 \end{array}$$

\begin{array}{cc|c}
  1&2&3\\
  4&5&6
\end{array}

---

$$\begin{align} \sqrt{37} & = \sqrt{\frac{73^2-1}{12^2}} \\ & = \sqrt{\frac{73^2}{12^2}\cdot\frac{73^2-1}{73^2}} \\ & = \sqrt{\frac{73^2}{12^2}}\sqrt{\frac{73^2-1}{73^2}} \\ & = \frac{73}{12}\sqrt{1 - \frac{1}{73^2}} \\ & \approx \frac{73}{12}\left(1 - \frac{1}{2\cdot73^2}\right) \end{align}$$

\begin{align}
\sqrt{37} & = \sqrt{\frac{73^2-1}{12^2}} \\
 & = \sqrt{\frac{73^2}{12^2}\cdot\frac{73^2-1}{73^2}} \\ 
 & = \sqrt{\frac{73^2}{12^2}}\sqrt{\frac{73^2-1}{73^2}} \\
 & = \frac{73}{12}\sqrt{1 - \frac{1}{73^2}} \\ 
 & \approx \frac{73}{12}\left(1 - \frac{1}{2\cdot73^2}\right)
\end{align}

---

$$f(n) = \begin{cases} n/2, & \text{if $n$ is even} \\ 3n+1, & \text{if $n$ is odd} \end{cases}$$

$$f(n) =
\begin{cases}
n/2,  & \text{if $n$ is even} \\
3n+1, & \text{if $n$ is odd}
\end{cases}
$$

---

$$\left. \begin{array}{l} \text{if $n$ is even:}&n/2\\ \text{if $n$ is odd:}&3n+1 \end{array} \right\} =f(n)$$

$$
\left.
\begin{array}{l}
\text{if $n$ is even:}&n/2\\
\text{if $n$ is odd:}&3n+1
\end{array}
\right\}
=f(n)
$$

---

$$f(n) = \begin{cases} \frac{n}{2}, & \text{if $n$ is even} \\[2ex] 3n+1, & \text{if $n$ is odd} \end{cases}$$

$$
f(n) =
\begin{cases}
\frac{n}{2},  & \text{if $n$ is even} \\[2ex]
3n+1, & \text{if $n$ is odd}
\end{cases}
$$

---

$$\begin{array}{c|lcr} n & \text{Left} & \text{Center} & \text{Right} \\ \hline 1 & 0.24 & 1 & 125 \\ 2 & -1 & 189 & -8 \\ 3 & -20 & 2000 & 1+10i \end{array}$$

$$
\begin{array}{c|lcr}
n & \text{Left} & \text{Center} & \text{Right} \\
\hline
1 & 0.24 & 1 & 125 \\
2 & -1 & 189 & -8 \\
3 & -20 & 2000 & 1+10i
\end{array}
$$

---

$$\begin{array}{ll} \mathrm{Bad} & \mathrm{Better} \\ \hline \\ e^{i\frac{\pi}2} \quad e^{\frac{i\pi}2}& e^{i\pi/2} \\ \int_{-\frac\pi2}^\frac\pi2 \sin x\,dx & \int_{-\pi/2}^{\pi/2}\sin x\,dx \\ \end{array}$$

\begin{array}{ll} \hfill\mathrm{Bad}\hfill & \hfill\mathrm{Better}\hfill \\ \hline \\ e^{i\frac{\pi}2} \quad e^{\frac{i\pi}2}& e^{i\pi/2} \\ \int_{-\frac\pi2}^\frac\pi2 \sin x\,dx & \int_{-\pi/2}^{\pi/2}\sin x\,dx \\ \end{array}

---

$$\begin{array}{cc} \mathrm{Bad} & \mathrm{Better} \\ \hline \\ \{x|x^2\in\Bbb Z\} & \{x\mid x^2\in\Bbb Z\} \\ \end{array}$$

\begin{array}{cc}
\mathrm{Bad} & \mathrm{Better} \\
\hline \\
\{x|x^2\in\Bbb Z\} & \{x\mid x^2\in\Bbb Z\} \\
\end{array}

---

$$\begin{array}{cc} \mathrm{Bad} & \mathrm{Better} \\ \hline \\ \int\int_S f(x)\,dy\,dx & \iint_S f(x)\,dy\,dx \\ \int\int\int_V f(x)\,dz\,dy\,dx & \iiint_V f(x)\,dz\,dy\,dx \end{array}$$

\begin{array}{cc}
\mathrm{Bad} & \mathrm{Better} \\
\hline \\
\int\int_S f(x)\,dy\,dx & \iint_S f(x)\,dy\,dx \\
\int\int\int_V f(x)\,dz\,dy\,dx & \iiint_V f(x)\,dz\,dy\,dx
\end{array}

---

$$\left\{x\middle | \frac{x^2}{2} \in \mathbb{z}\right\}$$

$$\left\{x\middle | \frac{x^2}{2} \in \mathbb{z}\right\}$$

---

$$\begin{array}{|rc|} \hline \verb+\color{black}{text}+ & \color{black}{text} \\ \verb+\color{gray}{text}+ & \color{gray}{text} \\ \verb+\color{silver}{text}+ & \color{silver}{text} \\ \verb+\color{white}{text}+ & \color{white}{text} \\ \hline \verb+\color{maroon}{text}+ & \color{maroon}{text} \\ \verb+\color{red}{text}+ & \color{red}{text} \\ \verb+\color{yellow}{text}+ & \color{yellow}{text} \\ \verb+\color{lime}{text}+ & \color{lime}{text} \\ \verb+\color{olive}{text}+ & \color{olive}{text} \\ \verb+\color{green}{text}+ & \color{green}{text} \\ \verb+\color{teal}{text}+ & \color{teal}{text} \\ \verb+\color{aqua}{text}+ & \color{aqua}{text} \\ \verb+\color{blue}{text}+ & \color{blue}{text} \\ \verb+\color{navy}{text}+ & \color{navy}{text} \\ \verb+\color{purple}{text}+ & \color{purple}{text} \\ \verb+\color{fuchsia}{text}+ & \color{magenta}{text} \\ \hline \end{array}$$

\begin{array}{|rc|}
\hline
\verb+\color{black}{text}+ & \color{black}{text} \\
\verb+\color{gray}{text}+ & \color{gray}{text} \\
\verb+\color{silver}{text}+ & \color{silver}{text} \\
\verb+\color{white}{text}+ & \color{white}{text} \\
\hline
\verb+\color{maroon}{text}+ & \color{maroon}{text} \\
\verb+\color{red}{text}+ & \color{red}{text} \\
\verb+\color{yellow}{text}+ & \color{yellow}{text} \\
\verb+\color{lime}{text}+ & \color{lime}{text} \\
\verb+\color{olive}{text}+ & \color{olive}{text} \\
\verb+\color{green}{text}+ & \color{green}{text} \\
\verb+\color{teal}{text}+ & \color{teal}{text} \\
\verb+\color{aqua}{text}+ & \color{aqua}{text} \\
\verb+\color{blue}{text}+ & \color{blue}{text} \\
\verb+\color{navy}{text}+ & \color{navy}{text} \\
\verb+\color{purple}{text}+ & \color{purple}{text} \\ 
\verb+\color{fuchsia}{text}+ & \color{magenta}{text} \\
\hline
\end{array}

---

$$\begin{array}{|rrrrrrrr|}\hline \verb+#000+ & \color{#000}{text} & & & \verb+#00F+ & \color{#00F}{text} & & \\ & & \verb+#0F0+ & \color{#0F0}{text} & & & \verb+#0FF+ & \color{#0FF}{text}\\ \verb+#F00+ & \color{#F00}{text} & & & \verb+#F0F+ & \color{#F0F}{text} & & \\ & & \verb+#FF0+ & \color{#FF0}{text} & & & \verb+#FFF+ & \color{#FFF}{text}\\ \hline \end{array}$$

$$\begin{array}{|rrrrrrrr|} \hline \verb+#000+ & \color{#000}{text} & \verb+#005+ & \color{#005}{text} & \verb+#00A+ & \color{#00A}{text} & \verb+#00F+ & \color{#00F}{text} \\ \verb+#500+ & \color{#500}{text} & \verb+#505+ & \color{#505}{text} & \verb+#50A+ & \color{#50A}{text} & \verb+#50F+ & \color{#50F}{text} \\ \verb+#A00+ & \color{#A00}{text} & \verb+#A05+ & \color{#A05}{text} & \verb+#A0A+ & \color{#A0A}{text} & \verb+#A0F+ & \color{#A0F}{text} \\ \verb+#F00+ & \color{#F00}{text} & \verb+#F05+ & \color{#F05}{text} & \verb+#F0A+ & \color{#F0A}{text} & \verb+#F0F+ & \color{#F0F}{text} \\ \hline \verb+#080+ & \color{#080}{text} & \verb+#085+ & \color{#085}{text} & \verb+#08A+ & \color{#08A}{text} & \verb+#08F+ & \color{#08F}{text} \\ \verb+#580+ & \color{#580}{text} & \verb+#585+ & \color{#585}{text} & \verb+#58A+ & \color{#58A}{text} & \verb+#58F+ & \color{#58F}{text} \\ \verb+#A80+ & \color{#A80}{text} & \verb+#A85+ & \color{#A85}{text} & \verb+#A8A+ & \color{#A8A}{text} & \verb+#A8F+ & \color{#A8F}{text} \\ \verb+#F80+ & \color{#F80}{text} & \verb+#F85+ & \color{#F85}{text} & \verb+#F8A+ & \color{#F8A}{text} & \verb+#F8F+ & \color{#F8F}{text} \\ \hline \verb+#0F0+ & \color{#0F0}{text} & \verb+#0F5+ & \color{#0F5}{text} & \verb+#0FA+ & \color{#0FA}{text} & \verb+#0FF+ & \color{#0FF}{text} \\ \verb+#5F0+ & \color{#5F0}{text} & \verb+#5F5+ & \color{#5F5}{text} & \verb+#5FA+ & \color{#5FA}{text} & \verb+#5FF+ & \color{#5FF}{text} \\ \verb+#AF0+ & \color{#AF0}{text} & \verb+#AF5+ & \color{#AF5}{text} & \verb+#AFA+ & \color{#AFA}{text} & \verb+#AFF+ & \color{#AFF}{text} \\ \verb+#FF0+ & \color{#FF0}{text} & \verb+#FF5+ & \color{#FF5}{text} & \verb+#FFA+ & \color{#FFA}{text} & \verb+#FFF+ & \color{#FFF}{text} \\ \hline \end{array}$$

[引用文献][1]
[1]: https://math.meta.stackexchange.com/questions/5020/mathjax-basic-tutorial-and-quick-reference
[2]:http://blog.youkuaiyun.com/zdk930519/article/details/54137476