# Help:数学公式

（重定向自Help:數學公式

## 函数、符号及特殊字符

#### 声调/变音符号

\dot{a}, \ddot{a}, \acute{a}, \grave{a} ${\displaystyle {\dot {a}},{\ddot {a}},{\acute {a}},{\grave {a}}}$
\check{a}, \breve{a}, \tilde{a}, \bar{a} ${\displaystyle {\check {a}},{\breve {a}},{\tilde {a}},{\bar {a}}}$
\hat{a}, \widehat{a}, \vec{a} ${\displaystyle {\hat {a}},{\widehat {a}},{\vec {a}}}$

#### 标准函数

\exp_a b = a^b, \exp b = e^b, 10^m ${\displaystyle \exp _{a}b=a^{b},\exp b=e^{b},10^{m}}$
\ln c, \lg d = \log e, \log_{10} f ${\displaystyle \ln c,\lg d=\log e,\log _{10}f}$
\sin a, \cos b, \tan c, \cot d, \sec e, \csc f ${\displaystyle \sin a,\cos b,\tan c,\cot d,\sec e,\csc f}$
\arcsin a, \arccos b, \arctan c ${\displaystyle \arcsin a,\arccos b,\arctan c}$
\arccot d, \arcsec e, \arccsc f ${\displaystyle \operatorname {arccot} d,\operatorname {arcsec} e,\operatorname {arccsc} f}$
\sinh a, \cosh b, \tanh c, \coth d ${\displaystyle \sinh a,\cosh b,\tanh c,\coth d}$
\operatorname{sh}k, \operatorname{ch}l, \operatorname{th}m, \operatorname{coth}n ${\displaystyle \operatorname {sh} k,\operatorname {ch} l,\operatorname {th} m,\operatorname {coth} n}$
\operatorname{argsh}o, \operatorname{argch}p, \operatorname{argth}q ${\displaystyle \operatorname {argsh} o,\operatorname {argch} p,\operatorname {argth} q}$
\sgn r, \left\vert s \right\vert ${\displaystyle \operatorname {sgn} r,\left\vert s\right\vert }$
\min(x,y), \max(x,y) ${\displaystyle \min(x,y),\max(x,y)}$

#### 極限

\min x, \max y, \inf s, \sup t ${\displaystyle \min x,\max y,\inf s,\sup t}$
\lim u, \liminf v, \limsup w ${\displaystyle \lim u,\liminf v,\limsup w}$
\dim p, \deg q, \det m, \ker\phi ${\displaystyle \dim p,\deg q,\det m,\ker \phi }$

#### 投射

\Pr j, \hom l, \lVert z \rVert, \arg z ${\displaystyle \Pr j,\hom l,\lVert z\rVert ,\arg z}$

#### 微分及导数

dt, \mathrm{d}t, \partial t, \nabla\psi ${\displaystyle dt,\mathrm {d} t,\partial t,\nabla \psi }$
dy/dx, \mathrm{d}y/\mathrm{d}x, \frac{dy}{dx}, \frac{\mathrm{d}y}{\mathrm{d}x}, \frac{\partial^2}{\partial x_1\partial x_2}y ${\displaystyle dy/dx,\mathrm {d} y/\mathrm {d} x,{\frac {dy}{dx}},{\frac {\mathrm {d} y}{\mathrm {d} x}},{\frac {\partial ^{2}}{\partial x_{1}\partial x_{2}}}y}$
\prime, \backprime, f^\prime, f', f'', f^{(3)}, \dot y, \ddot y ${\displaystyle \prime ,\backprime ,f^{\prime },f',f'',f^{(3)}\!,{\dot {y}},{\ddot {y}}}$

#### 类字母符号及常数

\infty, \aleph, \complement, \backepsilon, \eth, \Finv, \hbar ${\displaystyle \infty ,\aleph ,\complement ,\backepsilon ,\eth ,\Finv ,\hbar }$
\Im, \imath, \jmath, \Bbbk, \ell, \mho, \wp, \Re, \circledS, \S, \P, \AA ${\displaystyle \Im ,\imath ,\jmath ,\Bbbk ,\ell ,\mho ,\wp ,\Re ,\circledS ,\S ,\P ,\mathrm {\AA} }$

#### 模算数

s_k \equiv 0 \pmod{m} ${\displaystyle s_{k}\equiv 0{\pmod {m}}}$
a \bmod b ${\displaystyle a{\bmod {b}}}$
\gcd(m, n), \operatorname{lcm}(m, n) ${\displaystyle \gcd(m,n),\operatorname {lcm} (m,n)}$
\mid, \nmid, \shortmid, \nshortmid ${\displaystyle \mid ,\nmid ,\shortmid ,\nshortmid }$

#### 根号

\surd, \sqrt{2}, \sqrt[n]{}, \sqrt[3]{\frac{x^3+y^3}{2}} ${\displaystyle \surd ,{\sqrt {2}},{\sqrt[{n}]{}},{\sqrt[{3}]{\frac {x^{3}+y^{3}}{2}}}}$

#### 运算符

+, -, \pm, \mp, \dotplus ${\displaystyle +,-,\pm ,\mp ,\dotplus }$
\times, \div, \divideontimes, /, \backslash ${\displaystyle \times ,\div ,\divideontimes ,/,\backslash }$
\cdot, * \ast, \star, \circ, \bullet ${\displaystyle \cdot ,*\ast ,\star ,\circ ,\bullet }$
\boxplus, \boxminus, \boxtimes, \boxdot ${\displaystyle \boxplus ,\boxminus ,\boxtimes ,\boxdot }$
\oplus, \ominus, \otimes, \oslash, \odot ${\displaystyle \oplus ,\ominus ,\otimes ,\oslash ,\odot }$
\circleddash, \circledcirc, \circledast ${\displaystyle \circleddash ,\circledcirc ,\circledast }$
\bigoplus, \bigotimes, \bigodot ${\displaystyle \bigoplus ,\bigotimes ,\bigodot }$

#### 集合

\{ \}, \O \empty \emptyset, \varnothing ${\displaystyle \{\},\emptyset \emptyset \emptyset ,\varnothing }$
\in, \notin \not\in, \ni, \not\ni ${\displaystyle \in ,\notin \not \in ,\ni ,\not \ni }$
\cap, \Cap, \sqcap, \bigcap ${\displaystyle \cap ,\Cap ,\sqcap ,\bigcap }$
\cup, \Cup, \sqcup, \bigcup, \bigsqcup, \uplus, \biguplus ${\displaystyle \cup ,\Cup ,\sqcup ,\bigcup ,\bigsqcup ,\uplus ,\biguplus }$
\setminus, \smallsetminus, \times ${\displaystyle \setminus ,\smallsetminus ,\times }$
\subset, \Subset, \sqsubset ${\displaystyle \subset ,\Subset ,\sqsubset }$
\supset, \Supset, \sqsupset ${\displaystyle \supset ,\Supset ,\sqsupset }$
\subseteq, \nsubseteq, \subsetneq, \varsubsetneq, \sqsubseteq ${\displaystyle \subseteq ,\nsubseteq ,\subsetneq ,\varsubsetneq ,\sqsubseteq }$
\supseteq, \nsupseteq, \supsetneq, \varsupsetneq, \sqsupseteq ${\displaystyle \supseteq ,\nsupseteq ,\supsetneq ,\varsupsetneq ,\sqsupseteq }$
\subseteqq, \nsubseteqq, \subsetneqq, \varsubsetneqq ${\displaystyle \subseteqq ,\nsubseteqq ,\subsetneqq ,\varsubsetneqq }$
\supseteqq, \nsupseteqq, \supsetneqq, \varsupsetneqq ${\displaystyle \supseteqq ,\nsupseteqq ,\supsetneqq ,\varsupsetneqq }$

#### 关系符号

=, \ne, \neq, \equiv, \not\equiv ${\displaystyle =,\neq ,\neq ,\equiv ,\not \equiv }$
\doteq, \doteqdot, \overset{\underset{\mathrm{def}}{}}{=}, := ${\displaystyle \doteq ,\doteqdot ,{\overset {\underset {\mathrm {def} }{}}{=}},:=}$
\sim, \nsim, \backsim, \thicksim, \simeq, \backsimeq, \eqsim, \cong, \ncong ${\displaystyle \sim ,\nsim ,\backsim ,\thicksim ,\simeq ,\backsimeq ,\eqsim ,\cong ,\ncong }$
\approx, \thickapprox, \approxeq, \asymp, \propto, \varpropto ${\displaystyle \approx ,\thickapprox ,\approxeq ,\asymp ,\propto ,\varpropto }$
<, \nless, \ll, \not\ll, \lll, \not\lll, \lessdot ${\displaystyle <,\nless ,\ll ,\not \ll ,\lll ,\not \lll ,\lessdot }$
>, \ngtr, \gg, \not\gg, \ggg, \not\ggg, \gtrdot ${\displaystyle >,\ngtr ,\gg ,\not \gg ,\ggg ,\not \ggg ,\gtrdot }$
\le, \leq, \lneq, \leqq, \nleq, \nleqq, \lneqq, \lvertneqq ${\displaystyle \leq ,\leq ,\lneq ,\leqq ,\nleq ,\nleqq ,\lneqq ,\lvertneqq }$
\ge, \geq, \gneq, \geqq, \ngeq, \ngeqq, \gneqq, \gvertneqq ${\displaystyle \geq ,\geq ,\gneq ,\geqq ,\ngeq ,\ngeqq ,\gneqq ,\gvertneqq }$
\lessgtr, \lesseqgtr, \lesseqqgtr, \gtrless, \gtreqless, \gtreqqless ${\displaystyle \lessgtr ,\lesseqgtr ,\lesseqqgtr ,\gtrless ,\gtreqless ,\gtreqqless }$
\leqslant, \nleqslant, \eqslantless ${\displaystyle \leqslant ,\nleqslant ,\eqslantless }$
\geqslant, \ngeqslant, \eqslantgtr ${\displaystyle \geqslant ,\ngeqslant ,\eqslantgtr }$
\lesssim, \lnsim, \lessapprox, \lnapprox ${\displaystyle \lesssim ,\lnsim ,\lessapprox ,\lnapprox }$
\gtrsim, \gnsim, \gtrapprox, \gnapprox ${\displaystyle \gtrsim ,\gnsim ,\gtrapprox ,\gnapprox }$
\prec, \nprec, \preceq, \npreceq, \precneqq ${\displaystyle \prec ,\nprec ,\preceq ,\npreceq ,\precneqq }$
\succ, \nsucc, \succeq, \nsucceq, \succneqq ${\displaystyle \succ ,\nsucc ,\succeq ,\nsucceq ,\succneqq }$
\preccurlyeq, \curlyeqprec ${\displaystyle \preccurlyeq ,\curlyeqprec }$
\succcurlyeq, \curlyeqsucc ${\displaystyle \succcurlyeq ,\curlyeqsucc }$
\precsim, \precnsim, \precapprox, \precnapprox ${\displaystyle \precsim ,\precnsim ,\precapprox ,\precnapprox }$
\succsim, \succnsim, \succapprox, \succnapprox ${\displaystyle \succsim ,\succnsim ,\succapprox ,\succnapprox }$

#### 几何符号

\parallel, \nparallel, \shortparallel, \nshortparallel ${\displaystyle \parallel ,\nparallel ,\shortparallel ,\nshortparallel }$
\perp, \angle, \sphericalangle, \measuredangle, 45^\circ ${\displaystyle \perp ,\angle ,\sphericalangle ,\measuredangle ,45^{\circ }}$
\Box, \blacksquare, \diamond, \Diamond \lozenge, \blacklozenge, \bigstar ${\displaystyle \Box ,\blacksquare ,\diamond ,\Diamond \lozenge ,\blacklozenge ,\bigstar }$
\bigcirc, \triangle, \bigtriangleup, \bigtriangledown ${\displaystyle \bigcirc ,\triangle ,\bigtriangleup ,\bigtriangledown }$
\vartriangle, \triangledown ${\displaystyle \vartriangle ,\triangledown }$
\blacktriangle, \blacktriangledown, \blacktriangleleft, \blacktriangleright ${\displaystyle \blacktriangle ,\blacktriangledown ,\blacktriangleleft ,\blacktriangleright }$

#### 逻辑符号

\forall, \exists, \nexists ${\displaystyle \forall ,\exists ,\nexists }$
\therefore, \because, \And ${\displaystyle \therefore ,\because ,\And }$
\or \lor \vee, \curlyvee, \bigvee ${\displaystyle \lor ,\lor ,\vee ,\curlyvee ,\bigvee }$
\and \land \wedge, \curlywedge, \bigwedge ${\displaystyle \land ,\land ,\wedge ,\curlywedge ,\bigwedge }$
\bar{q}, \bar{abc}, \overline{q}, \overline{abc},

\lnot \neg, \not\operatorname{R}, \bot, \top

${\displaystyle {\bar {q}},{\bar {abc}},{\overline {q}},{\overline {abc}},}$

${\displaystyle \lnot \neg ,\not \operatorname {R} ,\bot ,\top }$

\vdash \dashv, \vDash, \Vdash, \models ${\displaystyle \vdash ,\dashv ,\vDash ,\Vdash ,\models }$
\Vvdash \nvdash \nVdash \nvDash \nVDash ${\displaystyle \Vvdash ,\nvdash ,\nVdash ,\nvDash ,\nVDash }$
\ulcorner \urcorner \llcorner \lrcorner ${\displaystyle \ulcorner \urcorner \llcorner \lrcorner }$

#### 箭头

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

#### 特殊符号

\amalg \P \S \% \dagger \ddagger \ldots \cdots ${\displaystyle \amalg \P \S \%\dagger \ddagger \ldots \cdots }$
\smile \frown \wr \triangleleft \triangleright ${\displaystyle \smile \frown \wr \triangleleft \triangleright }$
\diamondsuit, \heartsuit, \clubsuit, \spadesuit, \Game, \flat, \natural, \sharp ${\displaystyle \diamondsuit ,\heartsuit ,\clubsuit ,\spadesuit ,\Game ,\flat ,\natural ,\sharp }$

#### 未排序

\diagup \diagdown \centerdot \ltimes \rtimes \leftthreetimes \rightthreetimes ${\displaystyle \diagup ,\diagdown ,\centerdot ,\ltimes ,\rtimes ,\leftthreetimes ,\rightthreetimes }$
\eqcirc \circeq \triangleq \bumpeq \Bumpeq \doteqdot \risingdotseq \fallingdotseq ${\displaystyle \eqcirc ,\circeq ,\triangleq ,\bumpeq ,\Bumpeq ,\doteqdot ,\risingdotseq ,\fallingdotseq }$
\intercal \barwedge \veebar \doublebarwedge \between \pitchfork ${\displaystyle \intercal ,\barwedge ,\veebar ,\doublebarwedge ,\between ,\pitchfork }$
\vartriangleleft \ntriangleleft \vartriangleright \ntriangleright ${\displaystyle \vartriangleleft ,\ntriangleleft ,\vartriangleright ,\ntriangleright }$
\trianglelefteq \ntrianglelefteq \trianglerighteq \ntrianglerighteq ${\displaystyle \trianglelefteq ,\ntrianglelefteq ,\trianglerighteq ,\ntrianglerighteq }$
\not6, \frac{1\not6}{\not64}=\frac{1}{4} ${\displaystyle \not 6,{\frac {1\not 6}{\not 64}}={\frac {1}{4}}}$

## 上标、下标及积分等

a_{i,j} ${\displaystyle a_{i,j}}$

HTML
x' ${\displaystyle x'}$

PNG
x^\prime ${\displaystyle x^{\prime }}$

x\prime ${\displaystyle x\prime }$

\ddot{y} ${\displaystyle {\ddot {y}}}$

\overleftarrow{a b} ${\displaystyle {\overleftarrow {ab}}}$
\overrightarrow{c d} ${\displaystyle {\overrightarrow {cd}}}$
\overleftrightarrow{a b} ${\displaystyle {\overleftrightarrow {ab}}}$
\widehat{e f g} ${\displaystyle {\widehat {efg}}}$

（註: 正確應該用 \overarc，但在這裡行不通。要用建議的語法作為解決辦法。）（使用\overarc時需要引入{arcs}套件。）
\overset{\frown} {AB} ${\displaystyle {\overset {\frown }{AB}}}$

\overbrace{ 1+2+\cdots+100 }^{5050} ${\displaystyle \overbrace {1+2+\cdots +100} ^{5050}}$

\underbrace{ a+b+\cdots+z }_{26} ${\displaystyle \underbrace {a+b+\cdots +z} _{26}}$

\begin{matrix} \sum_{k=1}^N k^2 \end{matrix} ${\displaystyle {\begin{matrix}\sum _{k=1}^{N}k^{2}\end{matrix}}}$

\begin{matrix} \prod_{i=1}^N x_i \end{matrix} ${\displaystyle {\begin{matrix}\prod _{i=1}^{N}x_{i}\end{matrix}}}$

\begin{matrix} \coprod_{i=1}^N x_i \end{matrix} ${\displaystyle {\begin{matrix}\coprod _{i=1}^{N}x_{i}\end{matrix}}}$

\begin{matrix} \lim_{n \to \infty}x_n \end{matrix} ${\displaystyle {\begin{matrix}\lim _{n\to \infty }x_{n}\end{matrix}}}$

\begin{matrix} \int_{-N}^{N} e^x\, \mathrm{d}x \end{matrix} ${\displaystyle {\begin{matrix}\int _{-N}^{N}e^{x}\,\mathrm {d} x\end{matrix}}}$

## 分数、矩阵和多行列式

{2 \over 3} ${\displaystyle {2 \over 3}}$
{{a+b} \over {a-b}} ${\displaystyle {{a+b} \over {a-b}}}$

n \choose n-r, n^2 \choose r_1, a-b \choose c+d, {n \choose 0}+{n \choose 1} ${\displaystyle n \choose n-r}$ ${\displaystyle n^{2} \choose r_{1}}$ ${\displaystyle a-b \choose c+d}$ ${\displaystyle {n \choose 0}+{n \choose 1}}$

\begin{matrix}
x & y \\
z & v
\end{matrix}
${\displaystyle {\begin{matrix}x&y\\z&v\end{matrix}}}$
\begin{vmatrix}
x & y \\
z & v
\end{vmatrix}
${\displaystyle {\begin{vmatrix}x&y\\z&v\end{vmatrix}}}$
\begin{Vmatrix}
x & y \\
z & v
\end{Vmatrix}
${\displaystyle {\begin{Vmatrix}x&y\\z&v\end{Vmatrix}}}$
\begin{bmatrix}
0      & \cdots & 0      \\
\vdots & \ddots & \vdots \\
0      & \cdots & 0
\end{bmatrix}
${\displaystyle {\begin{bmatrix}0&\cdots &0\\\vdots &\ddots &\vdots \\0&\cdots &0\end{bmatrix}}}$
\begin{Bmatrix}
x & y \\
z & v
\end{Bmatrix}
${\displaystyle {\begin{Bmatrix}x&y\\z&v\end{Bmatrix}}}$
\begin{pmatrix}
x & y \\
z & v
\end{pmatrix}
${\displaystyle {\begin{pmatrix}x&y\\z&v\end{pmatrix}}}$
\bigl( \begin{smallmatrix}
a&b\\ c&d
\end{smallmatrix} \bigr)

${\displaystyle {\bigl (}{\begin{smallmatrix}a&b\\c&d\end{smallmatrix}}{\bigr )}}$

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

\begin{align}
f(x) & = (m+n)^2 \\
& = m^2+2mn+n^2 \\
\end{align}

{\displaystyle {\begin{aligned}f(x)&=(m+n)^{2}\\&=m^{2}+2mn+n^{2}\\\end{aligned}}}
\begin{align}
3^{6n+3}+4^{6n+3}
& \equiv (3^3)^{2n+1}+(4^3)^{2n+1}\\
& \equiv 27^{2n+1}+64^{2n+1}\\
& \equiv 27^{2n+1}+(-27)^{2n+1}\\
& \equiv 27^{2n+1}-27^{2n+1}\\
& \equiv 0 \pmod{91}\\
\end{align}
{\displaystyle {\begin{aligned}3^{6n+3}+4^{6n+3}&\equiv (3^{3})^{2n+1}+(4^{3})^{2n+1}\\&\equiv 27^{2n+1}+64^{2n+1}\\&\equiv 27^{2n+1}+(-27)^{2n+1}\\&\equiv 27^{2n+1}-27^{2n+1}\\&\equiv 0{\pmod {91}}\\\end{aligned}}}
\begin{alignat}{3}
f(x) & = (m-n)^2 \\
f(x) & = (-m+n)^2 \\
& = m^2-2mn+n^2 \\
\end{alignat}

{\displaystyle {\begin{alignedat}{3}f(x)&=(m-n)^{2}\\f(x)&=(-m+n)^{2}\\&=m^{2}-2mn+n^{2}\\\end{alignedat}}}

\begin{array}{lcl}
z        & = & a \\
f(x,y,z) & = & x + y + z
\end{array}
${\displaystyle {\begin{array}{lcl}z&=&a\\f(x,y,z)&=&x+y+z\end{array}}}$

\begin{array}{lcr}
z        & = & a \\
f(x,y,z) & = & x + y + z
\end{array}
${\displaystyle {\begin{array}{lcr}z&=&a\\f(x,y,z)&=&x+y+z\end{array}}}$


<math>f(x) \,\!</math>
<math>= \sum_{n=0}^\infty a_n x^n </math>
<math>= a_0+a_1x+a_2x^2+\cdots</math>



${\displaystyle f(x)\,\!}$${\displaystyle =\sum _{n=0}^{\infty }a_{n}x^{n}}$${\displaystyle =a_{0}+a_{1}x+a_{2}x^{2}+\cdots }$

\begin{cases}
3x + 5y +  z \\
7x - 2y + 4z \\
-6x + 3y + 2z
\end{cases}
${\displaystyle {\begin{cases}3x+5y+z\\7x-2y+4z\\-6x+3y+2z\end{cases}}}$

\begin{array}{|c|c||c|} a & b & S \\
\hline
0&0&1\\
0&1&1\\
1&0&1\\
1&1&0\\
\end{array}

${\displaystyle {\begin{array}{|c|c||c|}a&b&S\\\hline 0&0&1\\0&1&1\\1&0&1\\1&1&0\\\end{array}}}$

## 字体

\Alpha \Beta \Gamma \Delta \Epsilon \Zeta \Eta \Theta ${\displaystyle \mathrm {A} \mathrm {B} \Gamma \Delta \mathrm {E} \mathrm {Z} \mathrm {H} \Theta }$
\Iota \Kappa \Lambda \Mu \Nu \Xi \Omicron \Pi ${\displaystyle \mathrm {I} \mathrm {K} \Lambda \mathrm {M} \mathrm {N} \Xi \mathrm {O} \Pi }$
\Rho \Sigma \Tau \Upsilon \Phi \Chi \Psi \Omega ${\displaystyle \mathrm {P} \Sigma \mathrm {T} \Upsilon \Phi \mathrm {X} \Psi \Omega }$
\alpha \beta \gamma \delta \epsilon \zeta \eta \theta ${\displaystyle \alpha \beta \gamma \delta \epsilon \zeta \eta \theta }$
\iota \kappa \lambda \mu \nu \xi \omicron \pi ${\displaystyle \iota \kappa \lambda \mu \nu \xi \mathrm {o} \pi }$
\rho \sigma \tau \upsilon \phi \chi \psi \omega ${\displaystyle \rho \sigma \tau \upsilon \phi \chi \psi \omega }$
\varepsilon \digamma \varkappa \varpi ${\displaystyle \varepsilon \digamma \varkappa \varpi }$
\varrho \varsigma \vartheta \varphi ${\displaystyle \varrho \varsigma \vartheta \varphi }$

\aleph \beth \gimel \daleth ${\displaystyle \aleph \beth \gimel \daleth }$

\mathbb{ABCDEFGHI} ${\displaystyle \mathbb {ABCDEFGHI} }$
\mathbb{JKLMNOPQR} ${\displaystyle \mathbb {JKLMNOPQR} }$
\mathbb{STUVWXYZ} ${\displaystyle \mathbb {STUVWXYZ} }$

\mathbf{ABCDEFGHI} ${\displaystyle \mathbf {ABCDEFGHI} }$
\mathbf{JKLMNOPQR} ${\displaystyle \mathbf {JKLMNOPQR} }$
\mathbf{STUVWXYZ} ${\displaystyle \mathbf {STUVWXYZ} }$
\mathbf{abcdefghijklm} ${\displaystyle \mathbf {abcdefghijklm} }$
\mathbf{nopqrstuvwxyz} ${\displaystyle \mathbf {nopqrstuvwxyz} }$
\mathbf{0123456789} ${\displaystyle \mathbf {0123456789} }$

\boldsymbol{\Alpha\Beta\Gamma\Delta\Epsilon\Zeta\Eta\Theta} ${\displaystyle {\boldsymbol {\mathrm {A} \mathrm {B} \Gamma \Delta \mathrm {E} \mathrm {Z} \mathrm {H} \Theta }}}$
\boldsymbol{\Iota\Kappa\Lambda\Mu\Nu\Xi\Pi\Rho} ${\displaystyle {\boldsymbol {\mathrm {I} \mathrm {K} \Lambda \mathrm {M} \mathrm {N} \Xi \Pi \mathrm {P} }}}$
\boldsymbol{\Sigma\Tau\Upsilon\Phi\Chi\Psi\Omega} ${\displaystyle {\boldsymbol {\Sigma \mathrm {T} \Upsilon \Phi \mathrm {X} \Psi \Omega }}}$
\boldsymbol{\alpha\beta\gamma\delta\epsilon\zeta\eta\theta} ${\displaystyle {\boldsymbol {\alpha \beta \gamma \delta \epsilon \zeta \eta \theta }}}$
\boldsymbol{\iota\kappa\lambda\mu\nu\xi\pi\rho} ${\displaystyle {\boldsymbol {\iota \kappa \lambda \mu \nu \xi \pi \rho }}}$
\boldsymbol{\sigma\tau\upsilon\phi\chi\psi\omega} ${\displaystyle {\boldsymbol {\sigma \tau \upsilon \phi \chi \psi \omega }}}$
\boldsymbol{\varepsilon\digamma\varkappa\varpi} ${\displaystyle {\boldsymbol {\varepsilon \digamma \varkappa \varpi }}}$
\boldsymbol{\varrho\varsigma\vartheta\varphi} ${\displaystyle {\boldsymbol {\varrho \varsigma \vartheta \varphi }}}$

\mathit{0123456789} ${\displaystyle {\mathit {0123456789}}}$

\mathit{\Alpha\Beta\Gamma\Delta\Epsilon\Zeta\Eta\Theta} ${\displaystyle {\mathit {\mathrm {A} \mathrm {B} \Gamma \Delta \mathrm {E} \mathrm {Z} \mathrm {H} \Theta }}}$
\mathit{\Iota\Kappa\Lambda\Mu\Nu\Xi\Pi\Rho} ${\displaystyle {\mathit {\mathrm {I} \mathrm {K} \Lambda \mathrm {M} \mathrm {N} \Xi \Pi \mathrm {P} }}}$
\mathit{\Sigma\Tau\Upsilon\Phi\Chi\Psi\Omega} ${\displaystyle {\mathit {\Sigma \mathrm {T} \Upsilon \Phi \mathrm {X} \Psi \Omega }}}$

\mathrm{ABCDEFGHI} ${\displaystyle \mathrm {ABCDEFGHI} }$
\mathrm{JKLMNOPQR} ${\displaystyle \mathrm {JKLMNOPQR} }$
\mathrm{STUVWXYZ} ${\displaystyle \mathrm {STUVWXYZ} }$
\mathrm{abcdefghijklm} ${\displaystyle \mathrm {abcdefghijklm} }$
\mathrm{nopqrstuvwxyz} ${\displaystyle \mathrm {nopqrstuvwxyz} }$
\mathrm{0123456789} ${\displaystyle \mathrm {0123456789} }$

\mathsf{ABCDEFGHI} ${\displaystyle {\mathsf {ABCDEFGHI}}}$
\mathsf{JKLMNOPQR} ${\displaystyle {\mathsf {JKLMNOPQR}}}$
\mathsf{STUVWXYZ} ${\displaystyle {\mathsf {STUVWXYZ}}}$
\mathsf{abcdefghijklm} ${\displaystyle {\mathsf {abcdefghijklm}}}$
\mathsf{nopqrstuvwxyz} ${\displaystyle {\mathsf {nopqrstuvwxyz}}}$
\mathsf{0123456789} ${\displaystyle {\mathsf {0123456789}}}$

\mathsf{\Alpha \Beta \Gamma \Delta \Epsilon \Zeta \Eta \Theta} ${\displaystyle {\mathsf {\mathrm {A} \mathrm {B} \Gamma \Delta \mathrm {E} \mathrm {Z} \mathrm {H} \Theta }}}$
\mathsf{\Iota \Kappa \Lambda \Mu \Nu \Xi \Pi \Rho} ${\displaystyle {\mathsf {\mathrm {I} \mathrm {K} \Lambda \mathrm {M} \mathrm {N} \Xi \Pi \mathrm {P} }}}$
\mathsf{\Sigma \Tau \Upsilon \Phi \Chi \Psi \Omega} ${\displaystyle {\mathsf {\Sigma \mathrm {T} \Upsilon \Phi \mathrm {X} \Psi \Omega }}}$

\mathcal{ABCDEFGHI} ${\displaystyle {\mathcal {ABCDEFGHI}}}$
\mathcal{JKLMNOPQR} ${\displaystyle {\mathcal {JKLMNOPQR}}}$
\mathcal{STUVWXYZ} ${\displaystyle {\mathcal {STUVWXYZ}}}$
Fraktur体
\mathfrak{ABCDEFGHI} ${\displaystyle {\mathfrak {ABCDEFGHI}}}$
\mathfrak{JKLMNOPQR} ${\displaystyle {\mathfrak {JKLMNOPQR}}}$
\mathfrak{STUVWXYZ} ${\displaystyle {\mathfrak {STUVWXYZ}}}$
\mathfrak{abcdefghijklm} ${\displaystyle {\mathfrak {abcdefghijklm}}}$
\mathfrak{nopqrstuvwxyz} ${\displaystyle {\mathfrak {nopqrstuvwxyz}}}$
\mathfrak{0123456789} ${\displaystyle {\mathfrak {0123456789}}}$

{\scriptstyle\text{abcdefghijklm}} ${\displaystyle {\scriptstyle {\text{abcdefghijklm}}}}$

## 括号

\left \Uparrow \frac{a}{b} \right \Downarrow ${\displaystyle \left\Uparrow {\frac {a}{b}}\right\Downarrow }$
\left \updownarrow \frac{a}{b} \right \Updownarrow ${\displaystyle \left\updownarrow {\frac {a}{b}}\right\Updownarrow }$

\left \langle \psi \right |
${\displaystyle \left[0,1\right)}$
${\displaystyle \left\langle \psi \right|}$

• 可以使用 \big, \Big, \bigg, \Bigg 控制括号的大小，比如代码
\Bigg ( \bigg [ \Big \{ \big \langle \left | \| \frac{a}{b} \| \right | \big \rangle \Big \} \bigg ] \Bigg )

显示︰

${\displaystyle {\Bigg (}{\bigg [}{\Big \{}{\big \langle }\left|\|{\frac {a}{b}}\|\right|{\big \rangle }{\Big \}}{\bigg ]}{\Bigg )}}$

## 空格

2个quad空格 \alpha\qquad\beta ${\displaystyle \alpha \qquad \beta }$ ${\displaystyle 2m\ }$
quad空格 \alpha\quad\beta ${\displaystyle \alpha \quad \beta }$ ${\displaystyle m\ }$

## 顏色

• 字體顏色︰{\color{色調}表達式}
• 背景顏色︰{\pagecolor{色調}表達式}[c]

 ${\displaystyle \color {Apricot}{\text{Apricot}}}$ ${\displaystyle \color {Aquamarine}{\text{Aquamarine}}}$ ${\displaystyle \color {Bittersweet}{\text{Bittersweet}}}$ ${\displaystyle \color {Black}{\text{Black}}}$ ${\displaystyle \color {Blue}{\text{Blue}}}$ ${\displaystyle \color {BlueGreen}{\text{BlueGreen}}}$ ${\displaystyle \color {BlueViolet}{\text{BlueViolet}}}$ ${\displaystyle \color {BrickRed}{\text{BrickRed}}}$ ${\displaystyle \color {Brown}{\text{Brown}}}$ ${\displaystyle \color {BurntOrange}{\text{BurntOrange}}}$ ${\displaystyle \color {CadetBlue}{\text{CadetBlue}}}$ ${\displaystyle \color {CarnationPink}{\text{CarnationPink}}}$ ${\displaystyle \color {Cerulean}{\text{Cerulean}}}$ ${\displaystyle \color {CornflowerBlue}{\text{CornflowerBlue}}}$ ${\displaystyle \color {Cyan}{\text{Cyan}}}$ ${\displaystyle \color {Dandelion}{\text{Dandelion}}}$ ${\displaystyle \color {DarkOrchid}{\text{DarkOrchid}}}$ ${\displaystyle \color {Emerald}{\text{Emerald}}}$ ${\displaystyle \color {ForestGreen}{\text{ForestGreen}}}$ ${\displaystyle \color {Fuchsia}{\text{Fuchsia}}}$ ${\displaystyle \color {Goldenrod}{\text{Goldenrod}}}$ ${\displaystyle \color {Gray}{\text{Gray}}}$ ${\displaystyle \color {Green}{\text{Green}}}$ ${\displaystyle \color {GreenYellow}{\text{GreenYellow}}}$ ${\displaystyle \color {JungleGreen}{\text{JungleGreen}}}$ ${\displaystyle \color {Lavender}{\text{Lavender}}}$ ${\displaystyle \color {LimeGreen}{\text{LimeGreen}}}$ ${\displaystyle \color {Magenta}{\text{Magenta}}}$ ${\displaystyle \color {Mahogany}{\text{Mahogany}}}$ ${\displaystyle \color {Maroon}{\text{Maroon}}}$ ${\displaystyle \color {Melon}{\text{Melon}}}$ ${\displaystyle \color {MidnightBlue}{\text{MidnightBlue}}}$ ${\displaystyle \color {Mulberry}{\text{Mulberry}}}$ ${\displaystyle \color {NavyBlue}{\text{NavyBlue}}}$ ${\displaystyle \color {OliveGreen}{\text{OliveGreen}}}$ ${\displaystyle \color {Orange}{\text{Orange}}}$ ${\displaystyle \color {OrangeRed}{\text{OrangeRed}}}$ ${\displaystyle \color {Orchid}{\text{Orchid}}}$ ${\displaystyle \color {Peach}{\text{Peach}}}$ ${\displaystyle \color {Periwinkle}{\text{Periwinkle}}}$ ${\displaystyle \color {PineGreen}{\text{PineGreen}}}$ ${\displaystyle \color {Plum}{\text{Plum}}}$ ${\displaystyle \color {ProcessBlue}{\text{ProcessBlue}}}$ ${\displaystyle \color {Purple}{\text{Purple}}}$ ${\displaystyle \color {RawSienna}{\text{RawSienna}}}$ ${\displaystyle \color {Red}{\text{Red}}}$ ${\displaystyle \color {RedOrange}{\text{RedOrange}}}$ ${\displaystyle \color {RedViolet}{\text{RedViolet}}}$ ${\displaystyle \color {Rhodamine}{\text{Rhodamine}}}$ ${\displaystyle \color {RoyalBlue}{\text{RoyalBlue}}}$ ${\displaystyle \color {RoyalPurple}{\text{RoyalPurple}}}$ ${\displaystyle \color {RubineRed}{\text{RubineRed}}}$ ${\displaystyle \color {Salmon}{\text{Salmon}}}$ ${\displaystyle \color {SeaGreen}{\text{SeaGreen}}}$ ${\displaystyle \color {Sepia}{\text{Sepia}}}$ ${\displaystyle \color {SkyBlue}{\text{SkyBlue}}}$ ${\displaystyle \color {SpringGreen}{\text{SpringGreen}}}$ ${\displaystyle \color {Tan}{\text{Tan}}}$ ${\displaystyle \color {TealBlue}{\text{TealBlue}}}$ ${\displaystyle \color {Thistle}{\text{Thistle}}}$ ${\displaystyle \color {Turquoise}{\text{Turquoise}}}$ ${\displaystyle \color {Violet}{\text{Violet}}}$ ${\displaystyle \color {VioletRed}{\text{VioletRed}}}$ ${\displaystyle \color {White}{\text{White}}}$ ${\displaystyle \color {WildStrawberry}{\text{WildStrawberry}}}$ ${\displaystyle \color {Yellow}{\text{Yellow}}}$ ${\displaystyle \color {YellowGreen}{\text{YellowGreen}}}$ ${\displaystyle \color {YellowOrange}{\text{YellowOrange}}}$

• {\color{Blue}x^2}+{\color{Brown}2x} - {\color{OliveGreen}1}
${\displaystyle {\color {Blue}x^{2}}+{\color {Brown}2x}-{\color {OliveGreen}1}}$
• x_{\color{Maroon}1,2}=\frac{-b\pm\sqrt{{\color{Maroon}b^2-4ac}}}{2a}
${\displaystyle x_{\color {Maroon}1,2}={\frac {-b\pm {\sqrt {\color {Maroon}b^{2}-4ac}}}{2a}}}$

## 小型數學公式

10 的 ${\displaystyle f(x)=5+{\frac {1}{5}}}$ 是 2。
• 並不好看。
10 的 ${\displaystyle {\begin{smallmatrix}f(x)=5+{\frac {1}{5}}\end{smallmatrix}}}$ 是 2。
• 好看些了。

   \begin{smallmatrix}...\end{smallmatrix}


   {{Smallmath|f=  f(x)=5+\frac{1}{5} }}


## 注释

1. ^ 虽然在所有情况下，TeX是由编译器而不是解释器生成，在高德纳TeX兰波特LaTeX及现有的实现之间存在着一个基本的区别：前两种情况下编译器产生“一体化”的可打印的输出成果，有着拥有全部章节的书籍的品质，没有一行是“特殊的”，现有的实现通常有着用于公式的TeX图像（更准确的说：PNG图像）的混合，嵌入一般的文本中，并含有简短的TeX元素常常被HTML部分取代。作为结果，多数情况下的TeX元素，如向量符号、伸出文本行的下方（或上方）的部分。这个“伸出”的部分不是上文中所提到情况下的原始产物，而且用于小号TeX附件到文本的HTML替代对于许多读者来说常常在质量上是不够充分的。虽然存在这些缺陷，以“最多嵌入的PNG图像”为特性的当前产物应该推荐使用于小号文本，在那里公式不是最主要的。
2. ^ 这个会造成的设置垂直对齐时的基线时的一些困难也会成为问题（参阅bug 32694
3. ^ 该命令已失效，参见Phabricator