LaTeX数学公式大全
本文参考:
希腊字母
\Alpha | \Beta | \Gamma | \Delta |
\Epsilon | \Zeta | \Eta | \Theta |
\Iota | \Kappa | \Lambda | \Mu |
\Nu | \Xi | \Omicron | \Pi |
\Rho | \Sigma | \Tau | \Upsilon |
\Phi | \Chi | \Psi | \Omega |
\varGamma | \varDelta | \varTheta | \varLambda |
\varXi | \varPi | \varSigma | \varUpsilon |
\varPhi | \varPsi | \varOmega | |
\alpha | \beta | \gamma | \delta |
\epsilon | \zeta | \eta | \theta |
\iota | \kappa | \lambda | \mu |
\nu | \xi | \omicron | \pi |
\rho | \sigma | \tau | \upsilon |
\phi | \chi | \psi | \omega |
\varepsilon | \varkappa | \vartheta | \thetasym |
\varpi | \varrho | \varsigma | \varphi |
\digamma |
其他字符
\imath | \nabla | \Im | \Reals | \text{\OE} |
\jmath | \partial | \image | \wp | \text{\o} |
\aleph | \Game | \Bbbk | \weierp | \text{\O} |
\alef | \Finv | \N | \Z | \text{\ss} |
\alefsym | \cnums | \natnums | \text{\aa} | \text{\i} |
\beth | \Complex | \R | \text{\AA} | \text{\j} |
\gimel | \ell | \Re | \text{\ae} | |
\daleth | \hbar | \real | \text{\AE} | |
\eth | \hslash | \reals | \text{\oe} |
运算符
\sum | \prod | \bigotimes | \bigvee |
\int | \coprod | \bigoplus | \bigwedge |
\iint | \intop | \bigodot | \bigcap |
\iiint | \smallint | \biguplus | \bigcup |
\oint | \oiint | \oiiint | \bigsqcup |
\frac{a}{b} | \tfrac{a}{b} | \genfrac ( ] {2pt}{1}a{a+1} |
{a \over b} | \dfrac{a}{b} | {a \above{2pt} b+1} |
a/b | \cfrac{a}{1 + \cfrac{1}{b}} |
\binom{n}{k} | \dbinom{n}{k} | {n\brace k} |
{n \choose k} | \tbinom{n}{k} | {n\brack k} |
\arcsin | \cosec | \deg | \sec |
\arccos | \cosh | \dim | \sin |
\arctan | \cot | \exp | \sinh |
\arctg | \cotg | \hom | \sh |
\arcctg | \coth | \ker | \tan |
\arg | \csc | \lg | \tanh |
\ch | \ctg | \ln | \tg |
\cos | \cth | \log | \th |
\operatorname{f} | |||
\argmax | \injlim | \min | \varinjlim |
\argmin | \lim | \plim | \varliminf |
\det | \liminf | \Pr | \varlimsup |
\gcd | \limsup | \projlim | \varprojlim |
\inf | \max | \sup | |
\operatorname*{f} | \operatornamewithlimits{f} |
+ | \cdot | \gtrdot | x \pmod a |
- | \cdotp | \intercal | x \pod a |
/ | \centerdot | \land | \rhd |
* | \circ | \leftthreetimes | \rightthreetimes |
\amalg | \circledast | \ldotp | \rtimes |
\And | \circledcirc | \lor | \setminus |
\ast | \circleddash | \lessdot | \smallsetminus |
\barwedge | \Cup | \lhd | \sqcap |
\bigcirc | \cup | \ltimes | \sqcup |
\bmod | \curlyvee | x\mod a | \times |
\boxdot | \curlywedge | \mp | \unlhd |
\boxminus | \div | \odot | \unrhd |
\boxplus | \divideontimes | \ominus | \uplus |
\boxtimes | \dotplus | \oplus | \vee |
\bullet | \doublebarwedge | \otimes | \veebar |
\Cap | \doublecap | \oslash | \wedge |
\cap | \doublecup | \pm or \plusmn | \wr |
a' | \tilde{a} | \mathring{g} |
a'' | \widetilde{ac} | \overgroup{AB} |
a^{\prime} | \utilde{AB} | \undergroup{AB} |
\acute{a} | \vec{F} | \Overrightarrow{AB} |
\bar{y} | \overleftarrow{AB} | \overrightarrow{AB} |
\breve{a} | \underleftarrow{AB} | \underrightarrow{AB} |
\check{a} | \overleftharpoon{ac} | \overrightharpoon{ac} |
\dot{a} | \overleftrightarrow{AB} | \overbrace{AB} |
\ddot{a} | \underleftrightarrow{AB} | \underbrace{AB} |
\grave{a} | \overline{AB} | \overlinesegment{AB} |
\hat{\theta} | \underline{AB} | \underlinesegment{AB} |
\widehat{ac} | \widecheck{ac} | \underbar{X} |
\'{a} | \~{a} | \.{a} | \H{a} |
\`{a} | \={a} | \"{a} | \v{a} |
\^{a} | \u{a} | \r{a} |
\Alpha | \Beta | \Gamma | \Delta |
\Epsilon | \Zeta | \Eta | \Theta |
\Iota | \Kappa | \Lambda | \Mu |
\Nu | \Xi | \Omicron | \Pi |
\Rho | \Sigma | \Tau | \Upsilon |
\Phi | \Chi | \Psi | \Omega |
\varGamma | \varDelta | \varTheta | \varLambda |
\varXi | \varPi | \varSigma | \varUpsilon |
\varPhi | \varPsi | \varOmega | |
\alpha | \beta | \gamma | \delta |
\epsilon | \zeta | \eta | \theta |
\iota | \kappa | \lambda | \mu |
\nu | \xi | \omicron | \pi |
\rho | \sigma | \tau | \upsilon |
\phi | \chi | \psi | \omega |
\varepsilon | \varkappa | \vartheta | \thetasym |
\varpi | \varrho | \varsigma | \varphi |
\digamma |
\imath | \nabla | \Im | \Reals | \text{\OE} |
\jmath | \partial | \image | \wp | \text{\o} |
\aleph | \Game | \Bbbk | \weierp | \text{\O} |
\alef | \Finv | \N | \Z | \text{\ss} |
\alefsym | \cnums | \natnums | \text{\aa} | \text{\i} |
\beth | \Complex | \R | \text{\AA} | \text{\j} |
\gimel | \ell | \Re | \text{\ae} | |
\daleth | \hbar | \real | \text{\AE} | |
\eth | \hslash | \reals | \text{\oe} |
Annotation
\cancel{5} | \overbrace{a+b+c}^{\text{note}} |
\bcancel{5} | \underbrace{a+b+c}_{\text{note}} |
\xcancel{ABC} | \not = |
\sout{abc} | \boxed{\pi=\frac c d} |
$a_{\angl n} | a_\angln |
\phase{-78^\circ} |
\forall | \complement | \therefore | \emptyset |
\exists | \subset | \because | \empty |
\exist | \supset | \mapsto | \varnothing |
\nexists | \mid | \to | \implies |
\in | \land | \gets | \impliedby |
\isin | \lor | \leftrightarrow | \iff |
\notin | \ni | \notni | \neg or \lnot |
关系
= | \doteqdot | \lessapprox | \smile |
< | \eqcirc | \lesseqgtr | \sqsubset |
> | \eqcolon or \minuscolon | \lesseqqgtr | \sqsubseteq |
: | \Eqcolon or \minuscoloncolon | \lessgtr | \sqsupset |
\approx | \eqqcolon or \equalscolon | \lesssim | \sqsupseteq |
\approxcolon | \Eqqcolon or \equalscoloncolon | \ll | \Subset |
\approxcoloncolon | \eqsim | \lll | \subset or \sub |
\approxeq | \eqslantgtr | \llless | \subseteq or \sube |
\asymp | \eqslantless | \lt | \subseteqq |
\backepsilon | \equiv | \mid | \succ |
\backsim | \fallingdotseq | \models | \succapprox |
\backsimeq | \frown | \multimap | \succcurlyeq |
\between | \ge | \origof | \succeq |
\bowtie | \geq | \owns | \succsim |
\bumpeq | \geqq | \parallel | \Supset |
\Bumpeq | \geqslant | \perp | \supset |
\circeq | \gg | \pitchfork | \supseteq or \supe |
\colonapprox | \ggg | \prec | \supseteqq |
\Colonapprox or \coloncolonapprox | \gggtr | \precapprox | \thickapprox |
\coloneq or \colonminus | \gt | \preccurlyeq | \thicksim |
\Coloneq or \coloncolonminus | \gtrapprox | \preceq | \trianglelefteq |
\coloneqq or \colonequals | \gtreqless | \precsim | \triangleq |
\Coloneqq or \coloncolonequals | \gtreqqless | \propto | \trianglerighteq |
\colonsim | \gtrless | \risingdotseq | \varpropto |
\Colonsim or \coloncolonsim | \gtrsim | \shortmid | \vartriangle |
\cong | \imageof | \shortparallel | \vartriangleleft |
\curlyeqprec | \in or \isin | \sim | \vartriangleright |
\curlyeqsucc | \Join | \simcolon | \vcentcolon or \ratio |
\dashv | \le | \simcoloncolon | \vdash |
\dblcolon or \coloncolon | \leq | \simeq | \vDash |
\doteq | \leqq | \smallfrown | \Vdash |
\Doteq | \leqslant | \smallsmile | \Vvdash |
\gnapprox | \ngeqslant | \nsubseteq | \precneqq |
\gneq | \ngtr | \nsubseteqq | \precnsim |
\gneqq | \nleq | \nsucc | \subsetneq |
\gnsim | \nleqq | \nsucceq | \subsetneqq |
\gvertneqq | \nleqslant | \nsupseteq | \succnapprox |
\lnapprox | \nless | \nsupseteqq | \succneqq |
\lneq | \nmid | \ntriangleleft | \succnsim |
\lneqq | \notin | \ntrianglelefteq | \supsetneq |
\lnsim | \notni | \ntriangleright | \supsetneqq |
\lvertneqq | \nparallel | \ntrianglerighteq | \varsubsetneq |
\ncong | \nprec | \nvdash | \varsubsetneqq |
\ne | \npreceq | \nvDash | \varsupsetneq |
\neq | \nshortmid | \nVDash | \varsupsetneqq |
\ngeq | \nshortparallel | \nVdash | |
\ngeqq | \nsim | \precnapprox |
箭头
\circlearrowleft | \leftharpoonup | \rArr |
\circlearrowright | \leftleftarrows | \rarr |
\curvearrowleft | \leftrightarrow | \restriction |
\curvearrowright | \Leftrightarrow | \rightarrow |
\Darr | \leftrightarrows | \Rightarrow |
\dArr | \leftrightharpoons | \rightarrowtail |
\darr | \leftrightsquigarrow | \rightharpoondown |
\dashleftarrow | \Lleftarrow | \rightharpoonup |
\dashrightarrow | \longleftarrow | \rightleftarrows |
\downarrow | \Longleftarrow | \rightleftharpoons |
\Downarrow | \longleftrightarrow | \rightrightarrows |
\downdownarrows | \Longleftrightarrow | \rightsquigarrow |
\downharpoonleft | \longmapsto | \Rrightarrow |
\downharpoonright | \longrightarrow | \Rsh |
\gets | \Longrightarrow | \searrow |
\Harr | \looparrowleft | \swarrow |
\hArr | \looparrowright | \to |
\harr | \Lrarr | \twoheadleftarrow |
\hookleftarrow | \lrArr | \twoheadrightarrow |
\hookrightarrow | \lrarr | \Uarr |
\iff | \Lsh | \uArr |
\impliedby | \mapsto | \uarr |
\implies | \nearrow | \uparrow |
\Larr | \nleftarrow | \Uparrow |
\lArr | \nLeftarrow | \updownarrow |
\larr | \nleftrightarrow | \Updownarrow |
\leadsto | \nLeftrightarrow | \upharpoonleft |
\leftarrow | \nrightarrow | \upharpoonright |
\Leftarrow | \nRightarrow | \upuparrows |
\leftarrowtail | \nwarrow | |
\leftharpoondown | \Rarr |
\xleftarrow{abc} | \xrightarrow[under]{over} |
\xLeftarrow{abc} | \xRightarrow{abc} |
\xleftrightarrow{abc} | \xLeftrightarrow{abc} |
\xhookleftarrow{abc} | \xhookrightarrow{abc} |
\xtwoheadleftarrow{abc} | \xtwoheadrightarrow{abc} |
\xleftharpoonup{abc} | \xrightharpoonup{abc} |
\xleftharpoondown{abc} | \xrightharpoondown{abc} |
\xleftrightharpoons{abc} | \xrightleftharpoons{abc} |
\xtofrom{abc} | \xmapsto{abc} |
\xlongequal{abc} |
符号和标点符号
% comment | \dots | \KaTeX |
\% | \cdots | \LaTeX |
\# | \ddots | \TeX |
\& | \ldots | \nabla |
\_ | \vdots | \infty |
\text{\textunderscore} | \dotsb | \infin |
\text{--} | \dotsc | \checkmark |
\text{\textendash} | \dotsi | \dag |
\text{---} | \dotsm | \dagger |
\text{\textemdash} | \dotso | \text{\textdagger} |
\text{\textasciitilde} | \sdot | \ddag |
\text{\textasciicircum} | \mathellipsis | \ddagger |
` | \text{\textellipsis} | \text{\textdaggerdbl} |
text{\textquoteleft} | \Box | \Dagger |
\lq | \square | \angle |
\text{\textquoteright} | \blacksquare | \measuredangle |
\rq | \triangle | \sphericalangle |
\text{\textquotedblleft} | \triangledown | \top |
" | \triangleleft | \bot |
\text{\textquotedblright} | \triangleright | \$ |
\colon | \bigtriangledown | \text{\textdollar} |
\backprime | \bigtriangleup | \pounds |
\prime | \blacktriangle | \mathsterling |
\text{\textless} | \blacktriangledown | \text{\textsterling} |
\text{\textgreater} | \blacktriangleleft | \yen |
\text{\textbar} | \blacktriangleright | \surd |
\text{\textbardbl} | \diamond | \degree |
\text{\textbraceleft} | \Diamond | \text{\textdegree} |
\text{\textbraceright} | \lozenge | \mho |
\text{\textbackslash} | \blacklozenge | \diagdown |
\text{\P} or \P | \star | \diagup |
\text{\S} or \S | \bigstar | \flat |
\text{\sect} | \clubsuit | \natural |
\copyright | \clubs | \sharp |
\circledR | \diamondsuit | \heartsuit |
\text{\textregistered} | \diamonds | \hearts |
\circledS | \spadesuit | \spades |
\text{\textcircled a} | \maltese | \minuso |
字体
LaTeX代码 | 效果 | LaTeX代码 | 效果 |
---|---|---|---|
\mathbb{A-Z} | \mathit{A-Z,a-z,0-9} | ||
\mathbf{A-Z,a-z,0-9} | \pmb{A-Z,a-z,0-9 | ||
\mathtt{A-Z,a-z,0-9} | \mathrm{A-Z,a-z,0-9} | ||
\mathsf{A-Z,a-z,0-9} | \mathcal{A-Z,a-z,0-9} | ||
\mathscr{A-Z,a-z} | \mathfrak{A-Z,a-z,0-9} |
上下标
a^b
a_c
a^b_c
a^{12}_{21}
分式和根式
3/8
\frac{3}{8}
\tfrac{3}{8}
\sqrt{x} \Leftrightarrow x^{1/2}
\sqrt[3]{2}
\sqrt{x^{2} + \sqrt{y}}
求和
\sum_{i=1}^n x_i
连乘
\prod_{i=0}^{n}x_i
极限
如果是行间公式,则如下:
\lim_{x \to \infty} f(x)
如果是行内公式,则如下:
\lim\limits_{x \to \infty} f(x)
其他案例:
e^x=\lim_{n\to\infty} \left( 1+\frac{x}{n} \right)^n
导数
\frac{\mathrm{d} y }{\mathrm{d} x}
\frac{\mathrm{d}^{n} y }{\mathrm{d} x^{n}}
\frac{\mathrm{d} }{\mathrm{d} x} y^2
\frac{ y^{'} }{ x^{'} }
偏导数
\frac{\partial f}{\partial x}
\frac{\partial ^{n} f}{\partial x^{n}}
积分
\int_a^b f(x)\mathrm{d}x
\int\int f(x)g(y) \mathrm{d}x\mathrm{d}y
\oint_0^{\frac{\pi}{2}}2\theta\mathrm{d}\theta
括号
LaTex表达式中的 ( ) 、 [ ] 均可以正常使用,但是对于 { } 需要使用转义字符使用,即使用 “{” 和 “}” 表示 { }
LaTeX代码 | 效果 |
---|---|
\left( \cdots \right) | |
\vert \cdots \vert | |
\Vert \cdots \Vert | |
\langle \cdots \rangle | |
\Biggl(\biggl(\Bigl(\bigl((\cdots)\bigr)\Bigr)\biggr)\Biggr) |
f\left(
\left[
\frac{
1+\left\{x,y\right\}
}{
\left(
\frac{x}{y}+\frac{y}{x}
\right)
\left(u+1\right)
}+a
\right]^{3/2}
\right)
对齐方程
\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}
f(x)&=\left(x^3\right)+\left(x^3+x^2+x^1\right)+\left(x^3+x^2\right)\\
f'(x)&=\left(3x^2+2x+1\right)+\left(3x^2+2x\right)\\
f''(x)&=\left(6x+2\right)\\
\end{align}
\begin{equation}
\begin{aligned}
f(x)&=\left(x^3\right)+\left(x^3+x^2+x^1\right)+\left(x^3+x^2\right)\\
f'(x)&=\left(3x^2+2x+1\right)+\left(3x^2+2x\right)\\
f''(x)&=\left(6x+2\right)\\
\end{aligned}
\end{equation}
矩阵
\begin{matrix}
a & b \\
c & d
\end{matrix}
\begin{pmatrix}
a & b \\
c & d
\end{pmatrix}
\begin{bmatrix}
a & b \\
c & d
\end{bmatrix}
\begin{vmatrix}
a & b \\
c & d
\end{vmatrix}
\begin{Vmatrix}
a & b \\
c & d
\end{Vmatrix}
\begin{Bmatrix}
a & b \\
c & d
\end{Bmatrix}
\begin{pmatrix}
1 & a_1 & a_1^2 & \cdots & a_1^n \\
1 & a_2 & a_2^2 & \cdots & a_2^n \\
\vdots & \vdots& \vdots & \ddots & \vdots \\
1 & a_m & a_m^2 & \cdots & a_m^n
\end{pmatrix}
分段函数
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)
f(n) =
\begin{cases}
\frac{n}{2}, & \text{if $n$ is even} \\[2ex]
3n+1, & \text{if $n$ is odd}
\end{cases}
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.
\begin{cases}
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{cases}
\left\{
\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.
\begin{cases}
a_1x+b_1y+c_1z=\frac{p_1}{q_1} \\[2ex]
a_2x+b_2y+c_2z=\frac{p_2}{q_2} \\[2ex]
a_3x+b_3y+c_3z=\frac{p_3}{q_3}
\end{cases}
\begin{cases}
a_1x+b_1y+c_1z=\frac{p_1}{q_1} \\
a_2x+b_2y+c_2z=\frac{p_2}{q_2} \\
a_3x+b_3y+c_3z=\frac{p_3}{q_3}
\end{cases}