Accents/Diacritics
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\acute{a} \grave{a} \hat{a} \tilde{a} \breve{a}
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\check{a} \bar{a} \ddot{a} \dot{a}
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Standard functions
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\sin a \cos b \tan c
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\sec d \csc e \cot f
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\arcsin h \arccos i \arctan j
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\sinh k \cosh l \tanh m \coth n\!
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\operatorname{sh}\,o\,\operatorname{ch}\,p\,\operatorname{th}\,q\!
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\operatorname{arsinh}\,r\,\operatorname{arcosh}\,s\,\operatorname{artanh}\,t
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\lim u \limsup v \liminf w \min x \max y\!
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\inf z \sup a \exp b \ln c \lg d \log e \log_{10} f \ker g\!
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\deg h \gcd i \Pr j \det k \hom l \arg m \dim n
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Modular arithmetic
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s_k \equiv 0 \pmod{m}
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a\,\bmod\,b
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Derivatives
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\nabla \, \partial x \, dx \, \dot x \, \ddot y\, dy/dx\, \frac{dy}{dx}\, \frac{\partial^2 y}{\partial x_1\,\partial x_2}
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Sets
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\forall \exists \empty \emptyset \varnothing
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\in \ni \not \in \notin \subset \subseteq \supset \supseteq
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\cap \bigcap \cup \bigcup \biguplus \setminus \smallsetminus
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\sqsubset \sqsubseteq \sqsupset \sqsupseteq \sqcap \sqcup \bigsqcup
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Operators
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+ \oplus \bigoplus \pm \mp -
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\times \otimes \bigotimes \cdot \circ \bullet \bigodot
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\star * / \div \frac{1}{2}
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Logic
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\land (or \and) \wedge \bigwedge \bar{q} \to p
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\lor \vee \bigvee \lnot \neg q \And
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Root
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\sqrt{2} \sqrt[n]{x}
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Relations
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\sim \approx \simeq \cong \dot= \overset{\underset{\mathrm{def}}{}}{=}
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\le < \ll \gg \ge > \equiv \not\equiv \ne \mbox{or} \neq \propto
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Geometric
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\Diamond \Box \triangle \angle \perp \mid \nmid \| 45^\circ
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Arrows
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\leftarrow (or \gets) \rightarrow (or \to) \nleftarrow \nrightarrow \leftrightarrow \nleftrightarrow \longleftarrow \longrightarrow \longleftrightarrow
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\Leftarrow \Rightarrow \nLeftarrow \nRightarrow \Leftrightarrow \nLeftrightarrow \Longleftarrow \Longrightarrow \Longleftrightarrow (or \iff)
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\uparrow \downarrow \updownarrow \Uparrow \Downarrow \Updownarrow \nearrow \searrow \swarrow \nwarrow
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\rightharpoonup \rightharpoondown \leftharpoonup \leftharpoondown \upharpoonleft \upharpoonright \downharpoonleft \downharpoonright \rightleftharpoons \leftrightharpoons
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\curvearrowleft \circlearrowleft \Lsh \upuparrows \rightrightarrows \rightleftarrows \Rrightarrow \rightarrowtail \looparrowright
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\curvearrowright \circlearrowright \Rsh \downdownarrows \leftleftarrows \leftrightarrows \Lleftarrow \leftarrowtail \looparrowleft
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\mapsto \longmapsto \hookrightarrow \hookleftarrow \multimap \leftrightsquigarrow \rightsquigarrow
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Special
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\And \eth \S \P \% \dagger \ddagger \ldots \cdots
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\smile \frown \wr \triangleleft \triangleright \infty \bot \top
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\vdash \vDash \Vdash \models \lVert \rVert \imath \hbar
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\ell \mho \Finv \Re \Im \wp \complement
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\diamondsuit \heartsuit \clubsuit \spadesuit \Game \flat \natural \sharp
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Unsorted (new stuff)
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\vartriangle \triangledown \lozenge \circledS \measuredangle \nexists \Bbbk \backprime \blacktriangle \blacktriangledown
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\blacksquare \blacklozenge \bigstar \sphericalangle \diagup \diagdown \dotplus \Cap \Cup \barwedge
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\veebar \doublebarwedge \boxminus \boxtimes \boxdot \boxplus \divideontimes \ltimes \rtimes \leftthreetimes
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\rightthreetimes \curlywedge \curlyvee \circleddash \circledast \circledcirc \centerdot \intercal \leqq \leqslant
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\eqslantless \lessapprox \approxeq \lessdot \lll \lessgtr \lesseqgtr \lesseqqgtr \doteqdot \risingdotseq
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\fallingdotseq \backsim \backsimeq \subseteqq \Subset \preccurlyeq \curlyeqprec \precsim \precapprox \vartriangleleft
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\Vvdash \bumpeq \Bumpeq \geqq \geqslant \eqslantgtr \gtrsim \gtrapprox \eqsim \gtrdot
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\ggg \gtrless \gtreqless \gtreqqless \eqcirc \circeq \triangleq \thicksim \thickapprox \supseteqq
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\Supset \succcurlyeq \curlyeqsucc \succsim \succapprox \vartriangleright \shortmid \shortparallel \between \pitchfork
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\varpropto \blacktriangleleft \therefore \backepsilon \blacktriangleright \because \nleqslant \nleqq \lneq \lneqq
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\lvertneqq \lnsim \lnapprox \nprec \npreceq \precneqq \precnsim \precnapprox \nsim \nshortmid
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\nvdash \nVdash \ntriangleleft \ntrianglelefteq \nsubseteq \nsubseteqq \varsubsetneq \subsetneqq \varsubsetneqq \ngtr
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\subsetneq
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\ngeqslant \ngeqq \gneq \gneqq \gvertneqq \gnsim \gnapprox \nsucc \nsucceq \succneqq
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\succnsim \succnapprox \ncong \nshortparallel \nparallel \nvDash \nVDash \ntriangleright \ntrianglerighteq \nsupseteq
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\nsupseteqq \varsupsetneq \supsetneqq \varsupsetneqq
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\jmath \surd \ast \uplus \diamond \bigtriangleup \bigtriangledown \ominus
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\oslash \odot \bigcirc \amalg \prec \succ \preceq \succeq
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\dashv \asymp \doteq \parallel
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\ulcorner \urcorner \llcorner \lrcorner
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Larger Expressions
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Subscripts, superscripts, integrals
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| Feature
| Syntax
| How it looks rendered
|
| PNG
|
| Superscript
| a^2
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| Subscript
| a_2
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| Grouping
| a^{2+2}
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a_{i,j}
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| Combining sub & super without and with horizontal separation
| x_2^3
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{x_2}^3
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| Super super
| 10^{10^{ \,\!{8} }
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| Super super
| 10^{10^{ \overset{8}{} }}
| 
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| Super super
| 10^{10^8}
| 
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| Preceding and/or Additional sub & super
| \sideset{_1^2}{_3^4}\prod_a^b
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{}_1^2\!\Omega_3^4
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| Stacking
| \overset{\alpha}{\omega}
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\underset{\alpha}{\omega}
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\overset{\alpha}{\underset{\gamma}{\omega}}
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\stackrel{\alpha}{\omega}
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| Derivative
| x', y'', f', f''\!
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| Derivative
| x', y'', f', f''
|
|
| Derivative (wrong in HTML)
| x^\prime, y^{\prime\prime}
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| Derivative (wrong in PNG)
| x\prime, y\prime\prime
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| Derivative dots
| \dot{x}, \ddot{x}
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| Underlines, overlines, vectors
| \hat a \ \bar b \ \vec c
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\overrightarrow{a b} \ \overleftarrow{c d} \ \\overleftrightarrow{a b} \ \widehat{d e f}
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\overline{g h i} \ \underline{j k l}
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| Arrows
| A \xleftarrow{n+\mu-1} B \xrightarrow[T]{n\pm i-1} C
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| Overbraces
| \overbrace{ 1+2+\cdots+100 }^{5050}
| 
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| Underbraces
| \underbrace{ a+b+\cdots+z }_{26}
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| Sum
| \sum_{k=1}^N k^2
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Sum (force \textstyle)
| \textstyle \sum_{k=1}^N k^2
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| Product
| \prod_{i=1}^N x_i
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Product (force \textstyle)
| \textstyle \prod_{i=1}^N x_i
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| Coproduct
| \coprod_{i=1}^N x_i
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Coproduct (force \textstyle)
| \textstyle \coprod_{i=1}^N x_i
| 
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| Limit
| \lim_{n \to \infty}x_n
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Limit (force \textstyle)
| \textstyle \lim_{n \to \infty}x_n
| 
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| Integral
| \int\limits_{1}^{3}\frac{e^3/x}{x^2}\, dx
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| Integral (alternate limits style)
| \int_{1}^{3}\frac{e^3/x}{x^2}\, dx
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Integral (force \textstyle)
| \textstyle \int\limits_{-N}^{N} e^x\, dx
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Integral (force \textstyle, alternate limits style)
| \textstyle \int_{-N}^{N} e^x\, dx
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| Double integral
| \iint\limits_D \, dx\,dy
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| Triple integral
| \iiint\limits_E \, dx\,dy\,dz
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| Quadruple integral
| \iiiint\limits_F \, dx\,dy\,dz\,dt
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| Line or path integral
| \int_C x^3\, dx + 4y^2\, dy
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| Closed line or path integral
| \oint_C x^3\, dx + 4y^2\, dy
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| Intersections
| \bigcap_1^n p
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| Unions
| \bigcup_1^k p
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| <h3>Fractions
|
| Fractions
| \frac{2}{4}=0.5
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| Small Fractions
| \tfrac{2}{4} = 0.5
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| Large (normal) Fractions
| \dfrac{2}{4} = 0.5 \qquad \dfrac{2}{c + \dfrac{2}{d + \dfrac{2}{4}}} = a
| 
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| Large (nested) Fractions
| \cfrac{2}{c + \cfrac{2}{d + \cfrac{2}{4}}} = a
| 
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| Binomial coefficients
| \binom{n}{k}
| 
|
| Small Binomial coefficients
| \tbinom{n}{k}
| 
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| Large (normal) Binomial coefficients
| \dbinom{n}{k}
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Matrices
|
\begin{matrix}
x & y \\
z & v
\end{matrix}
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\begin{vmatrix}
x & y \\
z & v
\end{vmatrix}
| 
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\begin{Vmatrix}
x & y \\
z & v
\end{Vmatrix}
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\begin{bmatrix}
0 & \cdots & 0 \\
\vdots & \ddots & \vdots \\
0 & \cdots & 0
\end{bmatrix}
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\begin{Bmatrix}
x & y \\
z & v
\end{Bmatrix}
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\begin{pmatrix}
x & y \\
z & v
\end{pmatrix}
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\bigl( \begin{smallmatrix}
a&b\\ c&d
\end{smallmatrix} \bigr)
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| Case distinctions
|
f(n) =
\begin{cases}
n/2, & \mbox{if }n\mbox{ is even} \\
3n+1, & \mbox{if }n\mbox{ is odd}
\end{cases}
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Multiline equations
|
| Example multiline equations
|
f(x) & = (a+b)^2 \\
& = a^2+2ab+b^2 \\
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|
|
|
\begin{array}{lcl}
z & = & a \\
f(x,y,z) & = & x + y + z
\end{array}
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|
|
|
\begin{array}{lcr}
z & = & a \\
f(x,y,z) & = & x + y + z
\end{array}
| 
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| Breaking up a long expression so that it wraps when necessary
|
<math>f(x) \,\!
= \sum_{n=0}^\infty a_n x^n\!
= a_0+a_1x+a_2x^2+\cdots</math>
|
  
|
| Simultaneous equations
| \begin{cases}
3x + 5y + z \\
7x - 2y + 4z \\
-6x + 3y + 2z
\end{cases}
| 
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| Arrays
|
\begin{array}{|c|c||c|} a & b & S \\
\hline
0&0&1\\
0&1&1\\
1&0&1\\
1&1&0\\
\end{array}
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Spacing
|
| Thick space
| \Delta\;x
| 
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| Medium space
| \Delta\:x
|
|
| Thin space
| \Delta\,x
| 
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| Negative thin space
| \Delta\!x
| 
|
Parenthesizing big expressions, brackets, bars
|
| Bad
| ( \frac{1}{2} )
| 
|
| Good
| \left ( \frac{1}{2} \right )
| 
You can use various delimiters with \left and \right.
|
| Parentheses
| \left ( \frac{a}{b} \right )
| 
|
| Brackets
| \left [ \frac{a}{b} \right ] \quad \left \lbrack \frac{a}{b} \right \rbrack
| 
|
| Braces
| \left \{ \frac{a}{b} \right \} \quad \left \lbrace \frac{a}{b} \right \rbrace
| 
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| Angle brackets
| \left \langle \frac{a}{b} \right \rangle
| 
|
| Bars and double bars
| \left | \frac{a}{b} \right \vert \left \Vert \frac{c}{d} \right \|
| 
|
| Floor and ceiling functions:
| \left \lfloor \frac{a}{b} \right \rfloor \left \lceil \frac{c}{d} \right \rceil
| 
|
| Slashes and backslashes
| \left / \frac{a}{b} \right \backslash
| 
|
| Up, down and up-down arrows
| \left \uparrow \frac{a}{b} \right \downarrow \quad \left \Uparrow \frac{a}{b} \right \Downarrow \quad \left \updownarrow \frac{a}{b} \right \Updownarrow
| 
|
Delimiters can be mixed,
as long as \left and \right match
| \left [ 0,1 \right )</code> <br/> <code>\left \langle \psi \right |
| 
|
Use \left. and \right. if you don't
want a delimiter to appear:
| \left . \frac{A}{B} \right \} \to X
| 
|
| Size of the delimiters
| \big( \Big( \bigg( \Bigg( \dots \Bigg] \bigg] \Big] \big]/<code>
| 
|
| <code>\big\{ \Big\{ \bigg\{ \Bigg\{ \dots \Bigg\rangle \bigg\rangle \Big\rangle \big\rangle
| 
|
\big\| \Big\| \bigg\| \Bigg\| \dots \Bigg| \bigg| \Big| \big|
| 
|
\big\lfloor \Big\lfloor \bigg\lfloor \Bigg\lfloor \dots \Bigg\rceil \bigg\rceil \Big\rceil \big\rceil
| 
|
\big\uparrow \Big\uparrow \bigg\uparrow \Bigg\uparrow \dots \Bigg\Downarrow \bigg\Downarrow \Big\Downarrow \big\Downarrow
| 
|
\big\updownarrow \Big\updownarrow \bigg\updownarrow \Bigg\updownarrow \dots \Bigg\Updownarrow \bigg\Updownarrow \Big\Updownarrow \big\Updownarrow
| 
|
\big / \Big / \bigg / \Bigg / \dots \Bigg\backslash \bigg\backslash \Big\backslash \big\backslash
| 
|
Alphabets and typefaces
|
|
Note: TeX cannot render arbitrary Unicode characters. Those it can handle can be entered by the expressions below.
For others, such as Cyrillic, they can be entered as Unicode or HTML entities in running text, but cannot be used in displayed formulas.
|
\rm{A} \rm{B} \Gamma \Delta \rm{E} \rm{Z}
| 
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\rm{H} \Theta \rm{I} \rm{K} \Lambda \rm{M}
| 
|
\rm{N} \Xi \Pi \rm{P} \Sigma \rm{T}
| 
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\rm{Y} \Phi \rm{X} \Psi \Omega
| 
|
\alpha \beta \gamma \delta \epsilon \zeta
| 
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\eta \theta \iota \kappa \lambda \mu
| 
|
\nu \xi \pi \rho \sigma \tau
| 
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\upsilon \phi \chi \psi \omega
| 
|
\varepsilon \digamma \vartheta \varkappa
| 
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\varpi \varrho \varsigma \varphi
| 
|
| Blackboard Bold/Scripts
|
\mathbb{A} \mathbb{B} \mathbb{C} \mathbb{D} \mathbb{E} \mathbb{F} \mathbb{G}
| 
|
\mathbb{H} \mathbb{I} \mathbb{J} \mathbb{K} \mathbb{L} \mathbb{M}
| 
|
\mathbb{N} \mathbb{O} \mathbb{P} \mathbb{Q} \mathbb{R} \mathbb{S} \mathbb{T}
| 
|
\mathbb{U} \mathbb{V} \mathbb{W} \mathbb{X} \mathbb{Y} \mathbb{Z}
| 
|
| boldface (vectors)
|
\mathbf{A} \mathbf{B} \mathbf{C} \mathbf{D} \mathbf{E} \mathbf{F} \mathbf{G}
| 
|
\mathbf{H} \mathbf{I} \mathbf{J} \mathbf{K} \mathbf{L} \mathbf{M}
| 
|
\mathbf{N} \mathbf{O} \mathbf{P} \mathbf{Q} \mathbf{R} \mathbf{S} \mathbf{T}
| 
|
\mathbf{U} \mathbf{V} \mathbf{W} \mathbf{X} \mathbf{Y} \mathbf{Z}
| 
|
\mathbf{a} \mathbf{b} \mathbf{c} \mathbf{d} \mathbf{e} \mathbf{f} \mathbf{g}
| 
|
\mathbf{h} \mathbf{i} \mathbf{j} \mathbf{k} \mathbf{l} \mathbf{m}
| 
|
\mathbf{n} \mathbf{o} \mathbf{p} \mathbf{q} \mathbf{r} \mathbf{s} \mathbf{t}
| 
|
\mathbf{u} \mathbf{v} \mathbf{w} \mathbf{x} \mathbf{y} \mathbf{z}
| 
|
\mathbf{0} \mathbf{1} \mathbf{2} \mathbf{3} \mathbf{4}
| 
|
\mathbf{5} \mathbf{6} \mathbf{7} \mathbf{8} \mathbf{9}
| 
|
| Italics
|
\mathit{A} \mathit{B} \mathit{C} \mathit{D} \mathit{E} \mathit{F} \mathit{G}
| 
|
\mathit{H} \mathit{I} \mathit{J} \mathit{K} \mathit{L} \mathit{M}
| 
|
\mathit{N} \mathit{O} \mathit{P} \mathit{Q} \mathit{R} \mathit{S} \mathit{T}
| 
|
\mathit{U} \mathit{V} \mathit{W} \mathit{X} \mathit{Y} \mathit{Z}
| 
|
\mathit{a} \mathit{b} \mathit{c} \mathit{d} \mathit{e} \mathit{f} \mathit{g}
| 
|
\mathit{h} \mathit{i} \mathit{j} \mathit{k} \mathit{l} \mathit{m}
| 
|
\mathit{n} \mathit{o} \mathit{p} \mathit{q} \mathit{r} \mathit{s} \mathit{t}
| 
|
\mathit{u} \mathit{v} \mathit{w} \mathit{x} \mathit{y} \mathit{z}
| 
|
\mathit{0} \mathit{1} \mathit{2} \mathit{3} \mathit{4}
| 
|
\mathit{5} \mathit{6} \mathit{7} \mathit{8} \mathit{9}
| 
|
| Roman typeface
|
\mathrm{A} \mathrm{B} \mathrm{C} \mathrm{D} \mathrm{E} \mathrm{F} \mathrm{G}
| 
|
\mathrm{H} \mathrm{I} \mathrm{J} \mathrm{K} \mathrm{L} \mathrm{M}
| 
|
\mathrm{N} \mathrm{O} \mathrm{P} \mathrm{Q} \mathrm{R} \mathrm{S} \mathrm{T}
| 
|
\mathrm{U} \mathrm{V} \mathrm{W} \mathrm{X} \mathrm{Y} \mathrm{Z}
| 
|
\mathrm{a} \mathrm{b} \mathrm{c} \mathrm{d} \mathrm{e} \mathrm{f} \mathrm{g}
| 
|
\mathrm{h} \mathrm{i} \mathrm{j} \mathrm{k} \mathrm{l} \mathrm{m}
| 
|
\mathrm{n} \mathrm{o} \mathrm{p} \mathrm{q} \mathrm{r} \mathrm{s} \mathrm{t}
| 
|
\mathrm{u} \mathrm{v} \mathrm{w} \mathrm{x} \mathrm{y} \mathrm{z}
| 
|
\mathrm{0} \mathrm{1} \mathrm{2} \mathrm{3} \mathrm{4}
| 
|
\mathrm{5} \mathrm{6} \mathrm{7} \mathrm{8} \mathrm{9}
| 
|
| Fraktur typeface
|
\mathfrak{A} \mathfrak{B} \mathfrak{C} \mathfrak{D} \mathfrak{E} \mathfrak{F} \mathfrak{G}
| 
|
\mathfrak{H} \mathfrak{I} \mathfrak{J} \mathfrak{K} \mathfrak{L} \mathfrak{M}
| 
|
\mathfrak{N} \mathfrak{O} \mathfrak{P} \mathfrak{Q} \mathfrak{R} \mathfrak{S} \mathfrak{T}
| 
|
\mathfrak{U} \mathfrak{V} \mathfrak{W} \mathfrak{X} \mathfrak{Y} \mathfrak{Z}
| 
|
\mathfrak{a} \mathfrak{b} \mathfrak{c} \mathfrak{d} \mathfrak{e} \mathfrak{f} \mathfrak{g}
| 
|
\mathfrak{h} \mathfrak{i} \mathfrak{j} \mathfrak{k} \mathfrak{l} \mathfrak{m}
| 
|
\mathfrak{n} \mathfrak{o} \mathfrak{p} \mathfrak{q} \mathfrak{r} \mathfrak{s} \mathfrak{t}
| 
|
\mathfrak{u} \mathfrak{v} \mathfrak{w} \mathfrak{x} \mathfrak{y} \mathfrak{z}
| 
|
\mathfrak{0} \mathfrak{1} \mathfrak{2} \mathfrak{3} \mathfrak{4}
| 
|
\mathfrak{5} \mathfrak{6} \mathfrak{7} \mathfrak{8} \mathfrak{9}
| 
|
| Calligraphy/Script
|
\mathcal{A} \mathcal{B} \mathcal{C} \mathcal{D} \mathcal{E} \mathcal{F} \mathcal{G}
| 
|
\mathcal{H} \mathcal{I} \mathcal{J} \mathcal{K} \mathcal{L} \mathcal{M}
| 
|
\mathcal{N} \mathcal{O} \mathcal{P} \mathcal{Q} \mathcal{R} \mathcal{S} \mathcal{T}
| 
|
\mathcal{U} \mathcal{V} \mathcal{W} \mathcal{X} \mathcal{Y} \mathcal{Z}
| 
|
| Hebrew
|
\aleph \beth \gimel \daleth
| 
|
