# LaTeX math markup

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## Subscripts, superscripts, integrals

Feature Syntax How it looks rendered
HTML PNG
Superscript a^2 ${\displaystyle a^{2}}$ ${\displaystyle a^{2}\,\!}$
Subscript a_2 ${\displaystyle a_{2}}$ ${\displaystyle a_{2}\,\!}$
Grouping a^{2+2} ${\displaystyle a^{2+2}}$ ${\displaystyle a^{2+2}\,\!}$
a_{i,j} ${\displaystyle a_{i,j}}$ ${\displaystyle a_{i,j}\,\!}$
Combining sub & super x_2^3 ${\displaystyle x_{2}^{3}}$
Preceding and/or Additional sub & super \sideset{_1^2}{_3^4}\prod_a^b ${\displaystyle \sideset {_{1}^{2}}{_{3}^{4}}\prod _{a}^{b}}$
{}_1^2\!\Omega_3^4 ${\displaystyle {}_{1}^{2}\!\Omega _{3}^{4}}$
Stacking \overset{\alpha}{\omega} ${\displaystyle {\overset {\alpha }{\omega }}}$
\underset{\alpha}{\omega} ${\displaystyle {\underset {\alpha }{\omega }}}$
\overset{\alpha}{\underset{\gamma}{\omega}} ${\displaystyle {\overset {\alpha }{\underset {\gamma }{\omega }}}}$
\stackrel{\alpha}{\omega} ${\displaystyle {\stackrel {\alpha }{\omega }}}$
Derivative (forced PNG) x', y, f', f\!   ${\displaystyle x',y'',f',f''\!}$
Derivative (f in italics may overlap primes in HTML) x', y, f', f ${\displaystyle x',y'',f',f''}$ ${\displaystyle x',y'',f',f''\!}$
Derivative (wrong in HTML) x^\prime, y^{\prime\prime} ${\displaystyle x^{\prime },y^{\prime \prime }}$ ${\displaystyle x^{\prime },y^{\prime \prime }\,\!}$
Derivative (wrong in PNG) x\prime, y\prime\prime ${\displaystyle x\prime ,y\prime \prime }$ ${\displaystyle x\prime ,y\prime \prime \,\!}$
Derivative dots \dot{x}, \ddot{x} ${\displaystyle {\dot {x}},{\ddot {x}}}$
Underlines, overlines, vectors \hat a \ \bar b \ \vec c ${\displaystyle {\hat {a}}\ {\bar {b}}\ {\vec {c}}}$
\overrightarrow{a b} \ \overleftarrow{c d} \ \widehat{d e f} ${\displaystyle {\overrightarrow {ab}}\ {\overleftarrow {cd}}\ {\widehat {def}}}$
\overline{g h i} \ \underline{j k l} ${\displaystyle {\overline {ghi}}\ {\underline {jkl}}}$
Arrows  A \xleftarrow{n+\mu-1} B \xrightarrow[T]{n\pm i-1} C ${\displaystyle A{\xleftarrow {n+\mu -1}}B{\xrightarrow[{T}]{n\pm i-1}}C}$
Overbraces \overbrace{ 1+2+\cdots+100 }^{5050} ${\displaystyle \overbrace {1+2+\cdots +100} ^{5050}}$
Underbraces \underbrace{ a+b+\cdots+z }_{26} ${\displaystyle \underbrace {a+b+\cdots +z} _{26}}$
Sum \sum_{k=1}^N k^2 ${\displaystyle \sum _{k=1}^{N}k^{2}}$
Sum (force \textstyle) \textstyle \sum_{k=1}^N k^2  ${\displaystyle \textstyle \sum _{k=1}^{N}k^{2}}$
Product \prod_{i=1}^N x_i ${\displaystyle \prod _{i=1}^{N}x_{i}}$
Product (force \textstyle) \textstyle \prod_{i=1}^N x_i ${\displaystyle \textstyle \prod _{i=1}^{N}x_{i}}$
Coproduct \coprod_{i=1}^N x_i ${\displaystyle \coprod _{i=1}^{N}x_{i}}$
Coproduct (force \textstyle) \textstyle \coprod_{i=1}^N x_i ${\displaystyle \textstyle \coprod _{i=1}^{N}x_{i}}$
Limit \lim_{n \to \infty}x_n ${\displaystyle \lim _{n\to \infty }x_{n}}$
Limit (force \textstyle) \textstyle \lim_{n \to \infty}x_n ${\displaystyle \textstyle \lim _{n\to \infty }x_{n}}$
Integral \int\limits_{-N}^{N} e^x\, dx ${\displaystyle \int \limits _{-N}^{N}e^{x}\,dx}$
Integral (force \textstyle) \textstyle \int\limits_{-N}^{N} e^x\, dx ${\displaystyle \textstyle \int \limits _{-N}^{N}e^{x}\,dx}$
Double integral \iint\limits_{D} \, dx\,dy ${\displaystyle \iint \limits _{D}\,dx\,dy}$
Triple integral \iiint\limits_{E} \, dx\,dy\,dz ${\displaystyle \iiint \limits _{E}\,dx\,dy\,dz}$
Quadruple integral \iiiint\limits_{F} \, dx\,dy\,dz\,dt ${\displaystyle \iiiint \limits _{F}\,dx\,dy\,dz\,dt}$
Path integral \oint\limits_{C} x^3\, dx + 4y^2\, dy ${\displaystyle \oint \limits _{C}x^{3}\,dx+4y^{2}\,dy}$
Intersections \bigcap_1^{n} p ${\displaystyle \bigcap _{1}^{n}p}$
Unions \bigcup_1^{k} p ${\displaystyle \bigcup _{1}^{k}p}$

## Fractions, matrices, multilines

Feature Syntax How it looks rendered
Fractions \frac{2}{4}=0.5 ${\displaystyle {\frac {2}{4}}=0.5}$
Small Fractions \tfrac{2}{4} = 0.5 ${\displaystyle {\tfrac {2}{4}}=0.5}$
Large (normal) Fractions \dfrac{2}{4} = 0.5 ${\displaystyle {\dfrac {2}{4}}=0.5}$
Large (nested) Fractions \cfrac{2}{c + \cfrac{2}{d + \cfrac{2}{4}}} = a ${\displaystyle {\cfrac {2}{c+{\cfrac {2}{d+{\cfrac {2}{4}}}}}}=a}$
Binomial coefficients \binom{n}{k} ${\displaystyle {\binom {n}{k}}}$
Small Binomial coefficients \tbinom{n}{k} ${\displaystyle {\tbinom {n}{k}}}$
Large (normal) Binomial coefficients \dbinom{n}{k} ${\displaystyle {\dbinom {n}{k}}}$
Matrices
\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)

${\displaystyle {\bigl (}{\begin{smallmatrix}a&b\\c&d\end{smallmatrix}}{\bigr )}}$
Case distinctions
f(n) =
\begin{cases}
n/2,  & \mbox{if }n\mbox{ is even} \\
3n+1, & \mbox{if }n\mbox{ is odd}
\end{cases}
${\displaystyle f(n)={\begin{cases}n/2,&{\mbox{if }}n{\mbox{ is even}}\\3n+1,&{\mbox{if }}n{\mbox{ is odd}}\end{cases}}}$
Multiline equations
\begin{align}
f(x) & = (a+b)^2 \\
& = a^2+2ab+b^2 \\
\end{align}

{\displaystyle {\begin{aligned}f(x)&=(a+b)^{2}\\&=a^{2}+2ab+b^{2}\\\end{aligned}}}
\begin{alignat}{2}
f(x) & = (a-b)^2 \\
& = a^2-2ab+b^2 \\
\end{alignat}

{\displaystyle {\begin{alignedat}{2}f(x)&=(a-b)^{2}\\&=a^{2}-2ab+b^{2}\\\end{alignedat}}}
Multiline equations (must define number of colums used ({lcr}) (should not be used unless needed)
\begin{array}{lcl}
z        & = & a \\
f(x,y,z) & = & x + y + z
\end{array}
${\displaystyle {\begin{array}{lcl}z&=&a\\f(x,y,z)&=&x+y+z\end{array}}}$
Multiline equations (more)
\begin{array}{lcr}
z        & = & a \\
f(x,y,z) & = & x + y + z
\end{array}
${\displaystyle {\begin{array}{lcr}z&=&a\\f(x,y,z)&=&x+y+z\end{array}}}$
Breaking up a long expression so that it wraps when necessary

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



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

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