The <math></math> tags can be used to give complex formulas in an understandable and readable format.

Contents 1 Functions, symbols, special characters 1.1 Accents/Diacritics 1.2 Standard functions 1.3 Modular arithmetic 1.4 Derivatives 1.5 Sets 1.6 Operators 1.7 Logic 1.8 Root 1.9 Relations 1.10 Geometric 1.11 Arrows 1.12 Special 1.13 Unsorted (new stuff) 1.14 Fractions, matrices, multilines 1.15 Subscripts, superscripts, integrals 1.16 Parenthesizing big expressions, brackets, bars 2 Alphabets and typefaces 3 Color 4 Formatting issues 4.1 Spacing 4.2 Forced PNG rendering

Functions, symbols, special characters

Accents/Diacritics
\acute{a} \grave{a} \hat{a} \tilde{a} \breve{a}
\check{a} \bar{a} \ddot{a} \dot{a}
Standard functions
\sin a \cos b \tan c
\sec d \csc e \cot f
\arcsin h \arccos i \arctan j
\sinh k \cosh l \tanh m \coth n
\operatorname{sh}o \operatorname{ch}p \operatorname{th}q
\operatorname{argsh}r \operatorname{argch}s \operatorname{argth}t
\lim u \limsup v \liminf w \min x \max y
\inf z \sup a \exp b \ln c \lg d \log e \log_{10} f \ker g
\deg h \gcd i \Pr j \det k \hom l \arg m \dim n
Modular arithmetic
s_k \equiv 0 \pmod{m} a \bmod b
Derivatives
\nabla \, \partial x \, dx \, \dot x \, \ddot y\, dy/dx\, \frac{dy}{dx}\, \frac{\partial^2 y}{\partial x_1\,\partial x_2}
Sets
\forall \exists \empty \emptyset \varnothing
\in \ni \not \in \notin \subset \subseteq \supset \supseteq
\cap \bigcap \cup \bigcup \biguplus \setminus \smallsetminus
\sqsubset \sqsubseteq \sqsupset \sqsupseteq \sqcap \sqcup \bigsqcup
Operators
+ \oplus \bigoplus \pm \mp -
\times \otimes \bigotimes \cdot \circ \bullet \bigodot
\star * / \div \frac{1}{2}
Logic
\land (or \and) \wedge \bigwedge \bar{q} \to p
\lor \vee \bigvee \lnot \neg q \And
Root
\sqrt{2} \sqrt[n]{x}
Relations
\sim \approx \simeq \cong \dot= \overset{\underset{\mathrm{def}}{}}{=}
\le < \ll \gg \ge > \equiv \not\equiv \ne \mbox{or} \neq \propto
Geometric
\Diamond \Box \triangle \angle \perp \mid \nmid \| 45^\circ
Arrows
\leftarrow (or \gets) \rightarrow (or \to) \nleftarrow \not\to \leftrightarrow \nleftrightarrow \longleftarrow \longrightarrow \longleftrightarrow
\Leftarrow \Rightarrow \nLeftarrow \nRightarrow \Leftrightarrow \nLeftrightarrow \Longleftarrow \Longrightarrow \Longleftrightarrow (or \iff)
\uparrow \downarrow \updownarrow \Uparrow \Downarrow \Updownarrow \nearrow \searrow \swarrow \nwarrow
\rightharpoonup \rightharpoondown \leftharpoonup \leftharpoondown \upharpoonleft \upharpoonright \downharpoonleft \downharpoonright \rightleftharpoons \leftrightharpoons
\mapsto \longmapsto \hookrightarrow \hookleftarrow \multimap \leftrightsquigarrow \rightsquigarrow
Special
\eth \S \P \% \dagger \ddagger \ldots \cdots
\smile \frown \wr \triangleleft \triangleright \infty \bot \top
\vdash \vDash \Vdash \models \lVert \rVert \imath \hbar
\ell \mho \Finv \Re \Im \wp \complement
\diamondsuit \heartsuit \clubsuit \spadesuit \Game \flat \natural \sharp
Unsorted (new stuff)
\jmath \surd \ast \uplus \diamond \bigtriangleup \bigtriangledown \ominus
\oslash \odot \bigcirc \amalg \prec \succ \preceq \succeq
\dashv \asymp \doteq \parallel

Fractions, matrices, multilines

Feature	Syntax	How it looks rendered
Fractions	\frac{2}{4}=0.5
Small Fractions	\tfrac{2}{4} = 0.5
Large (normal) Fractions	\dfrac{2}{4} = 0.5 \qquad \dfrac{2}{c + \dfrac{2}{d + \dfrac{2}{4}}} = a
Large (nested) Fractions	\cfrac{2}{c + \cfrac{2}{d + \cfrac{2}{4}}} = a
Binomial coefficients	\binom{n}{k}
Small Binomial coefficients	\tbinom{n}{k}
Large (normal) Binomial coefficients	\dbinom{n}{k}
Matrices	\begin{matrix} x & y \\ z & v \end{matrix}
	\begin{vmatrix} x & y \\ z & v \end{vmatrix}
	\begin{Vmatrix} x & y \\ z & v \end{Vmatrix}
	\begin{bmatrix} 0 & \cdots & 0 \\ \vdots & \ddots & \vdots \\ 0 & \cdots & 0 \end{bmatrix}
	\begin{Bmatrix} x & y \\ z & v \end{Bmatrix}
	\begin{pmatrix} x & y \\ z & v \end{pmatrix}
	\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}
Multiline equations	\begin{align} f(x) & = (a+b)^2 \\ & = a^2+2ab+b^2 \\ \end{align}
	\begin{alignat}{2} f(x) & = (a-b)^2 \\ & = a^2-2ab+b^2 \\ \end{alignat}
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}
Multiline equations (more)	\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	<math>f(x) \,\!</math> <math>= \sum_{n=0}^\infty a_n x^n </math> <math>= a_0+a_1x+a_2x^2+\cdots</math>
Simultaneous equations	\begin{cases} 3x + 5y + z \\ 7x - 2y + 4z \\ -6x + 3y + 2z \end{cases}
Arrays	\begin{array}{|c|c||c|} a & b & S \\ \hline 0&0&1\\ 0&1&1\\ 1&0&1\\ 1&1&0\\ \end{array}

Subscripts, superscripts, integrals

Feature	Syntax	How it looks rendered
		HTML	PNG
Superscript	a^2	a2
Subscript	a_2	a2
Grouping	a^{2+2}	a2 + 2
	a_{i,j}	ai,j
Combining sub & super	x_2^3
Super super	10^{10^{ \,\!{8} }
Super super	10^{10^{ \overset{8}{} }}
Super super (wrong in HTML in some browsers)	10^{10^8}
Preceding and/or Additional sub & super	\sideset{_1^2}{_3^4}\prod_a^b
	{}_1^2\!\Omega_3^4
Stacking	\overset{\alpha}{\omega}
	\underset{\alpha}{\omega}
	\overset{\alpha}{\underset{\gamma}{\omega}}
	\stackrel{\alpha}{\omega}
Derivative (forced PNG)	x', y'', f', f''\!
Derivative (f in italics may overlap primes in HTML)	x', y'', f', f''	x',y'',f',f''
Derivative (wrong in HTML)	x^\prime, y^{\prime\prime}
Derivative (wrong in PNG)	x\prime, y\prime\prime
Derivative dots	\dot{x}, \ddot{x}
Underlines, overlines, vectors	\hat a \ \bar b \ \vec c
	\overrightarrow{a b} \ \overleftarrow{c d} \ \widehat{d e f}
	\overline{g h i} \ \underline{j k l}
Arrows	A \xleftarrow{n+\mu-1} B \xrightarrow[T]{n\pm i-1} C
Overbraces	\overbrace{ 1+2+\cdots+100 }^{5050}
Underbraces	\underbrace{ a+b+\cdots+z }_{26}
Sum	\sum_{k=1}^N k^2
Sum (force \textstyle)	\textstyle \sum_{k=1}^N k^2
Product	\prod_{i=1}^N x_i
Product (force \textstyle)	\textstyle \prod_{i=1}^N x_i
Coproduct	\coprod_{i=1}^N x_i
Coproduct (force \textstyle)	\textstyle \coprod_{i=1}^N x_i
Limit	\lim_{n \to \infty}x_n
Limit (force \textstyle)	\textstyle \lim_{n \to \infty}x_n
Integral	\int\limits_{1}^{3}\frac{e^3/x}{x^2}\, dx
Integral (alternate limits style)	\int_{1}^{3}\frac{e^3/x}{x^2}\, dx
Integral (force \textstyle)	\textstyle \int\limits_{-N}^{N} e^x\, dx
Integral (force \textstyle, alternate limits style)	\textstyle \int_{-N}^{N} e^x\, dx
Double integral	\iint\limits_D \, dx\,dy
Triple integral	\iiint\limits_E \, dx\,dy\,dz
Quadruple integral	\iiiint\limits_F \, dx\,dy\,dz\,dt
Line or path integral	\int_C x^3\, dx + 4y^2\, dy
Closed line or path integral	\oint_C x^3\, dx + 4y^2\, dy
Intersections	\bigcap_1^n p
Unions	\bigcup_1^k p

Parenthesizing big expressions, brackets, bars

Feature	Syntax	How it looks rendered
Bad	( \frac{1}{2} )
Good	\left ( \frac{1}{2} \right )

You can use various delimiters with \left and \right:

Feature	Syntax	How it looks rendered
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
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 ) \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]
	\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

Texvc cannot render arbitrary Unicode characters. Those 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.

Greek alphabet
\Alpha \Beta \Gamma \Delta \Epsilon \Zeta
\Eta \Theta \Iota \Kappa \Lambda \Mu
\Nu \Xi \Pi \Rho \Sigma \Tau
\Upsilon \Phi \Chi \Psi \Omega
\alpha \beta \gamma \delta \epsilon \zeta
\eta \theta \iota \kappa \lambda \mu
\nu \xi \pi \rho \sigma \tau
\upsilon \phi \chi \psi \omega
\varepsilon \digamma \vartheta \varkappa
\varpi \varrho \varsigma \varphi
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}
Boldface (greek)
\boldsymbol{\Alpha} \boldsymbol{\Beta} \boldsymbol{\Gamma} \boldsymbol{\Delta} \boldsymbol{\Epsilon} \boldsymbol{\Zeta}
\boldsymbol{\Eta} \boldsymbol{\Theta} \boldsymbol{\Iota} \boldsymbol{\Kappa} \boldsymbol{\Lambda} \boldsymbol{\Mu}
\boldsymbol{\Nu} \boldsymbol{\Xi} \boldsymbol{\Pi} \boldsymbol{\Rho} \boldsymbol{\Sigma} \boldsymbol{\Tau}
\boldsymbol{\Upsilon} \boldsymbol{\Phi} \boldsymbol{\Chi} \boldsymbol{\Psi} \boldsymbol{\Omega}
\boldsymbol{\alpha} \boldsymbol{\beta} \boldsymbol{\gamma} \boldsymbol{\delta} \boldsymbol{\epsilon} \boldsymbol{\zeta}
\boldsymbol{\eta} \boldsymbol{\theta} \boldsymbol{\iota} \boldsymbol{\kappa} \boldsymbol{\lambda} \boldsymbol{\mu}
\boldsymbol{\nu} \boldsymbol{\xi} \boldsymbol{\pi} \boldsymbol{\rho} \boldsymbol{\sigma} \boldsymbol{\tau}
\boldsymbol{\upsilon} \boldsymbol{\phi} \boldsymbol{\chi} \boldsymbol{\psi} \boldsymbol{\omega}
\boldsymbol{\varepsilon} \boldsymbol{\digamma} \boldsymbol{\vartheta} \boldsymbol{\varkappa}
\boldsymbol{\varpi} \boldsymbol{\varrho} \boldsymbol{\varsigma} \boldsymbol{\varphi}
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}
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

Feature	Syntax	How it looks rendered
non-italicised characters	\mbox{abc}	abc
mixed italics (bad)	\mbox{if} n \mbox{is even}	ifnis even
mixed italics (good)	\mbox{if }n\mbox{ is even}	if n is even
mixed italics (more legible: ~ is a non-breaking space, while "\ " forces a space)	\mbox{if}~n\ \mbox{is even}

Color

Equations can use color:

• {\color{Blue}x^2}+{\color{YellowOrange}2x}-{\color{OliveGreen}1}

  

• x_{1,2}=\frac{-b\pm\sqrt{\color{Red}b^2-4ac}}{2a}

  

See here for all named colors supported by LaTeX.

Note that color should not be used as the only way to identify something, because it will become meaningless on black-and-white media or for color-blind people.

Formatting issues

Spacing

Note that TeX handles most spacing automatically, but you may sometimes want manual control.

Feature	Syntax	How it looks rendered
double quad space	a \qquad b
quad space	a \quad b
text space	a\ b
text space without PNG conversion	a \mbox{ } b	a b
large space	a\;b
medium space	a\>b	[not supported]
small space	a\,b
no space	ab
small negative space	a\!b

Forced PNG rendering

To force the formula to render as PNG, add \, (small space) at the end of the formula (where it is not rendered). This will force PNG if the user is in "HTML if simple" mode, but not for "HTML if possible" mode (math rendering settings in Preferences).

You can also use \,\! (small space and negative space, which cancel out) anywhere inside the math tags. This does force PNG even in "HTML if possible" mode, unlike \,.

This could be useful to keep the rendering of formulae in a proof consistent, for example, or to fix formulae that render incorrectly in HTML (at one time, a^{2+2} rendered with an extra underscore), or to demonstrate how something is rendered when it would normally show up as HTML (as in the examples above).

For instance:

Syntax	How it looks rendered
a^{c+2}	ac + 2
a^{c+2} \,
a^{\,\!c+2}
a^{b^{c+2}}	(WRONG with option "HTML if possible or else PNG"!)
a^{b^{c+2}} \,	(WRONG with option "HTML if possible or else PNG"!)
a^{b^{c+2}}\approx 5	(due to "" correctly displayed, no code "\,\!" needed)
a^{b^{\,\!c+2}}
\int_{-N}^{N} e^x\, dx