Help:Math

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    Only a limited part of the full TeX language is supported; see below for details.

    Contents


    Syntax

    Math markup goes inside 

    
:<math>
...
</math>

    The edit toolbar has a button for this. To number equations, write 

    :<math> \label{label} 
...
</math>

    and refer as \eqref{label}. For example, \[ \tag{1} x^7 \] is Eq.(1).

    Functions, symbols, special characters

    Accents/Diacritics

    \acute{a} \grave{a} \hat{a} \tilde{a} \breve{a} \(\acute{a} \grave{a} \hat{a} \tilde{a} \breve{a}\,\!\)
    \check{a} \bar{a} \ddot{a} \dot{a} \(\check{a} \bar{a} \ddot{a} \dot{a}\,\!\)

    Standard functions

    \sin a \cos b \tan c \cot d \sec e \csc f \arcsin k \arccos l \(\sin a \cos b \tan c \cot d \sec e \csc f \arcsin k \arccos l\,\!\)
    \arctan m \sinh g \cosh h \tanh i \coth j \operatorname{sh}g \operatorname{argsh}k \operatorname{ch}h \(\arctan m \sinh g \cosh h \tanh i \coth j \operatorname{sh}g \operatorname{argsh}k \operatorname{ch}h\,\!\)
    \operatorname{argch}l \ \operatorname{th}i \ \operatorname{argth}m \ \lim n \limsup o \liminf p \min q \max r \(\operatorname{argch}l \ \operatorname{th}i \ \operatorname{argth}m \lim n \limsup o \liminf p \min q \max r\,\!\)
    \inf s \sup t \exp u \ln v \lg w \log x \log_{10} y \ker x \(\inf s \sup t \exp u \ln v \lg w \log x \log_{10} y \ker x\,\!\)
    \deg x \gcd x \Pr x \det x \hom x \arg x \dim x \(\deg x \gcd x \Pr x \det x \hom x \arg x \dim x\,\!\)

    Modular arithmetic

    s_k \equiv 0 \pmod{m} a \bmod b \(s_k \equiv 0 \pmod{m} a \bmod b\,\!\)

    Derivatives

    \nabla \partial x dx \dot x \ddot y \(\nabla \partial x dx \dot x \ddot y\,\!\)

    Sets

    \forall \exists \empty \emptyset \varnothing \(\forall \exists \empty \emptyset \varnothing\,\!\)
    \in \ni \not \in \notin \subset \subseteq \supset \supseteq \(\in \ni \not \in \notin \subset \subseteq \supset \supseteq\,\!\)
    \cap \bigcap \cup \bigcup \biguplus \setminus \smallsetminus \(\cap \bigcap \cup \bigcup \biguplus \setminus \smallsetminus\,\!\)
    \sqsubset \sqsubseteq \sqsupset \sqsupseteq \sqcap \sqcup \bigsqcup \(\sqsubset \sqsubseteq \sqsupset \sqsupseteq \sqcap \sqcup \bigsqcup\,\!\)

    Operators

    + \oplus \bigoplus \pm \mp - \(+ \oplus \bigoplus \pm \mp - \,\!\)
    \times \otimes \bigotimes \cdot \circ \bullet \bigodot \(\times \otimes \bigotimes \cdot \circ \bullet \bigodot\,\!\)
    \star * / \div \frac{1}{2} \(\star * / \div \frac{1}{2}\,\!\)

    Logic

    \land \wedge \bigwedge \bar{q} \to p \(\land \wedge \bigwedge \bar{q} \to p\,\!\)
    \lor \vee \bigvee \lnot \neg q \And \(\lor \vee \bigvee \lnot \neg q \And\,\!\)

    Root

    \sqrt{2} \sqrt[n]{x} \(\sqrt{2} \sqrt[n]{x}\,\!\)

    Relations

    \sim \approx \simeq \cong \dot= \(\sim \approx \simeq \cong \dot=\)
    \le < \ll \gg \ge > \equiv \not\equiv \ne \mbox{or} \neq \propto \(\le < \ll \gg \ge > \equiv \not\equiv \ne \mbox{or} \neq \propto\,\!\)

    Geometric

    \Diamond \Box \triangle \angle \perp \mid \nmid \| 45^\circ \(\Diamond \, \Box \, \triangle \, \angle \perp \, \mid \; \nmid \, \| 45^\circ\,\!\)

    Arrows

    \leftarrow \gets \rightarrow \to \not\to \leftrightarrow \longleftarrow \longrightarrow \(\leftarrow \gets \rightarrow \to \not\to \leftrightarrow \longleftarrow \longrightarrow\,\!\)
    \mapsto \longmapsto \hookrightarrow \hookleftarrow \nearrow \searrow \swarrow \nwarrow \(\mapsto \longmapsto \hookrightarrow \hookleftarrow \nearrow \searrow \swarrow \nwarrow\,\!\)
    \uparrow \downarrow \updownarrow \rightharpoonup \rightharpoondown \leftharpoonup \leftharpoondown \upharpoonleft \(\uparrow \downarrow \updownarrow \rightharpoonup \rightharpoondown \leftharpoonup \leftharpoondown \upharpoonleft\,\!\)
    \upharpoonright \downharpoonleft \downharpoonright \rightleftharpoons \Leftarrow \Rightarrow \Leftrightarrow \Longleftarrow \(\upharpoonright \downharpoonleft \downharpoonright \rightleftharpoons \Leftarrow \Rightarrow \Leftrightarrow \Longleftarrow\,\!\)

    Special

    \eth \S \P \% \dagger \ddagger \ldots \cdots \(\eth \S \P \% \dagger \ddagger \ldots \cdots\,\!\)
    \smile \frown \wr \triangleleft \triangleright \infty \bot \top \(\smile \frown \wr \triangleleft \triangleright \infty \bot \top\,\!\)
    \vdash \vDash \Vdash \models \lVert \rVert \imath \hbar \(\vdash \vDash \Vdash \models \lVert \rVert \imath \hbar\,\!\)
    \ell \mho \Finv \Re \Im \wp \complement \diamondsuit \(\ell \mho \Finv \Re \Im \wp \complement \diamondsuit\,\!\)
    \heartsuit \clubsuit \spadesuit \Game \flat \natural \sharp \(\heartsuit \clubsuit \spadesuit \Game \flat \natural \sharp\,\!\)

    Subscripts, superscripts, integrals

    Feature Syntax How it looks rendered
    HTML PNG
    Superscript a^2 \(a^2\) \(a^2 \,\!\)
    Subscript a_2 \(a_2\) \(a_2 \,\!\)
    Grouping a^{2+2} \(a^{2+2}\) \(a^{2+2}\,\!\)
    a_{i,j} \(a_{i,j}\) \(a_{i,j}\,\!\)
    Combining sub & super x_2^3 \(x_2^3\)
    {}_1^2\!\Omega_3^4 \({}_1^2\!\Omega_3^4\)
    Stacking \stackrel{\alpha}{\omega} \(\stackrel{\alpha}{\omega}\)
    Derivative (forced PNG) x', y, f', f\!   \(x', y'', f', f''\!\)
    Derivative (f in italics may overlap primes in HTML) x', y, f', f \(x', y'', f', f''\) \(x', y'', f', f''\!\)
    Derivative (wrong in HTML) x^\prime, y^{\prime\prime} \(x^\prime, y^{\prime\prime}\) \(x^\prime, y^{\prime\prime}\,\!\)
    Derivative (wrong in PNG) x\prime, y\prime\prime \(x\prime, y\prime\prime\) \(x\prime, y\prime\prime\,\!\)
    Derivative dots \dot{x}, \ddot{x} \(\dot{x}, \ddot{x}\)
    Underlines, overlines, vectors \hat a \ \bar b \ \vec c \(\hat a \ \bar b \ \vec c\)
    \overrightarrow{a b} \ \overleftarrow{c d} \ \widehat{d e f} \(\overrightarrow{a b} \ \overleftarrow{c d} \ \widehat{d e f}\)
    \overline{g h i} \ \underline{j k l} \(\overline{g h i} \ \underline{j k l}\)
    Overbraces \overbrace{ 1+2+\cdots+100 }^{5050} \(\overbrace{ 1+2+\cdots+100 }^{5050}\)
    Underbraces \underbrace{ a+b+\cdots+z }_{26} \(\underbrace{ a+b+\cdots+z }_{26}\)
    Sum \sum_{k=1}^N k^2 \(\sum_{k=1}^N k^2\)
    Sum (force \textstyle) \textstyle \sum_{k=1}^N k^2 \(\textstyle \sum_{k=1}^N k^2\)
    Product \prod_{i=1}^N x_i \(\prod_{i=1}^N x_i\)
    Product (force \textstyle) \textstyle \prod_{i=1}^N x_i \(\textstyle \prod_{i=1}^N x_i\)
    Coproduct \coprod_{i=1}^N x_i \(\coprod_{i=1}^N x_i\)
    Coproduct (force \textstyle) \textstyle \coprod_{i=1}^N x_i \(\textstyle \coprod_{i=1}^N x_i\)
    Limit \lim_{n \to \infty}x_n \(\lim_{n \to \infty}x_n\)
    Limit (force \textstyle) \textstyle \lim_{n \to \infty}x_n \(\textstyle \lim_{n \to \infty}x_n\)
    Integral \int_{-N}^{N} e^x\, dx \(\int_{-N}^{N} e^x\, dx\)
    Integral (force \textstyle) \textstyle \int_{-N}^{N} e^x\, dx \(\textstyle \int_{-N}^{N} e^x\, dx\)
    Double integral \iint_{D}^{W} \, dx\,dy \(\iint_{D}^{W} \, dx\,dy\)
    Triple integral \iiint_{E}^{V} \, dx\,dy\,dz \(\iiint_{E}^{V} \, dx\,dy\,dz\)
    Quadruple integral \iiiint_{F}^{U} \, dx\,dy\,dz\,dt \(\iiiint_{F}^{U} \, dx\,dy\,dz\,dt\)
    Path integral \oint_{C} x^3\, dx + 4y^2\, dy \(\oint_{C} x^3\, dx + 4y^2\, dy\)
    Intersections \bigcap_1^{n} p \(\bigcap_1^{n} p\)
    Unions \bigcup_1^{k} p \(\bigcup_1^{k} p\)

    Fractions, matrices, multilines

    Feature Syntax How it looks rendered
    Fractions \frac{2}{4}=0.5 \(\frac{2}{4}=0.5\)
    Large (nestled) Fractions \cfrac{2}{c + \cfrac{2}{d + \cfrac{2}{4}}} = a \(\cfrac{2}{c + \cfrac{2}{d + \cfrac{2}{4}}} = a\)
    Matrices 
    \begin{matrix}
  x & y \\
  z & v 
\end{matrix}
    		 \(\begin{matrix} x & y \\ z & v \end{matrix}\) 
    \begin{vmatrix}
  x & y \\
  z & v 
\end{vmatrix}
    		 \(\begin{vmatrix} x & y \\ z & v \end{vmatrix}\) 
    \begin{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}
    		 \(\begin{bmatrix} 0 & \cdots & 0 \\ \vdots & \ddots & \vdots \\ 0 & \cdots & 0\end{bmatrix} \) 
    \begin{Bmatrix}
  x & y \\
  z & v
\end{Bmatrix}
    		 \(\begin{Bmatrix} x & y \\ z & v \end{Bmatrix}\) 
    \begin{pmatrix}
  x & y \\
  z & v 
\end{pmatrix}
    		 \(\begin{pmatrix} x & y \\ z & v \end{pmatrix}\)
    Case distinctions 
    f(n) = 
\begin{cases} 
  n/2,  & \mbox{if }n\mbox{ is even} \\
  3n+1, & \mbox{if }n\mbox{ is odd} 
\end{cases}
    		 \(f(n) = \begin{cases} n/2, & \mbox{if }n\mbox{ is even} \\ 3n+1, & \mbox{if }n\mbox{ is odd} \end{cases} \)
    Multiline equations (must define number of colums used ({lcr}) (should not be used unless needed) 
    \begin{array}{lcl}
 f(n+1) & = & (n+1)^2     \\
        & = & n^2 + 2n + 1 
\end{array}
    		 \(\begin{array}{lll} f(n+1) & = & (n+1)^2 \\ & = & n^2 + 2n + 1 \end{array}\)
    Multiline equations (more) 
    \begin{array}{lcr}
  f(x)   & = & x^2 + 2x + 1 \\
  f(n+1) & = & (n+1)^2 + 2(n+1) + 1     
\end{array}
    		 \(\begin{array}{lcr} f(x) & = & x^2 + 2x + 1 \\ f(n+1) & = & (n+1)^2 + 2(n+1) + 1 \end{array}\)
    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_1 x + a_2 x^2 + a_3 x^3 + \cdots</math>

    \(f(x) \,\!\)\(= \sum_{n=0}^\infty a_n x^n \)\(= a_0 + a_1 x + a_2 x^2 + a_3 x^3 + \cdots\)

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

    Alphabets and typefaces

    Greek alphabet 
    \Alpha \Beta \Gamma \Delta \Epsilon \Zeta
         		\(\Alpha \Beta \Gamma \Delta \Epsilon \Zeta \,\!\) 
    \Eta \Theta \Iota \Kappa \Lambda \Mu
         		\(\Eta \Theta \Iota \Kappa \Lambda \Mu \,\!\) 
    \Nu \Xi \Pi \Rho \Sigma \Tau
         		\(\Nu \Xi \Pi \Rho \Sigma \Tau\,\!\) 
    \Upsilon \Phi \Chi \Psi \Omega
         		\(\Upsilon \Phi \Chi \Psi \Omega \,\!\) 
    \alpha \beta \gamma \delta \epsilon \zeta
         		\(\alpha \beta \gamma \delta \epsilon \zeta \,\!\) 
    \eta \theta \iota \kappa \lambda \mu
         		\(\eta \theta \iota \kappa \lambda \mu \,\!\) 
    \nu \xi \pi \rho \sigma \tau
         		\(\nu \xi \pi \rho \sigma \tau \,\!\) 
    \upsilon \phi \chi \psi \omega
         		\(\upsilon \phi \chi \psi \omega \,\!\) 
    \varepsilon \digamma \vartheta \varkappa
         		\(\varepsilon \digamma \vartheta \varkappa \,\!\) 
    \varpi \varrho \varsigma \varphi
         		\(\varpi \varrho \varsigma \varphi\,\!\)
    Blackboard Bold/Scripts 
    \mathbb{A} \mathbb{B} \mathbb{C} \mathbb{D} \mathbb{E} \mathbb{F} \mathbb{G}
         		\(\mathbb{A} \mathbb{B} \mathbb{C} \mathbb{D} \mathbb{E} \mathbb{F} \mathbb{G} \,\!\) 
    \mathbb{H} \mathbb{I} \mathbb{J} \mathbb{K} \mathbb{L} \mathbb{M}
         		\(\mathbb{H} \mathbb{I} \mathbb{J} \mathbb{K} \mathbb{L} \mathbb{M} \,\!\) 
    \mathbb{N} \mathbb{O} \mathbb{P} \mathbb{Q} \mathbb{R} \mathbb{S} \mathbb{T}
         		\(\mathbb{N} \mathbb{O} \mathbb{P} \mathbb{Q} \mathbb{R} \mathbb{S} \mathbb{T} \,\!\) 
    \mathbb{U} \mathbb{V} \mathbb{W} \mathbb{X} \mathbb{Y} \mathbb{Z}
         		\(\mathbb{U} \mathbb{V} \mathbb{W} \mathbb{X} \mathbb{Y} \mathbb{Z}\,\!\)
    boldface (vectors) 
    \mathbf{A} \mathbf{B} \mathbf{C} \mathbf{D} \mathbf{E} \mathbf{F} \mathbf{G}
         		\(\mathbf{A} \mathbf{B} \mathbf{C} \mathbf{D} \mathbf{E} \mathbf{F} \mathbf{G} \,\!\) 
    \mathbf{H} \mathbf{I} \mathbf{J} \mathbf{K} \mathbf{L} \mathbf{M}
         		\(\mathbf{H} \mathbf{I} \mathbf{J} \mathbf{K} \mathbf{L} \mathbf{M} \,\!\) 
    \mathbf{N} \mathbf{O} \mathbf{P} \mathbf{Q} \mathbf{R} \mathbf{S} \mathbf{T}
         		\(\mathbf{N} \mathbf{O} \mathbf{P} \mathbf{Q} \mathbf{R} \mathbf{S} \mathbf{T} \,\!\) 
    \mathbf{U} \mathbf{V} \mathbf{W} \mathbf{X} \mathbf{Y} \mathbf{Z}
         		\(\mathbf{U} \mathbf{V} \mathbf{W} \mathbf{X} \mathbf{Y} \mathbf{Z} \,\!\) 
    \mathbf{a} \mathbf{b} \mathbf{c} \mathbf{d} \mathbf{e} \mathbf{f} \mathbf{g}
         		\(\mathbf{a} \mathbf{b} \mathbf{c} \mathbf{d} \mathbf{e} \mathbf{f} \mathbf{g} \,\!\) 
    \mathbf{h} \mathbf{i} \mathbf{j} \mathbf{k} \mathbf{l} \mathbf{m}
         		\(\mathbf{h} \mathbf{i} \mathbf{j} \mathbf{k} \mathbf{l} \mathbf{m} \,\!\) 
    \mathbf{n} \mathbf{o} \mathbf{p} \mathbf{q} \mathbf{r} \mathbf{s} \mathbf{t}
         		\(\mathbf{n} \mathbf{o} \mathbf{p} \mathbf{q} \mathbf{r} \mathbf{s} \mathbf{t} \,\!\) 
    \mathbf{u} \mathbf{v} \mathbf{w} \mathbf{x} \mathbf{y} \mathbf{z}
         		\(\mathbf{u} \mathbf{v} \mathbf{w} \mathbf{x} \mathbf{y} \mathbf{z} \,\!\) 
    \mathbf{0} \mathbf{1} \mathbf{2} \mathbf{3} \mathbf{4}
         		\(\mathbf{0} \mathbf{1} \mathbf{2} \mathbf{3} \mathbf{4} \,\!\) 
    \mathbf{5} \mathbf{6} \mathbf{7} \mathbf{8} \mathbf{9}
         		\(\mathbf{5} \mathbf{6} \mathbf{7} \mathbf{8} \mathbf{9}\,\!\)
    Boldface (greek) 
    \boldsymbol{\Alpha} \boldsymbol{\Beta} \boldsymbol{\Gamma} \boldsymbol{\Delta} \boldsymbol{\Epsilon} \boldsymbol{\Zeta}
         		\(\boldsymbol{\Alpha} \boldsymbol{\Beta} \boldsymbol{\Gamma} \boldsymbol{\Delta} \boldsymbol{\Epsilon} \boldsymbol{\Zeta} \,\!\) 
    \boldsymbol{\Eta} \boldsymbol{\Theta} \boldsymbol{\Iota} \boldsymbol{\Kappa} \boldsymbol{\Lambda} \boldsymbol{\Mu}
         		\(\boldsymbol{\Eta} \boldsymbol{\Theta} \boldsymbol{\Iota} \boldsymbol{\Kappa} \boldsymbol{\Lambda} \boldsymbol{\Mu}\,\!\) 
    \boldsymbol{\Nu} \boldsymbol{\Xi} \boldsymbol{\Pi} \boldsymbol{\Rho} \boldsymbol{\Sigma} \boldsymbol{\Tau}
         		\(\boldsymbol{\Nu} \boldsymbol{\Xi} \boldsymbol{\Pi} \boldsymbol{\Rho} \boldsymbol{\Sigma} \boldsymbol{\Tau}\,\!\) 
    \boldsymbol{\Upsilon} \boldsymbol{\Phi} \boldsymbol{\Chi} \boldsymbol{\Psi} \boldsymbol{\Omega}
         		\(\boldsymbol{\Upsilon} \boldsymbol{\Phi} \boldsymbol{\Chi} \boldsymbol{\Psi} \boldsymbol{\Omega}\,\!\) 
    \boldsymbol{\alpha} \boldsymbol{\beta} \boldsymbol{\gamma} \boldsymbol{\delta} \boldsymbol{\epsilon} \boldsymbol{\zeta}
         		\(\boldsymbol{\alpha} \boldsymbol{\beta} \boldsymbol{\gamma} \boldsymbol{\delta} \boldsymbol{\epsilon} \boldsymbol{\zeta}\,\!\) 
    \boldsymbol{\eta} \boldsymbol{\theta} \boldsymbol{\iota} \boldsymbol{\kappa} \boldsymbol{\lambda} \boldsymbol{\mu}
         		\(\boldsymbol{\eta} \boldsymbol{\theta} \boldsymbol{\iota} \boldsymbol{\kappa} \boldsymbol{\lambda} \boldsymbol{\mu}\,\!\) 
    \boldsymbol{\nu} \boldsymbol{\xi} \boldsymbol{\pi} \boldsymbol{\rho} \boldsymbol{\sigma} \boldsymbol{\tau}
         		\(\boldsymbol{\nu} \boldsymbol{\xi} \boldsymbol{\pi} \boldsymbol{\rho} \boldsymbol{\sigma} \boldsymbol{\tau}\,\!\) 
    \boldsymbol{\upsilon} \boldsymbol{\phi} \boldsymbol{\chi} \boldsymbol{\psi} \boldsymbol{\omega}
         		\(\boldsymbol{\upsilon} \boldsymbol{\phi} \boldsymbol{\chi} \boldsymbol{\psi} \boldsymbol{\omega}\,\!\) 
    \boldsymbol{\varepsilon} \boldsymbol{\digamma} \boldsymbol{\vartheta} \boldsymbol{\varkappa}
         		\(\boldsymbol{\varepsilon} \boldsymbol{\digamma} \boldsymbol{\vartheta} \boldsymbol{\varkappa} \,\!\) 
    \boldsymbol{\varpi} \boldsymbol{\varrho} \boldsymbol{\varsigma} \boldsymbol{\varphi}
         		\(\boldsymbol{\varpi} \boldsymbol{\varrho} \boldsymbol{\varsigma} \boldsymbol{\varphi}\,\!\)
    Italics 
    \mathit{A} \mathit{B} \mathit{C} \mathit{D} \mathit{E} \mathit{F} \mathit{G}
         		\(\mathit{A} \mathit{B} \mathit{C} \mathit{D} \mathit{E} \mathit{F} \mathit{G} \,\!\) 
    \mathit{H} \mathit{I} \mathit{J} \mathit{K} \mathit{L} \mathit{M}
         		\(\mathit{H} \mathit{I} \mathit{J} \mathit{K} \mathit{L} \mathit{M} \,\!\) 
    \mathit{N} \mathit{O} \mathit{P} \mathit{Q} \mathit{R} \mathit{S} \mathit{T}
         		\(\mathit{N} \mathit{O} \mathit{P} \mathit{Q} \mathit{R} \mathit{S} \mathit{T} \,\!\) 
    \mathit{U} \mathit{V} \mathit{W} \mathit{X} \mathit{Y} \mathit{Z}
         		\(\mathit{U} \mathit{V} \mathit{W} \mathit{X} \mathit{Y} \mathit{Z} \,\!\) 
    \mathit{a} \mathit{b} \mathit{c} \mathit{d} \mathit{e} \mathit{f} \mathit{g}
         		\(\mathit{a} \mathit{b} \mathit{c} \mathit{d} \mathit{e} \mathit{f} \mathit{g} \,\!\) 
    \mathit{h} \mathit{i} \mathit{j} \mathit{k} \mathit{l} \mathit{m}
         		\(\mathit{h} \mathit{i} \mathit{j} \mathit{k} \mathit{l} \mathit{m} \,\!\) 
    \mathit{n} \mathit{o} \mathit{p} \mathit{q} \mathit{r} \mathit{s} \mathit{t}
         		\(\mathit{n} \mathit{o} \mathit{p} \mathit{q} \mathit{r} \mathit{s} \mathit{t} \,\!\) 
    \mathit{u} \mathit{v} \mathit{w} \mathit{x} \mathit{y} \mathit{z}
         		\(\mathit{u} \mathit{v} \mathit{w} \mathit{x} \mathit{y} \mathit{z} \,\!\) 
    \mathit{0} \mathit{1} \mathit{2} \mathit{3} \mathit{4}
         		\(\mathit{0} \mathit{1} \mathit{2} \mathit{3} \mathit{4} \,\!\) 
    \mathit{5} \mathit{6} \mathit{7} \mathit{8} \mathit{9}
         		\(\mathit{5} \mathit{6} \mathit{7} \mathit{8} \mathit{9}\,\!\)
    Roman typeface 
    \mathrm{A} \mathrm{B} \mathrm{C} \mathrm{D} \mathrm{E} \mathrm{F} \mathrm{G}
         		\(\mathrm{A} \mathrm{B} \mathrm{C} \mathrm{D} \mathrm{E} \mathrm{F} \mathrm{G} \,\!\) 
    \mathrm{H} \mathrm{I} \mathrm{J} \mathrm{K} \mathrm{L} \mathrm{M}
         		\(\mathrm{H} \mathrm{I} \mathrm{J} \mathrm{K} \mathrm{L} \mathrm{M} \,\!\) 
    \mathrm{N} \mathrm{O} \mathrm{P} \mathrm{Q} \mathrm{R} \mathrm{S} \mathrm{T}
         		\(\mathrm{N} \mathrm{O} \mathrm{P} \mathrm{Q} \mathrm{R} \mathrm{S} \mathrm{T} \,\!\) 
    \mathrm{U} \mathrm{V} \mathrm{W} \mathrm{X} \mathrm{Y} \mathrm{Z}
         		\(\mathrm{U} \mathrm{V} \mathrm{W} \mathrm{X} \mathrm{Y} \mathrm{Z} \,\!\) 
    \mathrm{a} \mathrm{b} \mathrm{c} \mathrm{d} \mathrm{e} \mathrm{f} \mathrm{g}
         		\(\mathrm{a} \mathrm{b} \mathrm{c} \mathrm{d} \mathrm{e} \mathrm{f} \mathrm{g}\,\!\) 
    \mathrm{h} \mathrm{i} \mathrm{j} \mathrm{k} \mathrm{l} \mathrm{m}
         		\(\mathrm{h} \mathrm{i} \mathrm{j} \mathrm{k} \mathrm{l} \mathrm{m} \,\!\) 
    \mathrm{n} \mathrm{o} \mathrm{p} \mathrm{q} \mathrm{r} \mathrm{s} \mathrm{t}
         		\(\mathrm{n} \mathrm{o} \mathrm{p} \mathrm{q} \mathrm{r} \mathrm{s} \mathrm{t} \,\!\) 
    \mathrm{u} \mathrm{v} \mathrm{w} \mathrm{x} \mathrm{y} \mathrm{z}
         		\(\mathrm{u} \mathrm{v} \mathrm{w} \mathrm{x} \mathrm{y} \mathrm{z} \,\!\) 
    \mathrm{0} \mathrm{1} \mathrm{2} \mathrm{3} \mathrm{4}
         		\(\mathrm{0} \mathrm{1} \mathrm{2} \mathrm{3} \mathrm{4} \,\!\) 
    \mathrm{5} \mathrm{6} \mathrm{7} \mathrm{8} \mathrm{9}
         		\(\mathrm{5} \mathrm{6} \mathrm{7} \mathrm{8} \mathrm{9}\,\!\)
    Fraktur typeface 
    \mathfrak{A} \mathfrak{B} \mathfrak{C} \mathfrak{D} \mathfrak{E} \mathfrak{F} \mathfrak{G}
         		\(\mathfrak{A} \mathfrak{B} \mathfrak{C} \mathfrak{D} \mathfrak{E} \mathfrak{F} \mathfrak{G} \,\!\) 
    \mathfrak{H} \mathfrak{I} \mathfrak{J} \mathfrak{K} \mathfrak{L} \mathfrak{M}
         		\(\mathfrak{H} \mathfrak{I} \mathfrak{J} \mathfrak{K} \mathfrak{L} \mathfrak{M} \,\!\) 
    \mathfrak{N} \mathfrak{O} \mathfrak{P} \mathfrak{Q} \mathfrak{R} \mathfrak{S} \mathfrak{T}
         		\(\mathfrak{N} \mathfrak{O} \mathfrak{P} \mathfrak{Q} \mathfrak{R} \mathfrak{S} \mathfrak{T} \,\!\) 
    \mathfrak{U} \mathfrak{V} \mathfrak{W} \mathfrak{X} \mathfrak{Y} \mathfrak{Z}
         		\(\mathfrak{U} \mathfrak{V} \mathfrak{W} \mathfrak{X} \mathfrak{Y} \mathfrak{Z} \,\!\) 
    \mathfrak{a} \mathfrak{b} \mathfrak{c} \mathfrak{d} \mathfrak{e} \mathfrak{f} \mathfrak{g}
         		\(\mathfrak{a} \mathfrak{b} \mathfrak{c} \mathfrak{d} \mathfrak{e} \mathfrak{f} \mathfrak{g} \,\!\) 
    \mathfrak{h} \mathfrak{i} \mathfrak{j} \mathfrak{k} \mathfrak{l} \mathfrak{m}
         		\(\mathfrak{h} \mathfrak{i} \mathfrak{j} \mathfrak{k} \mathfrak{l} \mathfrak{m} \,\!\) 
    \mathfrak{n} \mathfrak{o} \mathfrak{p} \mathfrak{q} \mathfrak{r} \mathfrak{s} \mathfrak{t}
         		\(\mathfrak{n} \mathfrak{o} \mathfrak{p} \mathfrak{q} \mathfrak{r} \mathfrak{s} \mathfrak{t} \,\!\) 
    \mathfrak{u} \mathfrak{v} \mathfrak{w} \mathfrak{x} \mathfrak{y} \mathfrak{z}
         		\(\mathfrak{u} \mathfrak{v} \mathfrak{w} \mathfrak{x} \mathfrak{y} \mathfrak{z} \,\!\) 
    \mathfrak{0} \mathfrak{1} \mathfrak{2} \mathfrak{3} \mathfrak{4}
         		\(\mathfrak{0} \mathfrak{1} \mathfrak{2} \mathfrak{3} \mathfrak{4} \,\!\) 
    \mathfrak{5} \mathfrak{6} \mathfrak{7} \mathfrak{8} \mathfrak{9}
         		\(\mathfrak{5} \mathfrak{6} \mathfrak{7} \mathfrak{8} \mathfrak{9}\,\!\)
    Calligraphy/Script 
    \mathcal{A} \mathcal{B} \mathcal{C} \mathcal{D} \mathcal{E} \mathcal{F} \mathcal{G}
         		\(\mathcal{A} \mathcal{B} \mathcal{C} \mathcal{D} \mathcal{E} \mathcal{F} \mathcal{G} \,\!\) 
    \mathcal{H} \mathcal{I} \mathcal{J} \mathcal{K} \mathcal{L} \mathcal{M}
         		\(\mathcal{H} \mathcal{I} \mathcal{J} \mathcal{K} \mathcal{L} \mathcal{M} \,\!\) 
    \mathcal{N} \mathcal{O} \mathcal{P} \mathcal{Q} \mathcal{R} \mathcal{S} \mathcal{T}
         		\(\mathcal{N} \mathcal{O} \mathcal{P} \mathcal{Q} \mathcal{R} \mathcal{S} \mathcal{T} \,\!\) 
    \mathcal{U} \mathcal{V} \mathcal{W} \mathcal{X} \mathcal{Y} \mathcal{Z}
         		\(\mathcal{U} \mathcal{V} \mathcal{W} \mathcal{X} \mathcal{Y} \mathcal{Z}\,\!\)
    Hebrew 
    \aleph \beth \gimel \daleth
         		\(\aleph \beth \gimel \daleth\,\!\)
    Feature Syntax How it looks rendered
    non-italicised characters \mbox{abc} \(\mbox{abc}\) \(\mbox{abc} \,\!\)
    mixed italics (bad) \mbox{if} n \mbox{is even} \(\mbox{if} n \mbox{is even}\) \(\mbox{if} n \mbox{is even} \,\!\)
    mixed italics (good) \mbox{if }n\mbox{ is even} \(\mbox{if }n\mbox{ is even}\) \(\mbox{if }n\mbox{ is even} \,\!\)
    mixed italics (more legible: ~ is a non-breaking space, while "\ " forces a space) \mbox{if}~n\ \mbox{is even} \(\mbox{if}~n\ \mbox{is even}\) \(\mbox{if}~n\ \mbox{is even} \,\!\)

    Parenthesizing big expressions, brackets, bars

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

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

    Feature Syntax How it looks rendered
    Parentheses \left ( \frac{a}{b} \right ) \(\left ( \frac{a}{b} \right )\)
    Brackets \left [ \frac{a}{b} \right ] \quad \left \lbrack \frac{a}{b} \right \rbrack \(\left [ \frac{a}{b} \right ] \quad \left \lbrack \frac{a}{b} \right \rbrack\)
    Braces \left \{ \frac{a}{b} \right \} \quad \left \lbrace \frac{a}{b} \right \rbrace \(\left \{ \frac{a}{b} \right \} \quad \left \lbrace \frac{a}{b} \right \rbrace\)
    Angle brackets \left \langle \frac{a}{b} \right \rangle \(\left \langle \frac{a}{b} \right \rangle\)
    Bars and double bars \left | \frac{a}{b} \right \vert \left \Vert \frac{c}{d} \right \| \(\left | \frac{a}{b} \right \vert \left \Vert \frac{c}{d} \right \|\)
    Floor and ceiling functions: \left \lfloor \frac{a}{b} \right \rfloor \left \lceil \frac{c}{d} \right \rceil \(\left \lfloor \frac{a}{b} \right \rfloor \left \lceil \frac{c}{d} \right \rceil\)
    Slashes and backslashes \left / \frac{a}{b} \right \backslash \(\left / \frac{a}{b} \right \backslash\)
    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 \(\left \uparrow \frac{a}{b} \right \downarrow \quad \left \Uparrow \frac{a}{b} \right \Downarrow \quad \left \updownarrow \frac{a}{b} \right \Updownarrow\)

    Delimiters can be mixed,
    as long as \left and \right match

    \left [ 0,1 \right )
    \left \langle \psi \right |

    \(\left [ 0,1 \right )\)
    \(\left \langle \psi \right |\)

    Use \left. and \right. if you don't
    want a delimiter to appear:    		 \left . \frac{A}{B} \right \} \to X \(\left . \frac{A}{B} \right \} \to X\)
    Size of the delimiters \big( \Big( \bigg( \Bigg( ... \Bigg] \bigg] \Big] \big]

    \(\big( \Big( \bigg( \Bigg( ... \Bigg] \bigg] \Big] \big]\)

    \big\{ \Big\{ \bigg\{ \Bigg\{ ... \Bigg\rangle \bigg\rangle \Big\rangle \big\rangle

    \(\big\{ \Big\{ \bigg\{ \Bigg\{ ... \Bigg\rangle \bigg\rangle \Big\rangle \big\rangle\)

    \big\| \Big\| \bigg\| \Bigg\| ... \Bigg| \bigg| \Big| \big| \(\big\| \Big\| \bigg\| \Bigg\| ... \Bigg| \bigg| \Big| \big|\)
    \big\lfloor \Big\lfloor \bigg\lfloor \Bigg\lfloor ... \Bigg\rceil \bigg\rceil \Big\rceil \big\rceil

    \(\big\lfloor \Big\lfloor \bigg\lfloor \Bigg\lfloor ... \Bigg\rceil \bigg\rceil \Big\rceil \big\rceil\)

    \big\uparrow \Big\uparrow \bigg\uparrow \Bigg\uparrow ... \Bigg\Downarrow \bigg\Downarrow \Big\Downarrow \big\Downarrow

    \(\big\uparrow \Big\uparrow \bigg\uparrow \Bigg\uparrow ... \Bigg\Downarrow \bigg\Downarrow \Big\Downarrow \big\Downarrow\)

    \big\updownarrow \Big\updownarrow \bigg\updownarrow \Bigg\updownarrow ... \Bigg\Updownarrow \bigg\Updownarrow \Big\Updownarrow \big\Updownarrow

    \(\big\updownarrow \Big\updownarrow \bigg\updownarrow \Bigg\updownarrow ... \Bigg\Updownarrow \bigg\Updownarrow \Big\Updownarrow \big\Updownarrow\)

    \big / \Big / \bigg / \Bigg / ... \Bigg\backslash \bigg\backslash \Big\backslash \big\backslash

    \(\big / \Big / \bigg / \Bigg / ... \Bigg\backslash \bigg\backslash \Big\backslash \big\backslash\)

    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 \(a \qquad b\)
    quad space a \quad b \(a \quad b\)
    text space a\ b \(a\ b\)
    text space without PNG conversion a \mbox{ } b \(a \mbox{ } b\)
    large space a\;b \(a\;b\)
    medium space a\>b [not supported]
    small space a\,b \(a\,b\)
    no space ab \(ab\,\)
    small negative space a\!b \(a\!b\)

    Align with normal text flow

    Due to the default css 

    img.tex { vertical-align: middle; }

    an inline expression like \(\int_{-N}^{N} e^x\, dx\) should look good.

    If you need to align it otherwise, use <font style="vertical-align:-100%;"><math>...</math></font> and play with the vertical-align argument until you get it right; however, how it looks may depend on the browser and the browser settings.

    Also note that if you rely on this workaround, if/when the rendering on the server gets fixed in future releases, as a result of this extra manual offset your formulae will suddenly be aligned incorrectly. So use it sparingly, if at all.

    Color

    Equations can use color:

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

    See here for all named colours supported by LaTeX.

    Note that color should not be used as the only way to identify something because color blind people may not be able to distinguish between the two colors.

    Examples

    Quadratic Polynomial

    \(ax^2 + bx + c = 0\)

<math>ax^2 + bx + c = 0</math>

    Quadratic Formula

    \(x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}\)

<math>x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}</math>

    Tall Parentheses and Fractions 

    \(2 = \left( \frac{\left(3-x\right) \times 2}{3-x} \right)\)

<math>2 = \left( \frac{\left(3-x\right) \times 2}{3-x} \right)</math>

    \(S_{new} = S_{old} + \frac{ \left( 5-T \right) ^2} {2}\)

<math>S_{new} = S_{old} + \frac{ \left( 5-T \right) ^2} {2}</math>

    Integrals

    \(\int_a^x \int_a^s f(y)\,dy\,ds = \int_a^x f(y)(x-y)\,dy\)

<math>\int_a^x \int_a^s f(y)\,dy\,ds = \int_a^x f(y)(x-y)\,dy</math>

    Summation

    \(\sum_{m=1}^\infty\sum_{n=1}^\infty\frac{m^2\,n}{3^m\left(m\,3^n+n\,3^m\right)}\)

    <math>\sum_{m=1}^\infty\sum_{n=1}^\infty\frac{m^2\,n}
{3^m\left(m\,3^n+n\,3^m\right)}</math>

    Differential Equation 

    \(u'' + p(x)u' + q(x)u=f(x),\quad x>a\)

<math>u'' + p(x)u' + q(x)u=f(x),\quad x>a</math>

    Complex numbers

    \(|\bar{z}| = |z|, |(\bar{z})^n| = |z|^n, \arg(z^n) = n \arg(z)\,\)

<math>|\bar{z}| = |z|, |(\bar{z})^n| = |z|^n, \arg(z^n) = n \arg(z)\,</math>

    Limits

    \(\lim_{z\rightarrow z_0} f(z)=f(z_0)\,\)

<math>\lim_{z\rightarrow z_0} f(z)=f(z_0)\,</math>

    Integral Equation

    \(\phi_n(\kappa) = \frac{1}{4\pi^2\kappa^2} \int_0^\infty \frac{\sin(\kappa R)}{\kappa R} \frac{\partial}{\partial R}\left[R^2\frac{\partial D_n(R)}{\partial R}\right]\,dR\)

<math>\phi_n(\kappa) = \frac{1}{4\pi^2\kappa^2} \int_0^\infty
\frac{\sin(\kappa R)}{\kappa R} \frac{\partial}{\partial R}\left[R^2\frac{\partial
D_n(R)}{\partial R}\right]\,dR</math>

    Example

    \(\phi_n(\kappa) = 0.033C_n^2\kappa^{-11/3},\quad \frac{1}{L_0}\ll\kappa\ll\frac{1}{l_0}\,\)

<math>\phi_n(\kappa) = 
0.033C_n^2\kappa^{-11/3},\quad \frac{1}{L_0}\ll\kappa\ll\frac{1}{l_0}\,</math>

    Continuation and cases

    \(f(x) = \begin{cases}1 & -1 \le x < 0 \\
 \frac{1}{2} & x = 0 \\ 1 - x^2 & 0 < x \le 1\end{cases}\)

<math>f(x) = \begin{cases}1 & -1 \le x < 0 \\
\frac{1}{2} & x = 0 \\ 1 - x^2 & 0 < x\le 1\end{cases}</math>

    Prefixed subscript

    \({}_pF_q(a_1,...,a_p;c_1,...,c_q;z) = \sum_{n=0}^\infty \frac{(a_1)_n\cdot\cdot\cdot(a_p)_n}{(c_1)_n\cdot\cdot\cdot(c_q)_n}\frac{z^n}{n!}\,\)

 <math>{}_pF_q(a_1,...,a_p;c_1,...,c_q;z) = \sum_{n=0}^\infty
\frac{(a_1)_n\cdot\cdot\cdot(a_p)_n}{(c_1)_n\cdot\cdot\cdot(c_q)_n}\frac{z^n}{n!}\,</math>

    Acknowledgement

    This page was modified from Wikipedia help page http://en.wikipedia.org/wiki/Help:Displaying_a_formula

    Bug reports

    Please, report bugs to the editor-in-chief.

    External links

    Retrieved from "http://www.scholarpedia.org/w/index.php?title=Help:Math&oldid=121246"
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