# Giới thiệu latex

###

latex là 1 chương trình dùng để format document. Nó là: ” document markup language and document preparation system for the TeX typesetting program. Within the typesetting system, its name is styled as ” (-wikipedia).

latex là một hệ thống soạn thảo rất phù hợp với việc tạo ra các tài liệu khoa học và toán học với chất lượng bản in rất cao.
Nó rất mạnh trong việc hiển thị các biểu thức toán học với những ký tự khó như Sigma, Alpha, Square, exponent...
Nó ra đời khoảng chục năm nay, nhưng mau chóng trở thành lạc hậu vì sự tiến triển không người của các Word Editor trên Linux hay Unix như StarOffice hay OpenOffice.

## Hàm, biểu tượng, ký tự đặc biệt

### 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{arsinh}\,r\,\operatorname{arcosh}\,s\,\operatorname{artanh}\,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` |
`\mid \; \nmid` |  |
### 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 \nexists \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} \overline{q} \to \And` |
`\lor \vee \bigvee \lnot \neg q \leftrightarrow` |
### 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 \parallel 45^\circ` |
### Arrows
`\leftarrow (or \gets) \rightarrow (or \to) \nleftarrow \nrightarrow \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` |
`\curvearrowleft \circlearrowleft \Lsh \upuparrows \rightrightarrows \rightleftarrows \Rrightarrow \rightarrowtail \looparrowright` |
`\curvearrowright \circlearrowright \Rsh \downdownarrows \leftleftarrows \leftrightarrows \Lleftarrow \leftarrowtail \looparrowleft` |
`\mapsto \longmapsto \hookrightarrow \hookleftarrow \multimap \leftrightsquigarrow \rightsquigarrow \twoheadrightarrow \twoheadleftarrow` |
### Special
`\And \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)
`\vartriangle \triangledown \lozenge \circledS \measuredangle \Bbbk \backprime \blacktriangle \blacktriangledown` |
`\blacksquare \blacklozenge \bigstar \sphericalangle \diagup \diagdown \dotplus \Cap \Cup \barwedge` |
`\veebar \doublebarwedge \boxminus \boxtimes \boxdot \boxplus \divideontimes \ltimes \rtimes \leftthreetimes` |
`\rightthreetimes \curlywedge \curlyvee \circleddash \circledast \circledcirc \centerdot \intercal \leqq \leqslant` |
`\eqslantless \lessapprox \approxeq \lessdot \lll \lessgtr \lesseqgtr \lesseqqgtr \doteqdot \risingdotseq` |
`\fallingdotseq \backsim \backsimeq \subseteqq \Subset \preccurlyeq \curlyeqprec \precsim \precapprox \vartriangleleft` |
`\Vvdash \bumpeq \Bumpeq \geqq \geqslant \eqslantgtr \gtrsim \gtrapprox \eqsim \gtrdot` |
`\ggg \gtrless \gtreqless \gtreqqless \eqcirc \circeq \triangleq \thicksim \thickapprox \supseteqq` |
`\Supset \succcurlyeq \curlyeqsucc \succsim \succapprox \vartriangleright \shortmid \shortparallel \between \pitchfork` |
`\varpropto \blacktriangleleft \therefore \backepsilon \blacktriangleright \because \nleqslant \nleqq \lneq \lneqq` |
`\lvertneqq \lnsim \lnapprox \nprec \npreceq \precneqq \precnsim \precnapprox \nsim \nshortmid` |
`\nvdash \nVdash \ntriangleleft \ntrianglelefteq \nsubseteq \nsubseteqq \varsubsetneq \subsetneqq \varsubsetneqq \ngtr` |
`\subsetneq` |
`\ngeqslant \ngeqq \gneq \gneqq \gvertneqq \gnsim \gnapprox \nsucc \nsucceq \succneqq` |
`\succnsim \succnapprox \ncong \nshortparallel \nparallel \nvDash \nVDash \ntriangleright \ntrianglerighteq \nsupseteq` |
`\nsupseteqq \varsupsetneq \supsetneqq \varsupsetneqq` |
`\jmath \surd \ast \uplus \diamond \bigtriangleup \bigtriangledown \ominus` |
`\oslash \odot \bigcirc \amalg \prec \succ \preceq \succeq` |
`\dashv \asymp \doteq \parallel` |
`\ulcorner \urcorner \llcorner \lrcorner` |

## Các biểu thức phức tạp:

### 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 without and with horizontal separation | `x_2^3` |  |
`{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` |
Sum in a fraction (default `\textstyle`) | `\frac{\sum_{k=1}^N k^2}{a}` |
Sum in a fraction (force `\displaystyle`) | `\frac{\displaystyle \sum_{k=1}^N k^2}{a}` |
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` |

### 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, at the expense of destroying correct spacing |
    <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}

### 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 )</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]/` |
`\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 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.

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` |
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}` |
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}` |
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` |

### Mixed text faces

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} |  |

##

##

## Examples

### Quadratic polynomial

    ax2 + bx + c = 0

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

### Quadratic polynomial (force PNG rendering)

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

### Quadratic formula

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

### Tall parentheses and fractions

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

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

### Integrals

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

### Summation

    <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

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

### Complex numbers

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

### Limits

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

### Integral equation

    <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

    <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

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

### Prefixed subscript

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

### Fraction and small fraction

    <math> \frac {a}{b}\  \tfrac {a}{b} </math>

### Area of a Quadrilateral

    <math>S=\frac{1}{2}dD\sin\alpha </math>

### Volume of a sphere-stand

    <math>V=\frac{1}{6}\pi h[3(r_1^2+r_2^2)+h^2]</math>

Retrieved from "http://en.wikipedia.org/wiki/Help:Displaying_a_formula"