Maths

Functions, symbols, special characters[επεξεργασία]

Subscripts, superscripts, integrals[επεξεργασία]

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

Fractions, matrices, multilines[επεξεργασία]

Feature	Syntax	How it looks rendered
Fractions	`\frac{2}{4}=0.5`	<math>\frac{2}{4}=0.5</math>
Small Fractions	`\tfrac{2}{4} = 0.5`	<math>\tfrac{2}{4} = 0.5</math>
Large (normal) Fractions	`\dfrac{2}{4} = 0.5`	<math>\dfrac{2}{4} = 0.5</math>
Large (nestled) Fractions	`\cfrac{2}{c + \cfrac{2}{d + \cfrac{2}{4}}} = a`	<math>\cfrac{2}{c + \cfrac{2}{d + \cfrac{2}{4}}} = a</math>
Binomial coefficients	`\binom{n}{k}`	<math>\binom{n}{k}</math>
Small Binomial coefficients	`\tbinom{n}{k}`	<math>\tbinom{n}{k}</math>
Large (normal) Binomial coefficients	`\dbinom{n}{k}`	<math>\dbinom{n}{k}</math>
Matrices	\begin{matrix} x & y \\ z & v \end{matrix}	<math>\begin{matrix} x & y \\ z & v \end{matrix}</math>
	\begin{vmatrix} x & y \\ z & v \end{vmatrix}	<math>\begin{vmatrix} x & y \\ z & v \end{vmatrix}</math>
	\begin{Vmatrix} x & y \\ z & v \end{Vmatrix}	<math>\begin{Vmatrix} x & y \\ z & v \end{Vmatrix}</math>
	\begin{bmatrix} 0 & \cdots & 0 \\ \vdots & \ddots & \vdots \\ 0 & \cdots & 0 \end{bmatrix}	<math>\begin{bmatrix} 0 & \cdots & 0 \\ \vdots & \ddots & \vdots \\ 0 & \cdots & 0\end{bmatrix} </math>
	\begin{Bmatrix} x & y \\ z & v \end{Bmatrix}	<math>\begin{Bmatrix} x & y \\ z & v \end{Bmatrix}</math>
	\begin{pmatrix} x & y \\ z & v \end{pmatrix}	<math>\begin{pmatrix} x & y \\ z & v \end{pmatrix}</math>
	\bigl( \begin{smallmatrix} a&b\\ c&d \end{smallmatrix} \bigr)	<math> \bigl( \begin{smallmatrix} a&b\\ c&d \end{smallmatrix} \bigr) </math>
Case distinctions	f(n) = \begin{cases} n/2, & \mbox{if }n\mbox{ is even} \\ 3n+1, & \mbox{if }n\mbox{ is odd} \end{cases}	<math>f(n) = \begin{cases} n/2, & \mbox{if }n\mbox{ is even} \\ 3n+1, & \mbox{if }n\mbox{ is odd} \end{cases} </math>
Multiline equations	\begin{align} f(x) & = (a+b)^2 \\ & = a^2+2ab+b^2 \\ \end{align}	<math> \begin{align} f(x) & = (a+b)^2 \\ & = a^2+2ab+b^2 \\ \end{align} </math>
Multiline equations	\begin{alignat}{2} f(x) & = (a-b)^2 \\ & = a^2-2ab+b^2 \\ \end{alignat}	<math> \begin{alignat}{2} f(x) & = (a-b)^2 \\ & = a^2-2ab+b^2 \\ \end{alignat} </math>
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}	<math>\begin{array}{lcl} z & = & a \\ f(x,y,z) & = & x + y + z \end{array}</math>
Multiline equations (more)	\begin{array}{lcr} z & = & a \\ f(x,y,z) & = & x + y + z \end{array}	<math>\begin{array}{lcr} z & = & a \\ f(x,y,z) & = & x + y + z \end{array}</math>
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>	<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}	<math>\begin{cases} 3x + 5y + z \\ 7x - 2y + 4z \\ -6x + 3y + 2z \end{cases}</math>

Alphabets and typefaces[επεξεργασία]

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

Parenthesizing big expressions, brackets, bars[επεξεργασία]

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

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

Spacing[επεξεργασία]

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

Align with normal text flow[επεξεργασία]

Due to the default css

img.tex { vertical-align: middle; }

an inline expression like <math>\int_{-N}^{N} e^x\, dx = 2 \sinh N</math> 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.

Forced PNG rendering[επεξεργασία]

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}	<math>a^{c+2}</math>
a^{c+2} \,	<math>a^{c+2} \,</math>
a^{\,\!c+2}	<math>a^{\,\!c+2}</math>
a^{b^{c+2}}	<math>a^{b^{c+2}}</math> (WRONG with option "HTML if possible or else PNG"!)
a^{b^{c+2}} \,	<math>a^{b^{c+2}} \,</math> (WRONG with option "HTML if possible or else PNG"!)
a^{b^{c+2}}\approx 5	<math>a^{b^{c+2}}\approx 5</math> (due to "<math>\approx</math>" correctly displayed, no code "\,\!" needed)
a^{b^{\,\!c+2}}	<math>a^{b^{\,\!c+2}}</math>
\int_{-N}^{N} e^x\, dx	<math>\int_{-N}^{N} e^x\, dx</math>

This has been tested with most of the formulae on this page, and seems to work perfectly.

You might want to include a comment in the HTML so people don't "correct" the formula by removing it:

Color[επεξεργασία]

Equations can use color:

{\color{Blue}x^2}+{\color{Brown}2x}-{\color{OliveGreen}1}
<math>{\color{Blue}x^2}+{\color{Brown}2x}-{\color{OliveGreen}1}</math>

x_{1,2}=\frac{-b\pm\sqrt{\color{Red}b^2-4ac}}{2a}
<math>x_{1,2}=\frac{-b\pm\sqrt{\color{Red}b^2-4ac}}{2a}</math>

See here for all named colours supported by LaTeX.

Examples[επεξεργασία]

Quadratic Polynomial[επεξεργασία]

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

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

Quadratic Polynomial (Force PNG Rendering)[επεξεργασία]

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

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

Quadratic Formula[επεξεργασία]

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

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

Tall Parentheses and Fractions[επεξεργασία]

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

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

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

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

Integrals[επεξεργασία]

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

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

Summation[επεξεργασία]

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

<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[επεξεργασία]

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

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

Complex numbers[επεξεργασία]

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

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

Limits[επεξεργασία]

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

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

Integral Equation[επεξεργασία]

<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>

<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[επεξεργασία]

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

<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[επεξεργασία]

<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>

<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[επεξεργασία]

<math>{}_pF_q(a_1,\dots,a_p;c_1,\dots,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>

 <math>{}_pF_q(a_1,\dots,a_p;c_1,\dots,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>

Maths

Περιεχόμενα

Functions, symbols, special characters[επεξεργασία]

Accents/Diacritics

Standard functions

Modular arithmetic

Derivatives

Sets

Operators

Logic

Root

Relations

Geometric

Arrows

Special

Unsorted (new stuff)