20060701

From QED

< User:Peak | math(Link to this page as [[User:Peak/math/20060701]])
Jump to: navigation, search

This is Permalink11px.gif[1] from July 1, 2006.

Contents

Functions, symbols, special characters

Feature Syntax How it looks rendered
Accents/Diacritics 
\acute{a} \quad \grave{a} \quad \hat{a}
\tilde{a} \quad \breve{a} \quad \check{a} \quad \bar{a}
\ddot{a} \quad \dot{a}
 \acute{a} \quad \grave{a} \quad \hat{a}

\tilde{a} \quad \breve{a} \quad \check{a} \quad \bar{a}
\ddot{a} \quad \dot{a}

Std. functions (good) 
\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 \ \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 \ \deg x \ \gcd x \ \Pr x
\det x \ \hom x \ \arg x \ \dim x
 \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 \ \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 \ \deg x \ \gcd x \ \Pr x
\det x \ \hom x \ \arg x \ \dim x

Std. functions (wrong) 
sin x + ln y + sgn z
 sin x + ln y + sgn z\,\!
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

(Square symbols may not work for some wikis) 

\forall \; \exists \; \empty \; \emptyset \; \varnothing
\in \ni \not\in \notin \subset \subseteq
\supset \supseteq \cap \bigcap \cup \bigcup \biguplus
\setminus \; \smallsetminus
 \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
 \sqsubset \sqsubseteq \sqsupset \sqsupseteq

\sqcap \sqcup \bigsqcup

Operators 
+ \; \oplus \; \bigoplus \; \pm \; \mp \; -
\times \; \otimes \; \bigotimes 
\cdot \; \circ \; \bullet \; \bigodot \; \star \; *
/ \; \div \; \begin{matrix} \frac{1}{2} \end{matrix}
 + \; \oplus \; \bigoplus \; \pm \; \mp \; -

\times \; \otimes \; \bigotimes
\cdot \; \circ \; \bullet \; \bigodot \; \star \; *
/ \; \div \; \begin{matrix} \frac{1}{2} \end{matrix}

Logic 
p \land \wedge \; \bigwedge \; \bar{q} \to p
\lor \; \vee \; \bigvee \; \lnot \; \neg q
 p \land \wedge \; \bigwedge \; \bar{q} \to p

\lor \; \vee \; \bigvee \; \lnot \; \neg q

Root 
\sqrt{2}\approx 1.4
 \sqrt{2}\approx 1.4 
\sqrt[n]{x}
 \sqrt[n]{x}
Relations 
\sim \; \approx \; \simeq \; \cong \; \dot=
\le \; < \; \ll \; \gg \; \ge >
\equiv \; \not\equiv \; \ne \mbox{or} \neq \; \propto
 \sim \; \approx \; \simeq \; \cong \; \dot=

\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

(Harpoons may not work for some wikis) 

\leftarrow \; \gets \; \rightarrow \; \to \; \not\to
\leftrightarrow \; \longleftarrow \; \longrightarrow
\mapsto \; \longmapsto
\hookrightarrow \; \hookleftarrow
\nearrow \; \searrow \; \swarrow \; \nwarrow
\uparrow \; \downarrow \; \updownarrow
 \leftarrow \; \gets \; \rightarrow \; \to \; \not\to

\leftrightarrow \; \longleftarrow \; \longrightarrow
\mapsto \; \longmapsto
\hookrightarrow \; \hookleftarrow
\nearrow \; \searrow \; \swarrow \; \nwarrow
\uparrow \; \downarrow \; \updownarrow 

\rightharpoonup \; \rightharpoondown 
\; \leftharpoonup \; \leftharpoondown 
\; \upharpoonleft \; \upharpoonright 
\; \downharpoonleft \; \downharpoonright
 \rightharpoonup \; \rightharpoondown \; \leftharpoonup \; \leftharpoondown \; \upharpoonleft \; \upharpoonright \; \downharpoonleft \; \downharpoonright 
\Leftarrow \; \Rightarrow \; \Leftrightarrow
\Longleftarrow \; \Longrightarrow
\Longleftrightarrow (or \iff)
\Uparrow \; \Downarrow \; \Updownarrow
 \Leftarrow \; \Rightarrow \; \Leftrightarrow

\Longleftarrow \; \Longrightarrow
\Longleftrightarrow (or \iff)
\Uparrow \; \Downarrow \; \Updownarrow

Special 
\eth \; \S \; \P \; \% \; \dagger \; \ddagger
\ldots \smile \frown \wr
 \eth \; \S \; \P \; \% \; \dagger \; \ddagger

\ldots \; \smile \frown \wr 

\triangleleft \triangleright \infty \bot \top
\vdash \vDash \Vdash \models \lVert \rVert
 \triangleleft \triangleright \infty \bot \top

\vdash \vDash \Vdash \models \lVert \rVert 

\imath \; \hbar \; \ell \; \mho \; \Finv
\Re \; \Im \; \wp \; \complement
 \imath \; \hbar \; \ell \; \mho \; \Finv

\Re \; \Im \; \wp \; \complement 

\diamondsuit \; \heartsuit \; \clubsuit \; \spadesuit
\Game \; \flat \; \natural \; \sharp
 \diamondsuit \; \heartsuit \; \clubsuit \; \spadesuit

\Game \; \flat \; \natural \; \sharp

Lowercase \mathcal has some extras 
\mathcal{5} \; \mathcal{abcde \; pqs}
 \mathcal{5} \; \mathcal{abcde \; pqs}

Subscripts, superscripts, integrals

FeatureSyntaxHow it looks rendered
HTMLPNG
Superscript
a^2
a2a^2 \,\!
Subscript
a_2
a2a_2 \,\!
Grouping
a^{2+2}
a2 + 2a^{2+2}\,\! 
a_{i,j}
ai,ja_{i,j}\,\!
Combining sub & super
x_2^3
x_2^3
Preceding sub & super
{}_1^2\!X_3^4
{}_1^2\!X_3^4
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\primex\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
\begin{matrix} 5050 \\ \overbrace{ 1+2+\cdots+100 } \end{matrix}
\begin{matrix} 5050 \\ \overbrace{ 1+2+\cdots+100 } \end{matrix}
Underbraces
\begin{matrix} \underbrace{ a+b+\cdots+z } \\ 26 \end{matrix}
\begin{matrix} \underbrace{ a+b+\cdots+z } \\ 26 \end{matrix}
Sum
\sum_{k=1}^N k^2
\sum_{k=1}^N k^2
Sum (force \textstyle)
\begin{matrix} \sum_{k=1}^N k^2 \end{matrix}
\begin{matrix} \sum_{k=1}^N k^2 \end{matrix}
Product
\prod_{i=1}^N x_i
\prod_{i=1}^N x_i
Product (force \textstyle)
\begin{matrix} \prod_{i=1}^N x_i \end{matrix}
\begin{matrix} \prod_{i=1}^N x_i \end{matrix}
Coproduct
\coprod_{i=1}^N x_i
\coprod_{i=1}^N x_i
Coproduct (force \textstyle)
\begin{matrix} \coprod_{i=1}^N x_i \end{matrix}
\begin{matrix} \coprod_{i=1}^N x_i \end{matrix}
Limit
\lim_{n \to \infty}x_n
\lim_{n \to \infty}x_n
Limit (force \textstyle)
\begin{matrix} \lim_{n \to \infty}x_n \end{matrix}
\begin{matrix} \lim_{n \to \infty}x_n \end{matrix}
Integral
\int_{-N}^{N} e^x\, dx
\int_{-N}^{N} e^x\, dx
Integral (force \textstyle)
\begin{matrix} \int_{-N}^{N} e^x\, dx \end{matrix}
\begin{matrix} \int_{-N}^{N} e^x\, dx \end{matrix}
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 or {2 \over 4}=0.5 \frac{2}{4}=0.5
Small Fractions (force \textstyle) \begin{matrix} \frac{2}{4} \end{matrix} = 0.5 \begin{matrix} \frac{2}{4} \end{matrix} = 0.5
Binomial coefficients {n \choose k} {n \choose k}
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 \begin{matrix}f(n+1) & = & (n+1)^2 \\ \ & = & n^2 + 2n + 1 \end{matrix} \begin{matrix}f(n+1) & = & (n+1)^2 \\ \ & = & n^2 + 2n + 1 \end{matrix}
Alternative multiline equations (using tables) 

{| border="0" cellpadding="0" cellspacing="0"
|-
|<math>f(n+1)</math>
|<math>=(n+1)^2</math>
|-
|
|<math>=n^2 + 2n + 1</math>
|}
f(n+1) \,\! =(n+1)^2 \,\!
=n^2 + 2n + 1 \,\!
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

Feature Syntax How it looks rendered
Greek alphabet
(Note the lack of omicron; note also that several upper case Greek letters are rendered identically to the corresponding Roman ones)

\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

\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 \mathbb{N}\ \mathbb{Z}\ \mathbb{D}\ \mathbb{Q}\ \mathbb{R}\ \mathbb{C}\ \mathbb{H} \mathbb{N}\ \mathbb{Z}\ \mathbb{D}\ \mathbb{Q}\ \mathbb{R}\ \mathbb{C}\ \mathbb{H}
boldface (vectors) \mathbf{x}\cdot\mathbf{y} = 0 \mathbf{x}\cdot\mathbf{y} = 0
boldface (greek) \boldsymbol{\alpha} + \boldsymbol{\beta} + \boldsymbol{\gamma} \boldsymbol{\alpha} + \boldsymbol{\beta} + \boldsymbol{\gamma}
italics \mathit{ABCDE abcde 1234} \mathit{ABCDE abcde 1234}\,\!
Roman typeface \mathrm{ABCDE abcde 1234} \mathrm{ABCDE abcde 1234}\,\!
Fraktur typeface \mathfrak{ABCDE abcde 1234} \mathfrak{ABCDE abcde 1234}
Calligraphy/Script \mathcal{ABCDE abcde 1234} \mathcal{ABCDE abcde 1234}
Hebrew \aleph \beth \gimel \daleth \aleph\ \beth\ \gimel\ \daleth
non-italicised characters \mbox{abc} abc \mbox{abc} \,\!
mixed italics (bad) \mbox{if} n \mbox{is even} ifnis even \mbox{if} n \mbox{is even} \,\!
mixed italics (good) \mbox{if }n\mbox{ is even} if n 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 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.

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


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:

<!-- The \,\! is to keep the formula rendered as PNG instead of HTML. Please don't remove it.-->

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}

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. See en:Wikipedia:Manual of Style#Formatting issues.

Examples

Quadratic Polynomial

ax2 + bx + c = 0

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

Quadratic Polynomial (Force PNG Rendering)

ax^2 + bx + c = 0\,

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

Quadratic Formula

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

<math>x_{1,2}=\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>
Retrieved from "http://qed.princeton.edu/main/User:Peak/math/20060701"
Personal tools