Help:Formula

From Highland Terrace Neighborhood

Referencing

Formatting

Organizing

Fixing mistakes and vandalism

Saving effort

Communicating

Special characters

Extensions

WikiHiero syntax — warning: lots of images! (for Egyptian hieroglyphs)
EasyTimeline syntax

Frequently Asked Questions

[edit]

MediaWiki and TeX

MediaWiki uses a subset of TeX markup (including some extensions from LaTeX and AMSLaTeX) for mathematical formulae. It generates either PNG images or simple HTML markup, depending on user preferences and the complexity of the expression. In the future, as more browsers are smarter, it will be able to generate enhanced HTML or even MathML in many cases.

More precisely, MediaWiki filters the markup through Texvc, which in turn passes the commands to TeX for the actual rendering. Thus, only a limited part of the full TeX language is supported; see below for details.

[edit]

Syntax

Math markup goes inside <math> ... </math>. The edit toolbar has a button for this.

Similarly to HTML, in TeX extra spaces and newlines are ignored.

MediaWiki templates, variables and parameters cannot be used within math tags, see m:Template talk:Demo of attempt to use parameters within TeX.

[edit]

Rendering

The PNG images are black on white (not transparent). These colors, as well as font sizes and types, are independent of browser settings or CSS. Font sizes and types will often deviate from what HTML renders. Vertical alignment with the surrounding text can also be a problem. The css selector of the images is img.tex.

It should be pointed out that most of these shortcomings have been addressed by Maynard Handley, but have not been released yet.

The alt attribute of the PNG images (the text that is displayed if your browser can't display images; Internet Explorer shows it up in the hover box) is the wikitext that produced them, excluding the <math> and </math>.

Apart from function and operator names, as is customary in mathematics for variables, letters are in italics; digits are not. For other text, (like variable labels) to avoid being rendered in italics like variables, use \mbox or \mathrm. For example, <math>\mbox{abc}</math> gives Failed to parse (Can't write to or create math temp directory): \mbox{abc} .

[edit]

TeX vs HTML

Before introducing TeX markup for producing special characters, it should be noted that, as this comparison table shows, sometimes similar results can be achieved in HTML (see Help:Special characters).

TeX Syntax (forcing PNG)	TeX Rendering	HTML Syntax	HTML Rendering
`<math>\alpha\,</math>`	Failed to parse (Can't write to or create math temp directory): \alpha\,	`α`	α
`<math>\sqrt{2}</math>`	Failed to parse (Can't write to or create math temp directory): \sqrt{2}	`√2`	√2
`<math>\sqrt{1-e^2}</math>`	Failed to parse (Can't write to or create math temp directory): \sqrt{1-e^2}	`√(1-''e''²)`	√(1-e²)

The use of HTML instead of TeX is still under discussion. The arguments either way can be summarised as follows.

[edit]

Pros of HTML

In-line HTML formulae always align properly with the rest of the HTML text.
The formula's background, font size and face match the rest of HTML contents and the appearence respects CSS and browser settings.

[edit]

Pros of TeX

TeX is semantically superior to HTML. In TeX, "<math>x</math>" means "mathematical variable Failed to parse (Can't write to or create math temp directory): x

", whereas in HTML "x" could mean anything. Information has irremediably been lost.

TeX has been specifically designed for typesetting formulae, so input is easier and more natural, and output is more aesthetically pleasing. Also anybody who has written mathematics at a professional level is already familiar with TeX.
One consequence of point 1 is that TeX can be transformed in HTML, but not vice-versa. This means that on the server side we can always transform a formula, based on its complexity and location within the text, user preferences, type of browser, etc. Therefore, where possible, all the benefits of HTML can be retained, together with the benefits of TeX. It's true that the current situation is not ideal, but that's not a good reason to drop information/contents. It's more a reason to help improve the situation.
When writing in TeX, editors need not worry about whether this or that version of this or that browser supports this or that HTML entity. The burden of these decisions is put on the server. This doesn't hold for HTML formulae, which can easily end up being rendered wrongly or differently from the editor's intentions on a different browser.

[edit]

Functions, symbols, special characters

[edit]

Subscripts, superscripts, integrals

Feature	Syntax	How it looks rendered
Feature	Syntax	HTML	PNG
Superscript	a^2	Failed to parse (Can't write to or create math temp directory): a^2	Failed to parse (Can't write to or create math temp directory): a^2 \,\!
Subscript	a_2	Failed to parse (Can't write to or create math temp directory): a_2	Failed to parse (Can't write to or create math temp directory): a_2 \,\!
Grouping	a^{2+2}	Failed to parse (Can't write to or create math temp directory): a^{2+2}	Failed to parse (Can't write to or create math temp directory): a^{2+2}\,\!
Grouping	a_{i,j}	Failed to parse (Can't write to or create math temp directory): a_{i,j}	Failed to parse (Can't write to or create math temp directory): a_{i,j}\,\!
Combining sub & super	x_2^3	Failed to parse (Can't write to or create math temp directory): x_2^3
Preceding sub & super	{}_1^2\!X_3^4	Failed to parse (Can't write to or create math temp directory): {}_1^2\!X_3^4
Derivative (forced PNG)	x', y'', f', f''\!		Failed to parse (Can't write to or create math temp directory): x', y'', f', f''\!
Derivative (f in italics may overlap primes in HTML)	x', y'', f', f''	Failed to parse (Can't write to or create math temp directory): x', y'', f', f''	Failed to parse (Can't write to or create math temp directory): x', y'', f', f''\!
Derivative (wrong in HTML)	x^\prime, y^{\prime\prime}	Failed to parse (Can't write to or create math temp directory): x^\prime, y^{\prime\prime}	Failed to parse (Can't write to or create math temp directory): x^\prime, y^{\prime\prime}\,\!
Derivative (wrong in PNG)	x\prime, y\prime\prime	Failed to parse (Can't write to or create math temp directory): x\prime, y\prime\prime	Failed to parse (Can't write to or create math temp directory): x\prime, y\prime\prime\,\!
Derivative dots	\dot{x}, \ddot{x}	Failed to parse (Can't write to or create math temp directory): \dot{x}, \ddot{x}
Underlines, overlines, vectors	\hat a \ \bar b \ \vec c	Failed to parse (Can't write to or create math temp directory): \hat a \ \bar b \ \vec c
	\overrightarrow{a b} \ \overleftarrow{c d} \ \widehat{d e f}	Failed to parse (Can't write to or create math temp directory): \overrightarrow{a b} \ \overleftarrow{c d} \ \widehat{d e f}
	\overline{g h i} \ \underline{j k l}	Failed to parse (Can't write to or create math temp directory): \overline{g h i} \ \underline{j k l}
Overbraces	\begin{matrix} 5050 \ \overbrace{ 1+2+\cdots+100 } \end{matrix}	Failed to parse (Can't write to or create math temp directory): \begin{matrix} 5050 \ \overbrace{ 1+2+\cdots+100 } \end{matrix}
Underbraces	\begin{matrix} \underbrace{ a+b+\cdots+z } \ 26 \end{matrix}	Failed to parse (Can't write to or create math temp directory): \begin{matrix} \underbrace{ a+b+\cdots+z } \ 26 \end{matrix}
Sum	\sum_{k=1}^N k^2	Failed to parse (Can't write to or create math temp directory): \sum_{k=1}^N k^2
Sum (force `\textstyle`)	\begin{matrix} \sum_{k=1}^N k^2 \end{matrix}	Failed to parse (Can't write to or create math temp directory): \begin{matrix} \sum_{k=1}^N k^2 \end{matrix}
Product	\prod_{i=1}^N x_i	Failed to parse (Can't write to or create math temp directory): \prod_{i=1}^N x_i
Product (force `\textstyle`)	\begin{matrix} \prod_{i=1}^N x_i \end{matrix}	Failed to parse (Can't write to or create math temp directory): \begin{matrix} \prod_{i=1}^N x_i \end{matrix}
Coproduct	\coprod_{i=1}^N x_i	Failed to parse (Can't write to or create math temp directory): \coprod_{i=1}^N x_i
Coproduct (force `\textstyle`)	\begin{matrix} \coprod_{i=1}^N x_i \end{matrix}	Failed to parse (Can't write to or create math temp directory): \begin{matrix} \coprod_{i=1}^N x_i \end{matrix}
Limit	\lim_{n \to \infty}x_n	Failed to parse (Can't write to or create math temp directory): \lim_{n \to \infty}x_n
Limit (force `\textstyle`)	\begin{matrix} \lim_{n \to \infty}x_n \end{matrix}	Failed to parse (Can't write to or create math temp directory): \begin{matrix} \lim_{n \to \infty}x_n \end{matrix}
Integral	\int_{-N}^{N} e^x\, dx	Failed to parse (Can't write to or create math temp directory): \int_{-N}^{N} e^x\, dx
Integral (force `\textstyle`)	\begin{matrix} \int_{-N}^{N} e^x\, dx \end{matrix}	Failed to parse (Can't write to or create math temp directory): \begin{matrix} \int_{-N}^{N} e^x\, dx \end{matrix}
Double integral	\iint_{D}^{W} \, dx\,dy	Failed to parse (Can't write to or create math temp directory): \iint_{D}^{W} \, dx\,dy
Triple integral	\iiint_{E}^{V} \, dx\,dy\,dz	Failed to parse (Can't write to or create math temp directory): \iiint_{E}^{V} \, dx\,dy\,dz
Quadruple integral	\iiiint_{F}^{U} \, dx\,dy\,dz\,dt	Failed to parse (Can't write to or create math temp directory): \iiiint_{F}^{U} \, dx\,dy\,dz\,dt
Path integral	\oint_{C} x^3\, dx + 4y^2\, dy	Failed to parse (Can't write to or create math temp directory): \oint_{C} x^3\, dx + 4y^2\, dy
Intersections	\bigcap_1^{n} p	Failed to parse (Can't write to or create math temp directory): \bigcap_1^{n} p
Unions	\bigcup_1^{k} p	Failed to parse (Can't write to or create math temp directory): \bigcup_1^{k} p

</table>

[edit]

Fractions, matrices, multilines

Feature Syntax How it looks rendered

Fractions \frac{2}{4}=0.5 or {2 \over 4}=0.5 Failed to parse (Can't write to or create math temp directory): \frac{2}{4}=0.5

Small Fractions (force \textstyle) \begin{matrix} \frac{2}{4} \end{matrix} = 0.5 Failed to parse (Can't write to or create math temp directory): \begin{matrix} \frac{2}{4} \end{matrix} = 0.5

Binomial coefficients {n \choose k} Failed to parse (Can't write to or create math temp directory): {n \choose k}

Matrices \begin{matrix} x & y \\ z & v \end{matrix} Failed to parse (Can't write to or create math temp directory): \begin{matrix} x & y \\ z & v \end{matrix}

\begin{vmatrix} x & y \\ z & v \end{vmatrix} Failed to parse (Can't write to or create math temp directory): \begin{vmatrix} x & y \\ z & v \end{vmatrix}

\begin{Vmatrix} x & y \\ z & v \end{Vmatrix} Failed to parse (Can't write to or create math temp directory): \begin{Vmatrix} x & y \\ z & v \end{Vmatrix}

\begin{bmatrix} 0 & \cdots & 0 \\ \vdots &

\ddots & \vdots \\ 0 & \cdots &

0\end{bmatrix}

Failed to parse (Can't write to or create math temp directory): \begin{bmatrix} 0 & \cdots & 0 \\ \vdots & \ddots & \vdots \\ 0 & \cdots & 0\end{bmatrix}

\begin{Bmatrix} x & y \\ z & v \end{Bmatrix} Failed to parse (Can't write to or create math temp directory): \begin{Bmatrix} x & y \\ z & v \end{Bmatrix}

\begin{pmatrix} x & y \\ z & v \end{pmatrix} Failed to parse (Can't write to or create math temp directory): \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} Failed to parse (Can't write to or create math temp directory): 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} Failed to parse (Can't write to or create math temp directory): \begin{matrix}f(n+1) & = & (n+1)^2 \\ \ & = & n^2 + 2n + 1 \end{matrix}

Alternative multiline equations (using tables)


{|
|-
|<math>f(n+1)</math>
|<math>=(n+1)^2</math>
|-
|
|<math>=n^2 + 2n + 1</math>
|}

Failed to parse (Can't write to or create math temp directory): f(n+1) \,\!	Failed to parse (Can't write to or create math temp directory): =(n+1)^2 \,\!
	Failed to parse (Can't write to or create math temp directory): =n^2 + 2n + 1 \,\!

[edit]

Fonts

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	Failed to parse (Can't write to or create math temp directory): \Alpha\ \Beta\ \Gamma\ \Delta\ \Epsilon\ \Zeta\ \Eta\ \Theta\ \Iota\ \Kappa\ \Lambda\ \Mu\ \Nu\ \Xi\ \Pi\ \Rho\ \Sigma\ \Tau\ \Upsilon\ \Phi\ \Chi\ \Psi\ \Omega Failed to parse (Can't write to or create math temp directory): \alpha\ \beta\ \gamma\ \delta\ \epsilon\ \zeta\ \eta\ \theta\ \iota\ \kappa\ \lambda\ \mu\ \nu\ \xi\ \pi\ \rho\ \sigma\ \tau\ \upsilon\ \phi\ \chi\ \psi\ \omega Failed to parse (Can't write to or create math temp directory): \varepsilon\ \digamma\ \vartheta\ \varkappa\ \varpi\ \varrho\ \varsigma\ \varphi
blackboard bold	\mathbb{N}\ \mathbb{Z}\ \mathbb{Q}\ \mathbb{R}\ \mathbb{C}	Failed to parse (Can't write to or create math temp directory): \mathbb{N}\ \mathbb{Z}\ \mathbb{Q}\ \mathbb{R}\ \mathbb{C}
boldface (vectors)	\mathbf{x}\cdot\mathbf{y} = 0	Failed to parse (Can't write to or create math temp directory): \mathbf{x}\cdot\mathbf{y} = 0
boldface (greek)	\boldsymbol{\alpha} + \boldsymbol{\beta} + \boldsymbol{\gamma}	Failed to parse (Can't write to or create math temp directory): \boldsymbol{\alpha} + \boldsymbol{\beta} + \boldsymbol{\gamma}
italics	\mathit{ABCDE abcde 1234}	Failed to parse (Can't write to or create math temp directory): \mathit{ABCDE abcde 1234}\,\!
Roman typeface	\mathrm{ABCDE abcde 1234}	Failed to parse (Can't write to or create math temp directory): \mathrm{ABCDE abcde 1234}\,\!
Fraktur typeface	\mathfrak{ABCDE abcde 1234}	Failed to parse (Can't write to or create math temp directory): \mathfrak{ABCDE abcde 1234}
Calligraphy/Script	\mathcal{ABCDE abcde 1234}	Failed to parse (Can't write to or create math temp directory): \mathcal{ABCDE abcde 1234}
Hebrew	\aleph \beth \gimel \daleth	Failed to parse (Can't write to or create math temp directory): \aleph\ \beth\ \gimel\ \daleth
non-italicised characters	\mbox{abc}	Failed to parse (Can't write to or create math temp directory): \mbox{abc}	Failed to parse (Can't write to or create math temp directory): \mbox{abc} \,\!
mixed italics (bad)	\mbox{if} n \mbox{is even}	Failed to parse (Can't write to or create math temp directory): \mbox{if} n \mbox{is even}	Failed to parse (Can't write to or create math temp directory): \mbox{if} n \mbox{is even} \,\!
mixed italics (good)	\mbox{if }n\mbox{ is even}	Failed to parse (Can't write to or create math temp directory): \mbox{if }n\mbox{ is even}	Failed to parse (Can't write to or create math temp directory): \mbox{if }n\mbox{ is even} \,\!

[edit]

Parenthesizing big expressions, brackets, bars

Feature	Syntax	How it looks rendered
Bad	( \frac{1}{2} )	Failed to parse (Can't write to or create math temp directory): ( \frac{1}{2} )
Good	\left ( \frac{1}{2} \right )	Failed to parse (Can't write to or create math temp directory): \left ( \frac{1}{2} \right )

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

[edit]

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	Failed to parse (Can't write to or create math temp directory): a \qquad b
quad space	a \quad b	Failed to parse (Can't write to or create math temp directory): a \quad b
text space	a\ b	Failed to parse (Can't write to or create math temp directory): a\ b
text space without PNG conversion	a \mbox{ } b	Failed to parse (Can't write to or create math temp directory): a \mbox{ } b
large space	a\;b	Failed to parse (Can't write to or create math temp directory): a\;b
medium space	a\>b	[not supported]
small space	a\,b	Failed to parse (Can't write to or create math temp directory): a\,b
no space	ab	Failed to parse (Can't write to or create math temp directory): ab\,
small negative space	a\!b	Failed to parse (Can't write to or create math temp directory): a\!b

[edit]

Align with normal text flow

Due to the default css

img.tex { vertical-align: middle; }

an inline expression like Failed to parse (Can't write to or create math temp directory): \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.

[edit]

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}	Failed to parse (Can't write to or create math temp directory): a^{c+2}
a^{c+2} \,	Failed to parse (Can't write to or create math temp directory): a^{c+2} \,
a^{\,\!c+2}	Failed to parse (Can't write to or create math temp directory): a^{\,\!c+2}
a^{b^{c+2}}	Failed to parse (Can't write to or create math temp directory): a^{b^{c+2}} (WRONG with option "HTML if possible or else PNG"!)
a^{b^{c+2}} \,	Failed to parse (Can't write to or create math temp directory): a^{b^{c+2}} \, (WRONG with option "HTML if possible or else PNG"!)
a^{b^{c+2}}\approx 5	Failed to parse (Can't write to or create math temp directory): a^{b^{c+2}}\approx 5 (due to "Failed to parse (Can't write to or create math temp directory): \approx " correctly displayed, no code "\,\!" needed)
a^{b^{\,\!c+2}}	Failed to parse (Can't write to or create math temp directory): a^{b^{\,\!c+2}}
\int_{-N}^{N} e^x\, dx	Failed to parse (Can't write to or create math temp directory): \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:

[edit]

Examples

[edit]

Quadratic Polynomial

Failed to parse (Can't write to or create math temp directory): ax^2 + bx + c = 0

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

[edit]

Quadratic Polynomial (Force PNG Rendering)

Failed to parse (Can't write to or create math temp directory): ax^2 + bx + c = 0\,

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

[edit]

Quadratic Formula

Failed to parse (Can't write to or create math temp directory): x_{1,2}=\frac{-b\pm\sqrt{b^2-4ac}}{2a}

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

[edit]

Tall Parentheses and Fractions

Failed to parse (Can't write to or create math temp directory): 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>

[edit]

Integrals

Failed to parse (Can't write to or create math temp directory): \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>

[edit]

Summation

Failed to parse (Can't write to or create math temp directory): \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>

[edit]

Differential Equation

Failed to parse (Can't write to or create math temp directory): 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>

[edit]

Complex numbers

Failed to parse (Can't write to or create math temp directory): |\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>

[edit]

Limits

Failed to parse (Can't write to or create math temp directory): \lim_{z\rightarrow z_0} f(z)=f(z_0)\,

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

[edit]

Integral Equation

Failed to parse (Can't write to or create math temp directory): \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>

[edit]

Example

Failed to parse (Can't write to or create math temp directory): \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>

[edit]

Continuation and cases

Failed to parse (Can't write to or create math temp directory): f(x) = \begin{cases}1 & -1 \le x < 0\\  \frac{1}{2} & x = 0\\x&0<x\le 1\end{cases}

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

[edit]

Prefixed subscript

Failed to parse (Can't write to or create math temp directory): {}_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>

[edit]

Bug reports

Discussions, bug reports and feature requests should go to the Wikitech-l mailing list. These can also be filed on Mediazilla under MediaWiki extensions.

[edit]

External links

A LaTeX tutorial. http://www.maths.tcd.ie/~dwilkins/LaTeXPrimer/
A PDF document introducing TeX -- see page 39 onwards for a good introduction to the maths side of things: http://www.ctan.org/tex-archive/info/gentle/gentle.pdf
A PDF document introducing LaTeX -- skip to page 59 for the math section. See page 72 for a complete reference list of symbols included in LaTeX and AMS-LaTeX. http://www.ctan.org/tex-archive/info/lshort/english/lshort.pdf
TeX reference card: http://www.csit.fsu.edu/~mimi/tex/tex-refcard-letter.pdf
http://www.ams.org/tex/amslatex.html
A set of public domain fixed-size math symbol bitmaps: http://us.metamath.org/symbols/symbols.html
MathML - A product of the W3C Math working group, is a low-level specification for describing mathematics as a basis for machine to machine communication. http://www.w3.org/Math/

Template:Ph:Formula

[edit]

Links to other help pages

Help contents - all pages in the Help namespace: Meta b: c: n: w: q: wikisource wiktionary

Languages: Template:H-langs:Formula

Retrieved from "http://www.highland-terrace.org/wiki/index.php?title=Help:Formula"

Help:Formula

From Highland Terrace Neighborhood

Contents

MediaWiki and TeX

Syntax

Rendering

TeX vs HTML

Pros of HTML

Pros of TeX

Functions, symbols, special characters

Subscripts, superscripts, integrals

Fractions, matrices, multilines

Fonts

Parenthesizing big expressions, brackets, bars

Spacing

Align with normal text flow

Forced PNG rendering

Examples

Quadratic Polynomial

Quadratic Polynomial (Force PNG Rendering)

Quadratic Formula

Tall Parentheses and Fractions

Integrals

Summation

Differential Equation

Complex numbers

Limits

Integral Equation

Example

Continuation and cases

Prefixed subscript

Bug reports

See also

External links

Links to other help pages

Views

Personal tools

Navigation

Search

Toolbox

Feature	Syntax	How it looks rendered
Accents/Diacritics	\acute{a} \quad \grave{a} \quad \breve{a} \quad \check{a} \quad \tilde{a}	Failed to parse (Can't write to or create math temp directory): \acute{a} \quad \grave{a} \quad \breve{a} \quad \check{a} \quad \tilde{a}
Std. functions (good)	\sin x + \ln y +\operatorname{sgn} z< \sin a \ \cos b \ \tan c \ \cot d \ \sec e \ \csc f< \sinh g \ \cosh h \ \tanh i \ \coth j \arcsin k \ \arccos l \ \arctan m \lim n \ \limsup o \ \liminf p \min q \ \max r \ \inf s \ \sup t \exp u \ \lg v \ \log w \ker x \ \deg x \gcd x \Pr x \ \det x \hom x \ \arg x \dim x	Failed to parse (Can't write to or create math temp directory): \sin x + \ln y +\operatorname{sgn} z Failed to parse (Can't write to or create math temp directory): \sin a \ \cos b \ \tan c \ \cot d \ \sec e \ \csc f Failed to parse (Can't write to or create math temp directory): \sinh g \ \cosh h \ \tanh i \ \coth j Failed to parse (Can't write to or create math temp directory): \arcsin k \ \arccos l \ \arctan m Failed to parse (Can't write to or create math temp directory): \lim n \ \limsup o \ \liminf p Failed to parse (Can't write to or create math temp directory): \min q \ \max r \ \inf s \ \sup t Failed to parse (Can't write to or create math temp directory): \exp u \ \lg v \ \log w Failed to parse (Can't write to or create math temp directory): \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	Failed to parse (Can't write to or create math temp directory): sin x + ln y + sgn z\,\!
Modular arithmetic	s_k \equiv 0 \pmod{m} a \bmod b	Failed to parse (Can't write to or create math temp directory): s_k \equiv 0 \pmod{m} Failed to parse (Can't write to or create math temp directory): a \bmod b\,\!
Derivatives	\nabla \; \partial x \; dx \; \dot x \; \ddot y	Failed to parse (Can't write to or create math temp directory): \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	Failed to parse (Can't write to or create math temp directory): \forall \; \exists \; \empty \; \emptyset \; \varnothing \in \ni \not\in \notin Failed to parse (Can't write to or create math temp directory): \subset \subseteq \supset \supseteq \cap \bigcap \cup \bigcup \biguplus
Sets (Square symbols may not work for some wikis)	\sqsubset \sqsubseteq \sqsupset \sqsupseteq \sqcap \sqcup \bigsqcup	Failed to parse (Can't write to or create math temp directory): \sqsubset \sqsubseteq \sqsupset \sqsupseteq \sqcap \sqcup \bigsqcup
Logic	p \land \wedge \; \bigwedge \; \bar{q} \to p \; \lor \vee \; \bigvee \; \lnot \; \neg q \; \setminus \; \smallsetminus	Failed to parse (Can't write to or create math temp directory): p \land \wedge \; \bigwedge \; \bar{q} \to p \lor \vee \; \bigvee \; \lnot \; \neg q \; \setminus \; \smallsetminus
Root	\sqrt{2}\approx 1.4	Failed to parse (Can't write to or create math temp directory): \sqrt{2}\approx 1.4
Root	\sqrt[n]{x}	Failed to parse (Can't write to or create math temp directory): \sqrt[n]{x}
Relations	\sim \; \approx \; \simeq \; \cong \; \le \; < \; \ll \; \gg \; \ge \; > \; \equiv \; \not\equiv \; \ne \; \propto \; \pm \; \mp	Failed to parse (Can't write to or create math temp directory): \sim \; \approx \; \simeq \; \cong \; \le \; < \; \ll \; \gg \; \ge \; > \; \equiv \; \not\equiv \; \ne \; \propto \; \pm \; \mp
Geometric	\Diamond \; \Box \; \triangle \; \angle \; \perp \; \mid \; \nmid \; \\| \; 45^\circ	Failed to parse (Can't write to or create math temp directory): \Diamond \; \Box \; \triangle \; \angle \; \perp \; \mid \; \nmid \; \\| \; 45^\circ
Arrows (Harpoons may not work for some wikis)	\leftarrow \; \gets \; \rightarrow \; \to \; \leftrightarrow \longleftarrow \; \longrightarrow \mapsto \; \longmapsto \; \hookrightarrow \; \hookleftarrow \nearrow \; \searrow \; \swarrow \; \nwarrow \uparrow \; \downarrow \; \updownarrow	Failed to parse (Can't write to or create math temp directory): \leftarrow \; \gets \; \rightarrow \; \to \; \leftrightarrow Failed to parse (Can't write to or create math temp directory): \longleftarrow \; \longrightarrow Failed to parse (Can't write to or create math temp directory): \mapsto \; \longmapsto \; \hookrightarrow \; \hookleftarrow Failed to parse (Can't write to or create math temp directory): \nearrow \; \searrow \; \swarrow \; \nwarrow Failed to parse (Can't write to or create math temp directory): \uparrow \; \downarrow \; \updownarrow
	\rightharpoonup \; \rightharpoondown \; \leftharpoonup \; \leftharpoondown \; \upharpoonleft \; \upharpoonright \; \downharpoonleft \; \downharpoonright	Failed to parse (Can't write to or create math temp directory): \rightharpoonup \; \rightharpoondown \; \leftharpoonup \; \leftharpoondown \; \upharpoonleft \; \upharpoonright \; \downharpoonleft \; \downharpoonright
	\Leftarrow \; \Rightarrow \; \Leftrightarrow \Longleftarrow \; \Longrightarrow \; \Longleftrightarrow (or \iff) \Uparrow \; \Downarrow \; \Updownarrow	Failed to parse (Can't write to or create math temp directory): \Leftarrow \; \Rightarrow \; \Leftrightarrow Failed to parse (Can't write to or create math temp directory): \Longleftarrow \; \Longrightarrow \; \Longleftrightarrow (or \iff) Failed to parse (Can't write to or create math temp directory): \Uparrow \; \Downarrow \; \Updownarrow
Special	\eth \; \S \; \P \; \% \; \dagger \; \ddagger \; \star \; * \; \ldots \smile \frown \wr \oplus \bigoplus \otimes \bigotimes \times \cdot \circ \bullet \bigodot \triangleleft \triangleright \infty \bot \top \vdash \vDash \Vdash \models \lVert \rVert \imath \; \hbar \; \ell \; \mho \; \Finv \; \Re \; \Im \; \wp \; \complement \quad \diamondsuit \; \heartsuit \; \clubsuit \; \spadesuit \; \Game \quad \flat \; \natural \; \sharp	*Failed to parse (Can't write to or create math temp directory): \eth \; \S \; \P \; \% \; \dagger \; \ddagger \; \star \; \; \ldots Failed to parse (Can't write to or create math temp directory): \smile \frown \wr \oplus \bigoplus \otimes \bigotimes Failed to parse (Can't write to or create math temp directory): \times \cdot \circ \bullet \bigodot \triangleleft \triangleright \infty \bot \top \vdash \vDash \Vdash \models \lVert \rVert** Failed to parse (Can't write to or create math temp directory): \imath \; \hbar \; \ell \; \mho \; \Finv \; \Re \; \Im \; \wp \; \complement \quad \diamondsuit \; \heartsuit \; \clubsuit \; \spadesuit \; \Game \quad \flat \; \natural \; \sharp
Lowercase \mathcal has some extras	\mathcal {45abcdenpqs}	Failed to parse (Can't write to or create math temp directory): \mathcal {45abcdenpqs}

Feature	Syntax	How it looks rendered
Parentheses	\left ( \frac{a}{b} \right )	Failed to parse (Can't write to or create math temp directory): \left ( \frac{a}{b} \right )
Brackets	\left [ \frac{a}{b} \right ] \quad \left \lbrack \frac{a}{b} \right \rbrack	Failed to parse (Can't write to or create math temp directory): \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	Failed to parse (Can't write to or create math temp directory): \left \{ \frac{a}{b} \right \} \quad \left \lbrace \frac{a}{b} \right \rbrace
Angle brackets	\left \langle \frac{a}{b} \right \rangle	Failed to parse (Can't write to or create math temp directory): \left \langle \frac{a}{b} \right \rangle
Bars and double bars	\left \| \frac{a}{b} \right \vert \left \Vert \frac{c}{d} \right \\|	Failed to parse (Can't write to or create math temp directory): \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	Failed to parse (Can't write to or create math temp directory): \left \lfloor \frac{a}{b} \right \rfloor \left \lceil \frac{c}{d} \right \rceil
Slashes and backslashes	\left / \frac{a}{b} \right \backslash	Failed to parse (Can't write to or create math temp directory): \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	Failed to parse (Can't write to or create math temp directory): \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 \|	Failed to parse (Can't write to or create math temp directory): \left [ 0,1 \right ) Failed to parse (Can't write to or create math temp directory): \left \langle \psi \right \|
Use \left. and \right. if you don't want a delimiter to appear:	\left . \frac{A}{B} \right \} \to X	Failed to parse (Can't write to or create math temp directory): \left . \frac{A}{B} \right \} \to X
Size of the delimiters	\big( \Big( \bigg( \Bigg( ... \Bigg] \bigg] \Big] \big]	Failed to parse (Can't write to or create math temp directory): \big( \Big( \bigg( \Bigg( ... \Bigg] \bigg] \Big] \big]
	\big\{ \Big\{ \bigg\{ \Bigg\{ ... \Bigg\rangle \bigg\rangle \Big\rangle \big\rangle	Failed to parse (Can't write to or create math temp directory): \big\{ \Big\{ \bigg\{ \Bigg\{ ... \Bigg\rangle \bigg\rangle \Big\rangle \big\rangle
	\big\\| \Big\\| \bigg\\| \Bigg\\| ... \Bigg\| \bigg\| \Big\| \big\|	Failed to parse (Can't write to or create math temp directory): \big\\| \Big\\| \bigg\\| \Bigg\\| ... \Bigg\| \bigg\| \Big\| \big\|
	\big\lfloor \Big\lfloor \bigg\lfloor \Bigg\lfloor ... \Bigg\rceil \bigg\rceil \Big\rceil \big\rceil	Failed to parse (Can't write to or create math temp directory): \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	Failed to parse (Can't write to or create math temp directory): \big\uparrow \Big\uparrow \bigg\uparrow \Bigg\uparrow ... \Bigg\Downarrow \bigg\Downarrow \Big\Downarrow \big\Downarrow