Difference between revisions of "HowToEnterMathSymbols"
Jump to navigation
Jump to search
(Redirected page to Help:Entering mathematics) |
|||
| (12 intermediate revisions by 2 users not shown) | |||
| Line 1: | Line 1: | ||
| − | We use the [http://www.mediawiki.org/wiki/Extension:MathJax MathJax Extension] by [http://www.mediawiki.org/wiki/User:Dirk_Nuyens Dirk Nuyens]. This extension enables [http://www.mathjax.org/ MathJax] (http://www.mathjax.org/) which is a Javascript library written by Davide Cervone. |
||
| + | #REDIRECT[[Help:Entering mathematics]] |
||
| − | |||
| − | == Usage == |
||
| − | |||
| − | The following math environments are defined for inline style math: |
||
| − | * <code><nowiki>$...$</nowiki></code> (can be turned off, even per page), |
||
| − | * <code>\(...\)</code> and |
||
| − | * <code><math>...</math></code>. |
||
| − | And the following math environments are defined for display style math: |
||
| − | * <code><nowiki>$$...$$</nowiki></code> (can be turned off, even per page), |
||
| − | * <code>\[...\]</code>, |
||
| − | * <code>\begin{...}...\end{...}</code> and |
||
| − | * <code>:<math>...</math></code>. |
||
| − | MathJax produces nice and scalable mathematics, see their website (http://www.mathjax.org/) for a demonstration. This extension also enables the usage of <code>\label{}</code> and <code>\eqref{}</code> tags with automatic formula numbering. If needed you can still hand label by using <code>\tag{}</code>. |
||
| − | |||
| − | This extension allows for typical LaTeX math integration. |
||
| − | For example: |
||
| − | <syntaxhighlight lang="latex"> |
||
| − | <!-- some LaTeX macros we want to use: --> |
||
| − | $ |
||
| − | \newcommand{\Re}{\mathrm{Re}\,} |
||
| − | \newcommand{\pFq}[5]{{}_{#1}\mathrm{F}_{#2} \left( \genfrac{}{}{0pt}{}{#3}{#4} \bigg| {#5} \right)} |
||
| − | $ |
||
| − | |||
| − | We consider, for various values of $s$, the $n$-dimensional integral |
||
| − | \begin{align} |
||
| − | \label{def:Wns} |
||
| − | W_n (s) |
||
| − | &:= |
||
| − | \int_{[0, 1]^n} |
||
| − | \left| \sum_{k = 1}^n \mathrm{e}^{2 \pi \mathrm{i} \, x_k} \right|^s \mathrm{d}\boldsymbol{x} |
||
| − | \end{align} |
||
| − | which occurs in the theory of uniform random walk integrals in the plane, |
||
| − | where at each step a unit-step is taken in a random direction. As such, |
||
| − | the integral \eqref{def:Wns} expresses the $s$-th moment of the distance |
||
| − | to the origin after $n$ steps. |
||
| − | |||
| − | By experimentation and some sketchy arguments we quickly conjectured and |
||
| − | strongly believed that, for $k$ a nonnegative integer |
||
| − | \begin{align} |
||
| − | \label{eq:W3k} |
||
| − | W_3(k) &= \Re \, \pFq32{\frac12, -\frac k2, -\frac k2}{1, 1}{4}. |
||
| − | \end{align} |
||
| − | Appropriately defined, \eqref{eq:W3k} also holds for negative odd integers. |
||
| − | The reason for \eqref{eq:W3k} was long a mystery, but it will be explained |
||
| − | at the end of the paper. |
||
| − | </syntaxhighlight> |
||
| − | (Which comes from a preprint of ''Jon M. Borwein, et. al. Some arithmetic properties of short random walk integrals.'') |
||
| − | |||
| − | This renders as http://www.cs.kuleuven.be/~dirkn/Extension_MathJax/MathJaxExample.png. |
||
| − | |||
| − | <!-- some LaTeX macros we want to use: --> |
||
| − | $$ |
||
| − | \newcommand{\Re}{\mathrm{Re}\,} |
||
| − | \newcommand{\pFq}[5]{{}_{#1}\mathrm{F}_{#2} \left( \genfrac{}{}{0pt}{}{#3}{#4} \bigg| {#5} \right)} |
||
| − | $$ |
||
| − | |||
| − | We consider, for various values of $s$, the $n$-dimensional integral |
||
| − | \begin{align} |
||
| − | \label{def:Wns} |
||
| − | W_n (s) |
||
| − | &:= |
||
| − | \int_{[0, 1]^n} |
||
| − | \left| \sum_{k = 1}^n \mathrm{e}^{2 \pi \mathrm{i} \, x_k} \right|^s \mathrm{d}\boldsymbol{x} |
||
| − | \end{align} |
||
| − | which occurs in the theory of uniform random walk integrals in the plane, |
||
| − | where at each step a unit-step is taken in a random direction. As such, |
||
| − | the integral \eqref{def:Wns} expresses the $s$-th moment of the distance |
||
| − | to the origin after $n$ steps. |
||
| − | |||
| − | By experimentation and some sketchy arguments we quickly conjectured and |
||
| − | strongly believed that, for $k$ a nonnegative integer |
||
| − | \begin{align} |
||
| − | \label{eq:W3k} |
||
| − | W_3(k) &= \Re \, \pFq32{\frac12, -\frac k2, -\frac k2}{1, 1}{4}. |
||
| − | \end{align} |
||
| − | Appropriately defined, \eqref{eq:W3k} also holds for negative odd integers. |
||
| − | The reason for \eqref{eq:W3k} was long a mystery, but it will be explained |
||
| − | at the end of the paper. |
||
| − | |||
| − | This documentation comes from the [http://www.mediawiki.org/wiki/Extension:MathJax MathJax Extension page]. Additional documentation on using MathJax can be found at www.mathjax.org. |
||
Latest revision as of 14:34, 24 July 2012
Redirect to:
