Difference between revisions of "HowToEnterMathSymbols"
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| − | 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. |
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| + | #REDIRECT[[Help:Entering mathematics]] |
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| − | |||
| − | == Usage == |
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| − | |||
| − | The following math environments are defined for inline style math: |
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| − | * <code><nowiki>$...$</nowiki></code> (can be turned off, even per page), |
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| − | * <code>\(...\)</code> and |
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| − | * <code><math>...</math></code>. |
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| − | And the following math environments are defined for display style math: |
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| − | * <code><nowiki>$$...$$</nowiki></code> (can be turned off, even per page), |
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| − | * <code>\[...\]</code>, |
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| − | * <code>\begin{...}...\end{...}</code> and |
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| − | * <code>:<math>...</math></code>. |
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| − | 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>. |
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| − | |||
| − | This extension allows for typical LaTeX math integration. |
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| − | For example: |
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| − | <syntaxhighlight lang="latex"> |
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| − | <!-- some LaTeX macros we want to use: --> |
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| − | $ |
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| − | \newcommand{\Re}{\mathrm{Re}\,} |
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| − | \newcommand{\pFq}[5]{{}_{#1}\mathrm{F}_{#2} \left( \genfrac{}{}{0pt}{}{#3}{#4} \bigg| {#5} \right)} |
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| − | $ |
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| − | |||
| − | We consider, for various values of $s$, the $n$-dimensional integral |
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| − | \begin{align} |
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| − | \label{def:Wns} |
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| − | W_n (s) |
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| − | &:= |
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| − | \int_{[0, 1]^n} |
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| − | \left| \sum_{k = 1}^n \mathrm{e}^{2 \pi \mathrm{i} \, x_k} \right|^s \mathrm{d}\boldsymbol{x} |
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| − | \end{align} |
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| − | which occurs in the theory of uniform random walk integrals in the plane, |
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| − | where at each step a unit-step is taken in a random direction. As such, |
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| − | the integral \eqref{def:Wns} expresses the $s$-th moment of the distance |
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| − | to the origin after $n$ steps. |
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| − | |||
| − | By experimentation and some sketchy arguments we quickly conjectured and |
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| − | strongly believed that, for $k$ a nonnegative integer |
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| − | \begin{align} |
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| − | \label{eq:W3k} |
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| − | W_3(k) &= \Re \, \pFq32{\frac12, -\frac k2, -\frac k2}{1, 1}{4}. |
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| − | \end{align} |
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| − | Appropriately defined, \eqref{eq:W3k} also holds for negative odd integers. |
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| − | The reason for \eqref{eq:W3k} was long a mystery, but it will be explained |
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| − | at the end of the paper. |
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| − | </syntaxhighlight> |
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| − | (Which comes from a preprint of ''Jon M. Borwein, et. al. Some arithmetic properties of short random walk integrals.'') |
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| − | |||
| − | This renders as http://www.cs.kuleuven.be/~dirkn/Extension_MathJax/MathJaxExample.png. |
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| − | |||
| − | <!-- some LaTeX macros we want to use: --> |
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| − | $$ |
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| − | \newcommand{\Re}{\mathrm{Re}\,} |
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| − | \newcommand{\pFq}[5]{{}_{#1}\mathrm{F}_{#2} \left( \genfrac{}{}{0pt}{}{#3}{#4} \bigg| {#5} \right)} |
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| − | $$ |
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| − | |||
| − | 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} |
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| − | \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} |
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| − | \label{eq:W3k} |
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| − | W_3(k) &= \Re \, \pFq32{\frac12, -\frac k2, -\frac k2}{1, 1}{4}. |
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| − | \end{align} |
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| − | 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. |
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| − | |||
| − | 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. |
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Latest revision as of 13:34, 24 July 2012
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