Difference between revisions of "HowToEnterMathSymbols"

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== Additional Information ==
 
== Additional Information ==
   
This documentation comes from the [http://www.mediawiki.org/wiki/Extension:MathJax MathJax Extension page]. Additional documentation on using MathJax can be found at [http://www.mathjax.org www.mathjax.org].
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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 [http://www.mathjax.org www.mathjax.org].
  +
* See our [http://people.cs.kuleuven.be/~dirk.nuyens/Extension_MathJax/mwMathJaxConfig.js config file] for some custom macro definitions that may be helpful.

Revision as of 11:07, 24 July 2012

We use the MathJax Extension by Dirk Nuyens. This extension enables MathJax (http://www.mathjax.org/) which is a Javascript library written by Davide Cervone.

Usage

The following math environments are defined for inline style math:

  • $...$ (can be turned off, even per page),
  • \(...\) and
  • <math>...</math>.

And the following math environments are defined for display style math:

  • $$...$$ (can be turned off, even per page),
  • \[...\],
  • \begin{...}...\end{...} and
  • :<math>...</math>.

MathJax produces nice and scalable mathematics, see their website (http://www.mathjax.org/) for a demonstration. This extension also enables the usage of \label{} and \eqref{} tags with automatic formula numbering. If needed you can still hand label by using \tag{}.


Example

Latex Code

<syntaxhighlight lang="latex"> $

 \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.)

Rendered text

This renders as http://www.cs.kuleuven.be/~dirkn/Extension_MathJax/MathJaxExample.png.

$

\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.

Additional Information