# Help:Entering mathematics

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:

• $$...$$ and
• $...$.

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

• $$...$$ (can be turned off, even per page),
• $...$,
• \begin{...}...\end{...} and
• :$...$.

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"> $$ \newcommand{\Re}{\mathrm{Re}\,} \newcommand{\pFq}{{}_{#1}\mathrm{F}_{#2} \left( \genfrac{}{}{0pt}{}{#3}{#4} \bigg| {#5} \right)} $$

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

$$ \newcommand{\Re}{\mathrm{Re}\,} \newcommand{\pFq}{{}_{#1}\mathrm{F}_{#2} \left( \genfrac{}{}{0pt}{}{#3}{#4} \bigg| {#5} \right)} $$

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 MathJax Extension page. Additional documentation on using MathJax can be found at www.mathjax.org.
• Our MathJax config file defines some potentially helpful macros:

<syntaxhighlight lang="javascript"> //<![CDATA[

   MathJax.Hub.Config({
tex2jax: {
inlineMath: [ ["\$$","\$$"] ],
displayMath: [ ['$$','$$'], ["\$","\$"] ],
processEscapes: false,
element: "content",
ignoreClass: "(tex2jax_ignore|mw-search-results|searchresults)" /* note: this is part of a regex, check the docs! */
},
TeX: {
Macros: {
/* Wikipedia compatibility: these macros are used on Wikipedia */
empty: '\\emptyset',
P: '\\unicode{xb6}',
Alpha: '\\unicode{x391}', /* FIXME: These capital Greeks don't show up in bold in \boldsymbol ... */
Beta: '\\unicode{x392}',
Epsilon: '\\unicode{x395}',
Zeta: '\\unicode{x396}',
Eta: '\\unicode{x397}',
Iota: '\\unicode{x399}',
Kappa: '\\unicode{x39a}',
Mu: '\\unicode{x39c}',
Nu: '\\unicode{x39d}',
Pi: '\\unicode{x3a0}',
Rho: '\\unicode{x3a1}',
Sigma: '\\unicode{x3a3}',
Tau: '\\unicode{x3a4}',
Chi: '\\unicode{x3a7}',
C: '\\mathbb{C}',        /* the complex numbers */
N: '\\mathbb{N}',        /* the natural numbers */
Q: '\\mathbb{Q}',        /* the rational numbers */
R: '\\mathbb{R}',        /* the real numbers */
Z: '\\mathbb{Z}',        /* the integer numbers */
RR: '\\mathbb{R}',
ZZ: '\\mathbb{Z}',
NN: '\\mathbb{N}',
QQ: '\\mathbb{Q}',
CC: '\\mathbb{C}',
FF: '\\mathbb{F}'
}
}
});


//]]> </syntaxhighlight>