# Difference between revisions of "Help:Contents"

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As an example, the following lines with a reasonably complex set of equations | As an example, the following lines with a reasonably complex set of equations | ||

− | <pre>$ | + | <pre>$ |

+ | \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.$</pre> | ||

will result in the the following being displayed. | will result in the the following being displayed. | ||

− | Use of the < | + | Use of the <nowiki><math></nowiki> tag (the default maths display mechanism in MediaWiki) |

=== Collection === | === Collection === |

## Revision as of 14:21, 9 January 2012

## Contents

## Organisation of the Explanatoy Supplement

## Use of the available extensions

### MathJax

The MathJax extension allows the use of MathJax, a display engine for mathematics providing high quality mathematics fonts. The main interest for the ES lies in its ability to produce high quality display of latex formulae with no need for any extra tags. Equations may simply be written in Latex and MathJax will recognize the Latex Tags.

As an example, the following lines with a reasonably complex set of equations

$ \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.$

will result in the the following being displayed.

Use of the <math> tag (the default maths display mechanism in MediaWiki)