Difference between revisions of "Help:Contents"

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The [http://www.mediawiki.org/wiki/Extension:MathJax MathJax extension] allows the use of [http://www.mathjax.org/ 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.  
 
The [http://www.mediawiki.org/wiki/Extension:MathJax MathJax extension] allows the use of [http://www.mathjax.org/ 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
+
Simple mathematical expressions can be easily written inline. The following
<pre>$
+
<pre>
 +
$x^2 + y^2 +z^2 = 1$
 +
</pre>
 +
will be displayed by MathJax as $x^2 + y^2 +z^2 = 1$
 +
 
 +
We can write complex equations and even make use of <nowiki>\newcommand </nowiki> as illustrated by the following lines.
 +
<pre>
 +
$
 +
  \newcommand{\Re}{\mathrm{Re}\,}
 +
  \newcommand{\pFq}[5]{{}_{#1}\mathrm{F}_{#2} \left( \genfrac{}{}{0pt}{}{#3}{#4} \bigg| {#5} \right)}
 +
$
 +
\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}
 +
 
 +
\begin{align}
 +
  \label{eq:W3k}
 +
  W_3(k) &= \Re \, \pFq32{\frac12, -\frac k2, -\frac k2}{1, 1}{4}.
 +
\end{align}
 +
</pre>
 +
MathJax will display these as
 +
$
 
   \newcommand{\Re}{\mathrm{Re}\,}
 
   \newcommand{\Re}{\mathrm{Re}\,}
 
   \newcommand{\pFq}[5]{{}_{#1}\mathrm{F}_{#2} \left( \genfrac{}{}{0pt}{}{#3}{#4} \bigg| {#5} \right)}
 
   \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}
 
\begin{align}
 
   \label{def:Wns}
 
   \label{def:Wns}
Line 18: Line 41:
 
     \left| \sum_{k = 1}^n \mathrm{e}^{2 \pi \mathrm{i} \, x_k} \right|^s \mathrm{d}\boldsymbol{x}
 
     \left| \sum_{k = 1}^n \mathrm{e}^{2 \pi \mathrm{i} \, x_k} \right|^s \mathrm{d}\boldsymbol{x}
 
\end{align}
 
\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}
 
\begin{align}
 
   \label{eq:W3k}
 
   \label{eq:W3k}
 
   W_3(k) &= \Re \, \pFq32{\frac12, -\frac k2, -\frac k2}{1, 1}{4}.
 
   W_3(k) &= \Re \, \pFq32{\frac12, -\frac k2, -\frac k2}{1, 1}{4}.
 
\end{align}
 
\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.
 
  
Use of the <nowiki><math></nowiki> tag (the default maths display mechanism in MediaWiki)
+
We can also refer to equations with a valid \label tag using the latex \eqref tag
 +
 
 +
There is no harm in wrapping equations in the math tag ()
  
 
=== Collection ===
 
=== Collection ===

Revision as of 14:45, 9 January 2012

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.

Simple mathematical expressions can be easily written inline. The following

$x^2 + y^2 +z^2 = 1$

will be displayed by MathJax as $x^2 + y^2 +z^2 = 1$

We can write complex equations and even make use of \newcommand as illustrated by the following lines.

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

\begin{align}
  \label{eq:W3k}
  W_3(k) &= \Re \, \pFq32{\frac12, -\frac k2, -\frac k2}{1, 1}{4}.
\end{align}

MathJax will display these as $

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

$ \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}

\begin{align}

 \label{eq:W3k}
 W_3(k) &= \Re \, \pFq32{\frac12, -\frac k2, -\frac k2}{1, 1}{4}.

\end{align}

We can also refer to equations with a valid \label tag using the latex \eqref tag

There is no harm in wrapping equations in the math tag ()

Collection

CategoryTree

Common tasks

Including figures

Linking to other pages in the ES

Linking to external pages

Uploading documents

Adding new section