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Difference between revisions of "Main Page"

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(Replaced content with "Welcome to personal web site.")
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Welcome to personal web site.
__TOC__
 
<strong>MediaWiki has been installed.</strong>
 
Consult the [//meta.wikimedia.org/wiki/Help:Contents User's Guide] for information on using the wiki software.
 
Let's add a link to my [[Blog|blog]]
 
 
$\newcommand{\Re}{\mathrm{Re}\,}
\newcommand{\pFq}[5]{{}_{#1}\mathrm{F}_{#2} \left( \genfrac{}{}{0pt}{}{#3}{#4} \bigg| {#5} \right)}
\newcommand{\ket}[1]{\vert #1\rangle}$
 
Take a look at this beautifully typesetted equation:
\begin{equation}
p(n) = \mathcal{C}_n\times
  {}_1\!F_2\left(n+1;\frac{2n+1}{2}+\frac{\Gamma_\sigma}{\Gamma},
    n+\frac{\Gamma_\sigma}{\Gamma};
    -\frac{P_\sigma} {2\Gamma}
  \right)\, .
\end{equation}
 
 
 
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 \, \pFq 32{\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.
 
== First Section ==
 
=== First Subsection ===
 
==== First subsubsection ====
 
<m>x^2</m>
 
 
 
<i class="fa fa-file-pdf-o fa-2x" aria-hidden="true"></i> CV file
 
<i class="fa fa-camera-retro"></i> fa-camera-retro
 
<a class="list-group-item" href="#"><i class="fa fa-home fa-fw" aria-hidden="true"></i>&nbsp; Home</a>
<a class="list-group-item" href="#"><i class="fa fa-book fa-fw" aria-hidden="true"></i>&nbsp; Library</a>
<a class="list-group-item" href="#"><i class="fa fa-pencil fa-fw" aria-hidden="true"></i>&nbsp; Applications</a>
<a class="list-group-item" href="#"><i class="fa fa-cog fa-fw" aria-hidden="true"></i>&nbsp; Settings</a>
 
<div class="list-group">
  <a class="list-group-item" href="#"><i class="fa fa-home fa-fw" aria-hidden="true"></i>&nbsp; Home</a>
  <a class="list-group-item" href="#"><i class="fa fa-book fa-fw" aria-hidden="true"></i>&nbsp; Library</a>
  <a class="list-group-item" href="#"><i class="fa fa-pencil fa-fw" aria-hidden="true"></i>&nbsp; Applications</a>
  <a class="list-group-item" href="#"><i class="fa fa-cog fa-fw" aria-hidden="true"></i>&nbsp; Settings</a>
</div>
 
<ul class="fa-ul">
  <li><i class="fa-li fa fa-check-square"></i>List icons</li>
  <li><i class="fa-li fa fa-check-square"></i>can be used</li>
  <li><i class="fa-li fa fa-spinner fa-spin"></i>as bullets</li>
  <li><i class="fa-li fa fa-square"></i>in lists</li>
</ul>
 
 
<i class="fa fa-quote-left fa-3x fa-pull-left fa-border" aria-hidden="true"></i>
...tomorrow we will run faster, stretch out our arms farther...
And then one fine morning— So we beat on, boats against the
current, borne back ceaselessly into the past.
 
== Getting started ==
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Revision as of 18:05, 23 October 2016

Welcome to personal web site.