Help:Entering mathematics

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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.

Contents

Usage

The following math environments are defined for inline style math:

  • \(...\) 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

<!-- some LaTeX macros we want to use: -->
\(
  \newcommand{\Re}{\mathrm{Re}\,}
  \newcommand{\pFq}[5]{{}_{#1}\mathrm{F}_{#2} \left( \genfrac{}{}{0pt}{}{#3}{#4} \bigg| {#5} \right)}
\)
 
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.

(Which comes from a preprint of Jon M. Borwein, et. al. Some arithmetic properties of short random walk integrals.)

Rendered text

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

We consider, for various values of \(s\), the \(n\)-dimensional integral \begin{align} \tag{1} 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 (1) 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} \tag{2} W_3(k) &= \Re \, \pFq32{\frac12, -\frac k2, -\frac k2}{1, 1}{4}. \end{align} Appropriately defined, (2) also holds for negative odd integers. The reason for (2) was long a mystery, but it will be explained at the end of the paper.

Additional Information

  • 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:


//<![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}'
          }
        }
    });
//]]>
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