MathJax: Difference between revisions

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* MathJax supports LaTeX macros
* MathJax supports LaTeX macros
* Better LaTeX support
* Better LaTeX support

$\newcommand{\ud}{\,\mathrm{d}}$


== Example ==
== Example ==
Simple examples:

{| class=wikitable
|-
!formula!!Textstyle (<code>$...$</code>)!!Displaystyle (<code>$$...$$</code>)
|-
|<code>\frac{x}{1+\frac{x}{1+y}}</code>
|$\frac{x}{1+\frac{x}{1+y}}$
|$$\frac{x}{1+\frac{x}{1+y}}$$
|-
|<code>\newcommand{\ud}{\,\mathrm{d}}
\int_a^b f(x)\ud x</code>
|$\int_0^\infty f(x)\ud x$
|$$\int_0^\infty f(x)\ud x$$
|}


From [http://www.mediawiki.org/wiki/Extension:MathJax]:
From [http://www.mediawiki.org/wiki/Extension:MathJax]:


{| class=wikitable
<!-- some LaTeX macros we want to use: -->
|-
|<!-- some LaTeX macros we want to use: -->
$
$
\newcommand{\Re}{\mathrm{Re}\,}
\newcommand{\Re}{\mathrm{Re}\,}
Line 38: Line 59:
The reason for \eqref{eq:W3k} was long a mystery, but it will be explained
The reason for \eqref{eq:W3k} was long a mystery, but it will be explained
at the end of the paper.
at the end of the paper.

|}

Revision as of 13:56, 15 January 2014

MathJax is a client-side javascript that allows for very nice rendering of formula written in LaTeX, much like jsMath.

The advantages of MathJax over jsMath:

  • MathJax seems actively developed for now
  • MathJax uses server-side fonts, and so does not require any configuration on the client side to get better results
  • MathJax supports LaTeX macros
  • Better LaTeX support

$\newcommand{\ud}{\,\mathrm{d}}$

Example

Simple examples:

formula Textstyle ($...$) Displaystyle ($$...$$)
\frac{x}{1+\frac{x}{1+y}} $\frac{x}{1+\frac{x}{1+y}}$ $$\frac{x}{1+\frac{x}{1+y}}$$
\newcommand{\ud}{\,\mathrm{d}}

\int_a^b f(x)\ud x

$\int_0^\infty f(x)\ud x$ $$\int_0^\infty f(x)\ud x$$


From [1]:

$

 \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.