MathJax
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}}
|
$\int_0^\infty f(x)\ud x$ | $$\int_0^\infty f(x)\ud x$$ |
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. |