Elena & Fabrice's Web

## Contents |

* MathJax* is an open source Ajax-based framework to display mathematical notations in web browsers. It renders the input, entered as LaTeX or MathML expressions, as high-quality display in MathML or HTML with CSS and integrates well with text-based content, both in display mode and inline.

A result from Ramanujan:

\[ \frac{1}{\Bigl(\sqrt{\phi \sqrt{5}}-\phi\Bigr) e^{\frac25 \pi}} = 1+\frac{e^{-2\pi}} {1+\frac{e^{-4\pi}} {1+\frac{e^{-6\pi}} {1+\frac{e^{-8\pi}} {1+\ldots} } } }\,. \]

A result from Elena:

\begin{multline} \tag{1} S_\mathrm{inc}(\omega)=\Big(\frac{2P_\sigma}{\kappa_\sigma+\Gamma_\sigma}-\frac{\Gamma_\sigma}{\kappa_\sigma}\Big) \delta(\omega)+\frac{\frac{1}{2\pi}\frac{\Gamma_\sigma}{2}}{\big(\frac{\Gamma_\sigma}{2}\big)^2+\omega^2}+\\ \frac{(P_\sigma-\gamma_\sigma)\Big(3\Gamma_\sigma^3-(P_\sigma-5\gamma_\sigma)\Gamma_\sigma\kappa_\sigma+2\gamma_\sigma \kappa_\sigma^2\Big)-\Big(\Gamma_\sigma^2-(3P_\sigma-\gamma_\sigma)\kappa_\sigma\Big)\omega^2}{\pi(\kappa_\sigma+\Gamma_\sigma)\Big(9\Gamma_\sigma^2\omega^2+[2\omega^2-\kappa_\sigma(P_\sigma-\gamma_\sigma)]^2\Big)}\,, \end{multline}

A result from Fabrice:

\[ \tag{1} p(n_0,\Sigma) = \frac{(1-\theta_0)(1-\theta)^M\theta^{n_0+\Sigma}{M+n_0+\Sigma-1\choose M-1}{}_2F_1(1,-n_0+\Sigma,-M-n_0+\Sigma+1,\frac{\theta_0}{\theta})}{\left(\frac{\xi}{\xi-1}\right)^M-\frac1{\xi^{n_0+1}}{M+\Sigma+n_0\choose M-1}{}_2F_1(1,M+\Sigma+n_0+1,\Sigma+n_0+2,\frac{1}{\xi})}\,. \]

You may have noticed I could not resist the temptation to label them with our wz tooltips.

The beauty of it beyond perfect typesetting and integration in the flow of the text is that you can even label them. Equation (1) is the lineshape for the incoherent Mollow triplet, that is, the luminescence spectrum of a two-level emitter in strong-coupling with a cavity which it brought into lasing [1]. Equation (1) is the exact solution of quantum Boltzmann master equation which provides an analytical description of Bose-Einstein condensation.

And just when you thought you could not be impressed further, you have to get a look at inline display, like, Euler's formula $e^{i\pi}+1=0$, displayed idiotically to feature all the fundamental numbers, $e$, $i$, $\pi$, $0$ and $1$. See the Knuthian quality of the insert of math in the text? I'm doing that merely putting $\TeX$'s dollar signs around, I'm feeling at home on the web! What an age we live in!

<span style="color: red;">$$ax^2+bx+c$$</span> $$\color{red}{ax^2}+bx+c$$

yields:

$$ax^2+bx+c$$

$$\color{red}{ax^2}+bx+c$$

- http://www.mathjax.org — Webpage of the project.
- http://sourceforge.net/projects/mathjax — Sourceforge page of the project.
- http://www.mediawiki.org/wiki/Extension:MathJax — MediaWiki extension (thanks to Dirk Nuyens).