portails/content/docs/examples/math.md

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---
title: "Math"
description: "Math typesetting examples."
lead: "Math typesetting examples."
date: 2021-03-16T10:46:05+01:00
lastmod: 2021-03-16T10:46:05+01:00
draft: false
images: []
menu:
docs:
parent: "examples"
weight: 210
toc: true
---
[KaTeX](https://katex.org/) is switched off by default. Enable it by setting `kaTex = true` in the `[options]` section of `./config/_default/params.toml`.
## Example 1
_Excerpt taken from [Supernova Neutrinos](https://neutrino.leima.is/book/introduction/supernova-neutrinos/)_
### Markdown
```md
The average energy of the neutrinos $\langle E \rangle$ emitted during a supernova explosion is of the order of 10MeV, and the neutrino luminosity at the early epoch of the explosion is approximately $10^{52}\mathrm{ergs\cdot s^{-1}}$.
Therefore, the number density of the neutrinos at the radius $R$ is
$$
\begin{equation*}
n \sim 10^{18} \mathrm{cm^{-3}} \left(\frac{100\mathrm{km}}{R}\right)^2 \left(\frac{10\mathrm{MeV}}{\langle E \rangle}\right).
\end{equation*}
$$
```
### HTML
The average energy of the neutrinos $\langle E \rangle$ emitted during a supernova explosion is of the order of 10MeV, and the neutrino luminosity at the early epoch of the explosion is approximately $10^{52}\mathrm{ergs\cdot s^{-1}}$.
Therefore, the number density of the neutrinos at the radius $R$ is
$$
\begin{equation*}
n \sim 10^{18} \mathrm{cm^{-3}} \left(\frac{100\mathrm{km}}{R}\right)^2 \left(\frac{10\mathrm{MeV}}{\langle E \rangle}\right).
\end{equation*}
$$
It turns out that the ambient dense neutrino medium has a significant impact on neutrino oscillations, which has been intensely investigated in the last decade.