Difference between revisions of "HowToEnterMathSymbols"
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| − | We use the [http://www.mediawiki.org/wiki/Extension:MathJax MathJax Extension] by [http://www.mediawiki.org/wiki/User:Dirk_Nuyens Dirk Nuyens]. This extension enables [http://www.mathjax.org/ MathJax] (http://www.mathjax.org/) which is a Javascript library written by Davide Cervone. |
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| + | #REDIRECT[[Help:Entering mathematics]] |
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| − | |||
| − | == Usage == |
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| − | |||
| − | The following math environments are defined for inline style math: |
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| − | * <code>\(...\)</code> and |
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| − | * <code><math>...</math></code>. |
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| − | And the following math environments are defined for display style math: |
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| − | * <code><nowiki>$$...$$</nowiki></code> (can be turned off, even per page), |
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| − | * <code>\[...\]</code>, |
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| − | * <code>\begin{...}...\end{...}</code> and |
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| − | * <code>:<math>...</math></code>. |
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| − | MathJax produces nice and scalable mathematics, see their website (http://www.mathjax.org/) for a demonstration. This extension also enables the usage of <code>\label{}</code> and <code>\eqref{}</code> tags with automatic formula numbering. If needed you can still hand label by using <code>\tag{}</code>. |
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| − | |||
| − | == Example == |
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| − | |||
| − | === Latex Code === |
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| − | |||
| − | <syntaxhighlight lang="latex"> |
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| − | <!-- some LaTeX macros we want to use: --> |
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| − | \( |
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| − | \newcommand{\Re}{\mathrm{Re}\,} |
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| − | \newcommand{\pFq}[5]{{}_{#1}\mathrm{F}_{#2} \left( \genfrac{}{}{0pt}{}{#3}{#4} \bigg| {#5} \right)} |
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| − | \) |
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| − | |||
| − | We consider, for various values of \(s\), the \(n\)-dimensional integral |
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| − | \begin{align} |
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| − | \label{def:Wns} |
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| − | W_n (s) |
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| − | &:= |
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| − | \int_{[0, 1]^n} |
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| − | \left| \sum_{k = 1}^n \mathrm{e}^{2 \pi \mathrm{i} \, x_k} \right|^s \mathrm{d}\boldsymbol{x} |
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| − | \end{align} |
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| − | which occurs in the theory of uniform random walk integrals in the plane, |
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| − | where at each step a unit-step is taken in a random direction. As such, |
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| − | the integral \eqref{def:Wns} expresses the \(s\)-th moment of the distance |
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| − | to the origin after \(n\) steps. |
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| − | |||
| − | By experimentation and some sketchy arguments we quickly conjectured and |
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| − | strongly believed that, for \(k\) a nonnegative integer |
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| − | \begin{align} |
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| − | \label{eq:W3k} |
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| − | W_3(k) &= \Re \, \pFq32{\frac12, -\frac k2, -\frac k2}{1, 1}{4}. |
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| − | \end{align} |
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| − | Appropriately defined, \eqref{eq:W3k} also holds for negative odd integers. |
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| − | The reason for \eqref{eq:W3k} was long a mystery, but it will be explained |
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| − | at the end of the paper. |
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| − | </syntaxhighlight> |
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| − | |||
| − | (Which comes from a preprint of ''Jon M. Borwein, et. al. Some arithmetic properties of short random walk integrals.'') |
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| − | |||
| − | === Rendered text === |
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| − | |||
| − | <!-- This renders as http://www.cs.kuleuven.be/~dirkn/Extension_MathJax/MathJaxExample.png.--> |
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| − | |||
| − | <!-- some LaTeX macros we want to use: --> |
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| − | \( |
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| − | \newcommand{\Re}{\mathrm{Re}\,} |
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| − | \newcommand{\pFq}[5]{{}_{#1}\mathrm{F}_{#2} \left( \genfrac{}{}{0pt}{}{#3}{#4} \bigg| {#5} \right)} |
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| − | \) |
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| − | |||
| − | We consider, for various values of \(s\), the \(n\)-dimensional integral |
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| − | \begin{align} |
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| − | \label{def:Wns} |
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| − | W_n (s) |
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| − | &:= |
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| − | \int_{[0, 1]^n} |
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| − | \left| \sum_{k = 1}^n \mathrm{e}^{2 \pi \mathrm{i} \, x_k} \right|^s \mathrm{d}\boldsymbol{x} |
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| − | \end{align} |
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| − | 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 |
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| − | \begin{align} |
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| − | \label{eq:W3k} |
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| − | W_3(k) &= \Re \, \pFq32{\frac12, -\frac k2, -\frac k2}{1, 1}{4}. |
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| − | \end{align} |
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| − | Appropriately defined, \eqref{eq:W3k} also holds for negative odd integers. |
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| − | The reason for \eqref{eq:W3k} was long a mystery, but it will be explained |
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| − | at the end of the paper. |
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| − | |||
| − | == Additional Information == |
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| − | |||
| − | * This documentation comes from the [http://www.mediawiki.org/wiki/Extension:MathJax MathJax Extension page]. Additional documentation on using MathJax can be found at [http://www.mathjax.org www.mathjax.org]. |
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| − | * Our MathJax config file defines some potentially helpful macros: |
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| − | |||
| − | |||
| − | <syntaxhighlight lang="javascript"> |
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| − | //<![CDATA[ |
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| − | |||
| − | MathJax.Hub.Config({ |
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| − | |||
| − | tex2jax: { |
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| − | |||
| − | inlineMath: [ ["\\(","\\)"] ], |
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| − | |||
| − | displayMath: [ ['$$','$$'], ["\\[","\\]"] ], |
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| − | |||
| − | processEscapes: false, |
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| − | |||
| − | element: "content", |
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| − | |||
| − | ignoreClass: "(tex2jax_ignore|mw-search-results|searchresults)" /* note: this is part of a regex, check the docs! */ |
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| − | |||
| − | }, |
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| − | |||
| − | TeX: { |
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| − | |||
| − | Macros: { |
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| − | |||
| − | /* Wikipedia compatibility: these macros are used on Wikipedia */ |
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| − | |||
| − | empty: '\\emptyset', |
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| − | |||
| − | P: '\\unicode{xb6}', |
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| − | |||
| − | Alpha: '\\unicode{x391}', /* FIXME: These capital Greeks don't show up in bold in \boldsymbol ... */ |
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| − | |||
| − | Beta: '\\unicode{x392}', |
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| − | |||
| − | Epsilon: '\\unicode{x395}', |
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| − | |||
| − | Zeta: '\\unicode{x396}', |
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| − | |||
| − | Eta: '\\unicode{x397}', |
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| − | |||
| − | Iota: '\\unicode{x399}', |
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| − | |||
| − | Kappa: '\\unicode{x39a}', |
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| − | |||
| − | Mu: '\\unicode{x39c}', |
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| − | |||
| − | Nu: '\\unicode{x39d}', |
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| − | |||
| − | Pi: '\\unicode{x3a0}', |
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| − | |||
| − | Rho: '\\unicode{x3a1}', |
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| − | |||
| − | Sigma: '\\unicode{x3a3}', |
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| − | |||
| − | Tau: '\\unicode{x3a4}', |
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| − | |||
| − | Chi: '\\unicode{x3a7}', |
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| − | |||
| − | C: '\\mathbb{C}', /* the complex numbers */ |
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| − | |||
| − | N: '\\mathbb{N}', /* the natural numbers */ |
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| − | |||
| − | Q: '\\mathbb{Q}', /* the rational numbers */ |
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| − | |||
| − | R: '\\mathbb{R}', /* the real numbers */ |
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| − | |||
| − | Z: '\\mathbb{Z}', /* the integer numbers */ |
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| − | |||
| − | RR: '\\mathbb{R}', |
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| − | |||
| − | ZZ: '\\mathbb{Z}', |
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| − | |||
| − | NN: '\\mathbb{N}', |
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| − | |||
| − | QQ: '\\mathbb{Q}', |
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| − | |||
| − | CC: '\\mathbb{C}', |
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| − | |||
| − | FF: '\\mathbb{F}' |
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| − | |||
| − | } |
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| − | |||
| − | } |
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| − | |||
| − | }); |
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| − | |||
| − | //]]> |
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| − | </syntaxhighlight> |
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Latest revision as of 13:34, 24 July 2012
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