Difference between revisions of "Useful Examples"
Line 42: | Line 42: | ||
* Some special features: | * Some special features: | ||
Link to the internal page with all special features: [[Special:Version]] | Link to the internal page with all special features: [[Special:Version]] | ||
− | Syntax Highlighting: | + | |
+ | * Examples of Syntax Highlighting: | ||
+ | Some Fortran Code: | ||
+ | <syntaxhighlight lang="fortran" line> | ||
+ | program truc | ||
+ | implicit none | ||
+ | integer :: i | ||
+ | do i=1,10 | ||
+ | write(*,*) "i=",i | ||
+ | end do | ||
+ | end program | ||
+ | </syntaxhighlight> |
Revision as of 16:15, 6 April 2022
To Edit Sidebar (as admin only!!!)
Go to MediaWiki:Sidebar
To write some LateX
See e.g. LMDZPedia And check out this page in "edit" mode! $$\newcommand{\Re}{\mathrm{Re}\,} \newcommand{\pFq}[5]{{}_{#1}\mathrm{F}_{#2} \left( \genfrac{}{}{0pt}{}{#3}{#4} \bigg| {#5} \right)}$$
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.
Miscellaneous =
- HTML like syntax works! e.g. comments with
<!-- This is a comment in the page --> which you see because between "pre" tags
- Some special features:
Link to the internal page with all special features: Special:Version
- Examples of Syntax Highlighting:
Some Fortran Code:
1 program truc
2 implicit none
3 integer :: i
4 do i=1,10
5 write(*,*) "i=",i
6 end do
7 end program