It is presumed that any serious mathematics content contributor will be thoroughly familiar with [https://en.wikipedia.org/wiki/LaTeX LaTeX]. ▼==LaTeX formulae==
▲It is presumedhoped that any serious mathematics content contributor will be thoroughly familiar with [https://en.wikipedia.org/wiki/LaTeX LaTeX]. Otherwise to generate the text required to display equations, use the CodeCogs [http://www.codecogs.com/latex/eqneditor.php LaTeX Equation Generator].
SDIY wiki supports embedding mathematical formulas using <code><nowiki><m></nowiki></code> tags. Click the edit tab above to view the source: ▼<m>\operatorname{erfc}(x) = \frac{2}{\sqrt{\pi}} \int_x^{\infty} e^{-t^2}\,dt = \frac{e^{-x^2}}{x\sqrt{\pi}}\sum_{n=0}^\infty (-1)^n \frac{(2n)!}{n!(2x)^{2n}}</m>
▲SDIY{{SITENAME}} wiki supports embedding mathematical formulas using <code><nowiki>< mmath>...</math></nowiki></code> tags. Click the edit tab above to view the source:
===Not working yet===
Use <code><nowiki><math></nowiki></code> tags, [http://en.wikipedia.org/wiki/TeX TeX] or [https://en.wikipedia.org/wiki/LaTeX LaTeX] notation, [https://en.wikipedia.org/wiki/MathML MathML], or [https://en.wikipedia.org/wiki/ASCIIMathML AsciiMath] notation. See the [https://www.mediawiki.org/wiki/Extension:MathJax Extension:MathJax] and the [http://docs.mathjax.org/en/latest/index.html MathJax Documentation] for more information. Click the edit tab above to view the source:
===Example===
$
Click the edit link above to view the source.
\newcommand{\Re}{\mathrm{Re}\,}
\newcommand{\pFq}[5]{{}_{#1}\mathrm{F}_{#2} \left( \genfrac{}{}{0pt}{}{#3}{#4} \bigg| {#5} \right)}
$
It can easily be seen, by polynomial expansion, that the following equation is equivalent to the quadratic equation:
We consider, for various values of $s$, the $n$-dimensional integral
:<math>\left(x+\frac{b}{2a}\right)^2=\frac{b^2-4ac}{4a^2}</math>
\begin{align}
Taking the square root of both sides, and isolating <math>x</math>, gives:
\label{def:Wns}
:<math>x=\frac{-b\pm\sqrt{b^2-4ac\ }}{2a}</math>
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.
==Charts==
NotUse yetimages found a satisfactory way to implement. Usefrom your favoured applcation, or in the meantimealso see Wikipedia:[https://en.wikipedia.org/wiki/Wikipedia:How_to_create_charts_for_Wikipedia_articles How to create charts for Wikipedia articles].
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