Help:Editing/Mathematical

It is presumed that any serious mathematics content contributor will be thoroughly familiar with LaTeX.

LaTeX formulae
SDIY wiki supports embedding mathematical formulas using  tags. Click the edit tab above to view the source: \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}}

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Use  tags, TeX or LaTeX notation, MathML, or AsciiMath notation. See the Extension:MathJax and the MathJax Documentation for more information. Click the edit tab above to view the source:

$                                                                                                                                                                                                                                                             \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.

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