Help:Editing/Mathematical: Difference between revisions
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==LaTeX formulae== |
==LaTeX formulae== |
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It is hoped 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]. |
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<math>\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}}</math> |
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===Alternately (beta)=== |
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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: |
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===Example=== |
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$ |
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Click the edit link above to view the source. |
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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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It can easily be seen, by polynomial expansion, that the following equation is equivalent to the quadratic equation: |
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We consider, for various values of $s$, the $n$-dimensional integral |
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:<math>\left(x+\frac{b}{2a}\right)^2=\frac{b^2-4ac}{4a^2}</math> |
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\begin{align} |
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Taking the square root of both sides, and isolating <math>x</math>, gives: |
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\label{def:Wns} |
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:<math>x=\frac{-b\pm\sqrt{b^2-4ac\ }}{2a}</math> |
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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. |
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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. 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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==Charts== |
==Charts== |
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Use images from your favoured applcation, also 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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[[Category:Help:Editing]] |
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Latest revision as of 19:33, 17 January 2020
LaTeX formulae
It is hoped that any serious mathematics content contributor will be thoroughly familiar with LaTeX. Otherwise to generate the text required to display equations, use the CodeCogs LaTeX Equation Generator.
Synth DIY Wiki wiki supports embedding mathematical formulas using <math>...</math> tags.
Example
Click the edit link above to view the source.
It can easily be seen, by polynomial expansion, that the following equation is equivalent to the quadratic equation:
Taking the square root of both sides, and isolating , gives:
Charts
Use images from your favoured applcation, also see Wikipedia:How to create charts for Wikipedia articles.