Diferenças entre edições de "Teste/math"
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x = y^2 |
x = y^2 |
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\end{equation} |
\end{equation} |
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Equation \eqref{eq:2} here. |
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We consider, for various values of $s$, the $n$-dimensional integral |
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, |
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, |
where at each step a unit-step is taken in a random direction. As such, |
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to the origin after $n$ steps. |
to the origin after $n$ steps. |
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=== |
===Secção adicional=== |
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By experimentation and some sketchy arguments we quickly conjectured |
By experimentation and some sketchy arguments we quickly conjectured. Insert picture: |
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[[Ficheiro:Cat2.jpg|alt=Gato deitado|miniaturadaimagem|Legenda da imagem.]] |
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strongly believed that, for $k$ a nonnegative integer |
strongly believed that, for $k$ a nonnegative integer |
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\begin{equation} |
\begin{equation} |
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Algum texto final. |
Algum texto final. |
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[[Ficheiro:Figura 10..png|alt=Evaporador|miniaturadaimagem|Legenda por baixo.|nenhum]] |
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<br /> |
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[[Categoria:Teste]] |
[[Categoria:Teste]] |
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Edição atual desde as 23h30min de 17 de abril de 2019
$\newcommand{\Re}{\mathrm{Re}\,} \newcommand{\pFq}[5]{{}_{#1}\mathrm{F}_{#2} \left( \genfrac{}{}{0pt}{}{#3}{#4} \bigg| {#5} \right)}$ Teste onde <math>x</math> é definido por:
Falhou a verificação gramatical (MathML, com SVG ou PNG em alternativa (recomendado para navegadores modernos e ferramentas de acessibilidade): Resposta inválida ("Math extension cannot connect to Restbase.") do servidor "https://wikimedia.org/api/rest_v1/":): {\displaystyle \begin{align} \dot{x} & = \sigma(y-x) \label{eq:1}\\ \dot{y} & = \rho x - y - xz \\ \dot{z} & = -\beta z + xy \end{align}}
Equation \eqref{eq:1} above. \begin{equation} \label{eq:aa} x = y^2 \end{equation} Equation \eqref{eq:2} here.
We consider, for various values of $s$, the $n$-dimensional integral 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.
Secção adicional
By experimentation and some sketchy arguments we quickly conjectured. Insert picture:
strongly believed that, for $k$ a nonnegative integer
\begin{equation}
\label{eq:W3k}
W_3(k) = \Re \, \pFq32{\frac12, -\frac k2, -\frac k2}{1, 1}{4}.
\end{equation} 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.
$\ce{HCl}$ dissociates in water as follows: $$\ce{H2O + HCl <=> H3O+ + Cl-}$$.
A equação que define $x$ é a seguinte, onde $x = a^2 + b_2$: \[ x = \frac{a+b}{c} + \sum_{i=1}^{n} B_i \alpha \beta \gamma \phi_k \]
Uma frase de teste[1]. Uma ligação a integração de processos. Mais referências.[2]
Bibliografia recomendada:
Algum texto final.
