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| | W_3(k) &= \Re \, \pFq32{\frac12, -\frac k2, -\frac k2}{1, 1}{4} | | W_3(k) &= \Re \, \pFq32{\frac12, -\frac k2, -\frac k2}{1, 1}{4} |
| − | \end{align}
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| − | </math>
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| − |
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| − |
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| − |
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| − | <math>
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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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| − | </math>
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| − |
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| − | <math>
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| − | \begin{align}
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| − |
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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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| − | \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} | | \end{align} |
| | </math> | | </math> |
Latest revision as of 13:23, 21 September 2012
[math]
\begin{align}
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}
[/math]
[math]
\begin{align}
\newcommand{\Re}{\mathrm{Re}\,}
\newcommand{\pFq}[5]{{}_{#1}\mathrm{F}_{#2} \left( \genfrac{}{}{0pt}{}{#3}{#4} \bigg| {#5} \right)}
W_3(k) &= \Re \, \pFq32{\frac12, -\frac k2, -\frac k2}{1, 1}{4}
\end{align}
[/math]
