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|
| Line 16: |
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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} |
| | + | </math> |
| | + | |
| | + | <math> |
| | + | \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} |
| | + | |
| | + | \begin{align} |
| | + | \newcommand{\Re}{\mathrm{Re}\,} |
| | + | \newcommand{\pFq}[5]{{}_{#1}\mathrm{F}_{#2} \left( \genfrac{}{}{0pt}{}{#3}{#4} \bigg| {#5} \right)} |
| | + | |
| | + | \label{eq:W3k} |
| | + | W_3(k) &= \Re \, \pFq32{\frac12, -\frac k2, -\frac k2}{1, 1}{4}. |
| | \end{align} | | \end{align} |
| | </math> | | </math> |
Revision as of 13:17, 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]
[math]
\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}
\begin{align}
\newcommand{\Re}{\mathrm{Re}\,}
\newcommand{\pFq}[5]{{}_{#1}\mathrm{F}_{#2} \left( \genfrac{}{}{0pt}{}{#3}{#4} \bigg| {#5} \right)}
\label{eq:W3k}
W_3(k) &= \Re \, \pFq32{\frac12, -\frac k2, -\frac k2}{1, 1}{4}.
\end{align}
[/math]
