Difference between revisions of "MJaxEq"

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<math>
 
<math>
 
\begin{align}
 
\begin{align}
   W_n (s)
+
   \label{def:Wns}  W_n (s)
 
   &:=  
 
   &:=  
 
   \int_{[0, 1]^n}  
 
   \int_{[0, 1]^n}  
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\end{align}
 
\end{align}
 
</math>
 
</math>
 +
 
<math>
 
<math>
 
\begin{align}
 
\begin{align}
 +
 
\newcommand{\Re}{\mathrm{Re}\,}
 
\newcommand{\Re}{\mathrm{Re}\,}
 
\newcommand{\pFq}[5]{{}_{#1}\mathrm{F}_{#2} \left( \genfrac{}{}{0pt}{}{#3}{#4} \bigg| {#5} \right)}
 
\newcommand{\pFq}[5]{{}_{#1}\mathrm{F}_{#2} \left( \genfrac{}{}{0pt}{}{#3}{#4} \bigg| {#5} \right)}

Revision as of 13:20, 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} [/math]

[math] \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]