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Commit d62ef077 authored by Wuttke, Joachim's avatar Wuttke, Joachim
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same handling of triple product in all formulae

parent 34c429f1
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......@@ -179,7 +179,7 @@ The removable singularity for $\qp\E_j=0$
can be handled by a sinc function, as discussed in Sec.~\ref{SShapeTrafIntro}:
\begin{equation}\label{Effpolygon2}
F_\parallel(\qp)
= \frac{2\n\times\uqp^*}{ip}
= \frac{2\,\n\times\uqp^*}{ip}
\sum_{j=0}^{N-1} \E_j \sinc(\qp\E_j) \e^{i\qp\R_j}.
\end{equation}
Furthermore, there is a singularity at $p=0$.
......@@ -190,7 +190,7 @@ To avoid cancellation near this singularity, we subtract $\E_j$ from each summan
\Emph{
\begin{equation}\label{Effpolygon3}
F_\parallel(\qp)
= 2\n\times\uqp^*
= 2\,\n\times\uqp^*
\sum_{j=0}^{N-1} \E_j \frac{\sinc(\qp\E_j) \e^{i\qp\R_j} - 1}{ip}.
\end{equation}
}
......@@ -205,8 +205,8 @@ We write $N\eqqcolon2n$
and make use of $\V_{j+n}=-\V_j$ to transform~(\ref{Effpolygon2}) into
\Emph{
\begin{equation}\label{Eff2ngon}
F_\parallel(\qp) = \displaystyle 4 \sum_{j=0}^{n-1}
\n(\uqp^*\times\E_j) (\uqp\R_j) \sinc(\qp\E_j) \sinc(\qp\R_j),
F_\parallel(\qp) = \displaystyle 4\, \n\times\uqp^*\sum_{j=0}^{n-1}
\E_j (\uqp\R_j) \sinc(\qp\E_j) \sinc(\qp\R_j),
\end{equation}
}
where the singularity at $p=0$ is absorbed in a second sinc function.
......
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