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\title{DoDeCalculator User Manual}
\author{Philipp von den Hoff}




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\begin{document}
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% !!! IMAGES START HERE !!!

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\( \nu_{dip}\)%
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$C7_2^1$%
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$|\kappa|$%
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\lthtmldisplayA{eqnarraystar251}%
\begin{eqnarray*}
\frac{S_{DQ}(\tau_{1}=0,\tau_{2}=\tau)}{S_{DQ}(\tau_{1}=\frac{\tau}{2},\tau_{2}=\frac{\tau}{2})} & \approx & 1-5.92176\,(\kappa\nu_{dip}\tau)^{2}+10.8542(\kappa\nu_{dip}\tau)^{4}\\
&&+66.0045(\kappa\nu_{dip}\tau)^{6}+75.7769(\kappa\nu_{dip}\tau)^{8}\\
& &-257.0597(\kappa\nu_{dip}\tau)^{10}-1042.1838(\kappa\nu_{dip}\tau)^{12}
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\frac{S_{DQ}(\tau_{1}=0,\tau_{2}=\tau)}{S_{DQ}(\tau_{1}=\frac{\tau}{2},\tau_{2}=\frac{\tau}{2})} & \approx & 1-8.45966\,(\kappa\nu_{dip}\tau)^{2}+0.688133(\kappa\nu_{dip}\tau)^{4}\\
&& +82.9188(\kappa\nu_{dip}\tau)^{6}+356.496(\kappa\nu_{dip}\tau)^{8}\\
&  & +917.248(\kappa\nu_{dip}\tau)^{10}+19.3511\kappa^{4}\nu_{dip}^{4}\tau^{2}\tau_{exc}^{2}\\
&&+78.1164\kappa^{6}\nu_{dip}^{6}\tau^{4}\tau_{exc}^{2}-112.42\kappa^{8}\nu_{dip}^{8}\tau^{6}\tau_{exc}^{2}\\
&  & -2436.81\kappa^{10}\nu_{dip}^{10}\tau^{8}\tau_{exc}^{2}-13453.3\kappa^{12}\nu_{dip}^{12}\tau^{10}\tau_{exc}^{2}\\
&&+146.459\kappa^{6}\nu_{dip}^{6}\tau^{2}\tau_{exc}^{4}+361.662\kappa^{8}\nu_{dip}^{8}\tau^{4}\tau_{exc}^{4}\\
&  & -2364.13\kappa^{10}\nu_{dip}^{10}\tau^{6}\tau_{exc}^{4}-19351.1\kappa^{12}\nu_{dip}^{12}\tau^{8}\tau_{exc}^{4}\\
&&-59052.6\kappa^{14}\nu_{dip}^{14}\tau^{10}\tau_{exc}^{4}+912.66\kappa^{8}\nu_{dip}^{8}\tau^{2}\tau_{exc}^{6}\\
&  & -339.254\kappa^{10}\nu_{dip}^{10}\tau^{4}\tau_{exc}^{6}-28544.7\kappa^{12}\nu_{dip}^{12}\tau^{6}\tau_{exc}^{6}\\
&&-106658.0\kappa^{14}\nu_{dip}^{14}\tau^{8}\tau_{exc}^{6}+112723.0\kappa^{16}\nu_{dip}^{16}\tau^{10}\tau_{exc}^{6}\\
&  & +4205.54\kappa^{10}\nu_{dip}^{10}\tau^{2}\tau_{exc}^{8}-26880.1\kappa^{12}\nu_{dip}^{12}\tau^{4}\tau_{exc}^{8}\\
&&-224842.0\kappa^{14}\nu_{dip}^{14}\tau^{6}\tau_{exc}^{8}-31429.2\kappa^{16}\nu_{dip}^{16}\tau^{8}\tau_{exc}^{8}\\
 &  & +5635312.6\kappa^{18}\nu_{dip}^{18}\tau^{10}\tau_{exc}^{8}
\end{eqnarray*}%
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$\tau_{exc}=\tau_{recon}$%
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