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\begin{eqnarray}
&&\epsilon_{zz} = \epsilon_{zz}^{\prime}+i\epsilon_{zz}^{\prime{\prime}} \label{4e} \\
&&\epsilon_{zz}^{\prime} = 1+\frac{\alpha\mu ^2}{\pi\omega ^2}\sum\limits_{s=\pm}\frac{1}{\beta ^3_{s}}\left\{\frac{8}{3}\beta_{s} - 4\arctanh{\beta_{s}}+ \ln{\vert\frac{4\mu ^2-\omega ^2(1+\beta_{s})^2}{4\mu ^2-\omega ^2(1-\beta_{s})^2}\vert} \nonumber \\
&&+\frac{\omega ^2}{12\mu ^2}\sum\limits_{t=\pm}(t(1+2t\beta_{s})(1-t\beta_{s})^2\ln{\vert\frac{4\Gamma ^2(1-i\beta_{s})^2}{4\mu ^2 -\omega ^2(1-i\beta_{s})^2}\vert}-\frac{2\mu}{\omega}(\frac{4\mu ^2}{\omega ^2}+3-3\beta ^2_{s})\ln{\vert\frac{2\mu -t\omega(1+t\beta_{s})}{2\mu +t\omega(1+t\beta_{s})}\vert})\right\} 
\end{eqnarray}





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