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\begin{eqnarray}  N(\omega)&=&(4e^2/h)\sum_{k\beta,q\gamma, \nu\mu} \int \frac{d\epsilon}{2\pi}   [G_{\beta\nu}^r(\omega+\epsilon) \Gamma{\nu\gamma} \Gamma_{\nu\gamma}  G_{\gamma\mu}^r(\omega) \Gamma{\mu\beta} \Gamma_{\mu\beta}  (1-f_e(\omega+\epsilon) f_{h})(\omega)] f_{h}(\omega)]  \\ \nonumber  &&\sum_{\lambda\delta}[G_{\beta\nu}^r(\omega+\epsilon) \Gamma_{0,\nu\gamma} G_{\gamma\lambda}^<(\omega) \Gamma{\lmabda\delta}G^a_{\delta\mu}(\omega+\epsilon)[i\Gamma_{\mu\beta}](1-f_e(\omega+\epsilon)f_{h}(\omega))] \Gamma{\lambda\delta}G^a_{\delta\mu}(\omega+\epsilon)[i\Gamma_{\mu\beta}](1-f_e(\omega+\epsilon)f_{h}(\omega))]  \\ \nonumber  &&[G_{\beta\nu}^>(\omega+\epsilon) \Sigma_{0,\nu\gamma}^a(\omega+\epsilon) G_{\gamma\mu}^r(\omega)\Sigma_{0,\mu\beta}^{<,h}(\omega+\epsilon)] &&[\sum_{\lambda\delta} G_{\beta\lambda}^r(\omega+\epsilon)\Gamma_{\lambda\delta} G_{\delta\nu}^a(\omega+\epsilon)[i\Gamma_{\nu\gamma}] G_{\gamma\mu}^r(\omega)(1-f_{e}(\omega+\epsilon)+1-f_{h}(\omega+\epsilon))f_h(\omega+\epsilon)]  \\ \nonumber  &&[G_{\beta\nu}^>(\omega+\epsilon) \Sigma_{0,\nu\gamma}^a(\omega+\epsilon) G_{\gamma\mu}^<(\omega) \Sigma_{0,\mu\beta}^{a,h}(\omega+\epsilon)]   \end{eqnarray}