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@ -871,12 +871,13 @@ values given as follows, respectively,
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.. math::
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&D_2^{(1)}(\mathbf{q}, \omega) = \frac{1}{N}
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\sum_{\lambda_1,\lambda_2}
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\left[\delta(\omega+\omega_{\lambda_1}-\omega_{\lambda_2}) +
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\delta(\omega-\omega_{\lambda_1}+\omega_{\lambda_2}) \right], \\
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\sum_{\lambda',\lambda''} \Delta(-\mathbf{q}+\mathbf{q}'+\mathbf{q}'')
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\left[\delta(\omega+\omega_{\lambda'}-\omega_{\lambda''}) +
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\delta(\omega-\omega_{\lambda'}+\omega_{\lambda''}) \right], \\
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&D_2^{(2)}(\mathbf{q}, \omega) = \frac{1}{N}
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\sum_{\lambda_1,\lambda_2}\delta(\omega-\omega_{\lambda_1}
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-\omega_{\lambda_2}).
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\sum_{\lambda',\lambda''}
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\Delta(-\mathbf{q}+\mathbf{q}'+\mathbf{q}'') \delta(\omega-\omega_{\lambda'}
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-\omega_{\lambda''}).
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::
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