En posant \chi(\omega) = \chi'(\omega) + i \chi''(\omega) on a :

\chi'(\omega) = \frac{1}{\pi}\int_{-\infty}^{\infty} \frac{\chi''(\Omega)} {(\Omega - \omega)} d\Omega

\chi''(\omega) = -\frac{1}{\pi}\int_{-\infty}^{\infty} \frac{\chi'(\Omega)} {(\Omega - \omega)} d\Omega