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2.7: Відносини Крамерса-Кроеніга
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$\chi_r (\Omega) = \dfrac{2}{\pi} \int_{0}^{\infty} \dfrac{\omega \chi_i (\omega)}{\omega^2 - \Omega^2} d\omega = n^2 (\Omega) - 1, \nonumber$ \[\chi_i (\Omega) = -\dfrac{2}{\pi} \int_{0}^{\infty} ... $\chi_r (\Omega) = \dfrac{2}{\pi} \int_{0}^{\infty} \dfrac{\omega \chi_i (\omega)}{\omega^2 - \Omega^2} d\omega = n^2 (\Omega) - 1, \nonumber$ $\chi_i (\Omega) = -\dfrac{2}{\pi} \int_{0}^{\infty} \dfrac{\Omega \chi_r (\omega)}{\omega^2 - \Omega^2} d\omega. \nonumber$ $\begin{align*} n^2 (\Omega) &= 1 + \sum_i A_i \dfrac{\omega_i}{\omega_i^2 - \Omega^2} \\[4pt] &= 1 + \sum_i a_i \dfrac{\lambda}{\lambda^2 - \lambda_i^2} \end{align*} \nonumber$