Formula_4531

\[n(\omega)=1+\frac{1}{\pi} \int_{0}^{\infty} \frac{d x^{2} x(x)}{x^{2}-\omega^{2}}=n(0)+\frac{\omega^{2}}{\pi} \int_{0}^{\infty} \frac{d x^{2} x(x)}{x^{2}\left(x^{2}-\omega^{2}\right)}\]