I am looking for the proof of The general result for $N(\lambda)$ for a Sturm-Liouville operator.
$$\lim_{\lambda \to \infty} \frac{N(\lambda)}{\lambda^{d/2}} = \frac{v_d}{(2 \pi)^2}\int_{\Omega} dx \bigg(\frac{\rho(x)}{p(x)} \bigg)^{d/2} $$
for general shaped $\Omega \subset \mathbb{R}^d $ and dimension $ \geq 1$, where $v_d$ is the volume of a unit sphere in $d$ dimensions.
For $d=2$ and $d=3$ I proved them. I am trying to find it in Courant and Hilbert Volume I, chapter 6, section 4 (p 436..) but I can't find it. Is there other literature where this derivation can be found. (I already consulted the original paper of Weyl 1912. (German Version )
Any help or reference(s), would be much appreciated.