Spin-weighted spheroidal harmonic module#
The spin-weighted spheroidal harmonics \(S_{sjm\gamma}(\theta)\) satisfy the equation
\[
\left[\frac{1}{\sin\theta}\frac{d}{d\theta}\left(\sin\theta \frac{d}{d\theta} \right)
- \left(\gamma^2\sin^2\theta+\frac{(m+s\cos\theta)^2}{\sin^2\theta}
+2\gamma s\cos\theta-s-2m\gamma-\lambda_{sjm\gamma} \right)\right]S_{sjm\gamma} = 0,
\]
with eigenvalues \(\lambda_{sjm\gamma}\) and spheroidicity \(\gamma\). For the Teukolsky equation, \(\gamma = a\omega\).