harmonic#
- spheroidal.wrapper.harmonic(s, ell, m, g, method='spectral', num_terms=None, n_max=100)[source]#
Computes the spin-weighted spheroidal harmonic with spin-weight s, degree l, order m, and spheroidicity g. Specifically, this function returns \(S_{l m}^\gamma(\theta)e^{im\phi}\) where \(S_{l m}^\gamma(\theta)\) is a solution to the following equation.
\[\small \left[\frac{1}{\sin \theta} \frac{d}{d \theta}\left(\sin \theta \frac{d}{d \theta}\right) -\gamma^2 \sin ^2 \theta-\frac{(m+s \cos \theta)^2}{\sin ^2 \theta}-2 \gamma s \cos \theta+s+2m\gamma + { }_s \lambda_{l m}\right]{ }_s S_{l m}^\gamma(\theta)=0\]Supported methods:
- “spectral” (default): spherical expansion method described in Appendix A of
- “leaver”: continued fraction method described in
- Parameters:
s (int or half-integer float) – spin-weight
ell (int or half-integer float) – degree
m (int or half-integer float) – order
g (complex) – spheroidicity
method (str, optional) – method used to compute the harmonic (options are “spectral” and “leaver”), defaults to “leaver”
num_terms (int, optional) – number of terms used in the expansion, automatic by default
n_max (int, optional) – maximum number of terms in the expansion, defaults to 100
- Returns:
spin-weighted spheroidal harmonic \({}_{s}S_{lm}(\theta,\phi)\)
- Return type:
function