Is there an algorithm to evaluate spin-weighted spherical harmonics (swSH) at arbitrary points on the sphere? In particular I am looking for, e.g. a recursion relation to evaluate the "spin weighted Legendre functions" ${}_sP^m_l$, which satisfy the follow Sturm-Liouville equation
$ \frac{d}{dx}\left(\left(1-x^2\right)\frac{d{}_sP^m_l(x)}{dx}\right)+\left(s-\frac{(m-sx)^2}{1-x^2}\right){}_sP^m_l(x)=-(l-s)(l+s+1){}_sP^m_l(x) $
over the interval $x\in[-1,1]$. Classic papers on swSH inclde this and this (note I took the above equation from 2.5 of this paper substituting $x\equiv-\mathrm{cos}\vartheta$). In particular, I'd like to evaluate integrals such as
$ \int_{-1}^1dx {}_sP^m_l(x)f(x) $
(where f is some function I do know how to evaluate) using Gaussian quadrature.
For context: there exist algorithms to compute discrete spherical harmonic transforms, which require the evaluation of the associated Legendre functions (note $P^m_l={}_0P^m_l$). Is there something similar for swSH?