Spherical-harmonic streaming recurrence
= Spherical-harmonic streaming recurrence
{title2=$\mu Y_{\ell m}=a_{\ell+1,m}Y_{\ell+1,m}+a_{\ell,m}Y_{\ell-1,m}$}
Here $\mu=\cos\theta$ and $a_{\ell,m}=\sqrt{(\ell^2-m^2)/[(2\ell+1)(2\ell-1)]}$. This follows by combining the <associated Legendre function> recurrence $(2\ell+1)\mu P_\ell^m=(\ell-m+1)P_{\ell+1}^m+(\ell+m)P_{\ell-1}^m$ with the normalized <spherical harmonic> constants. It gives the adjacent-multipole couplings in a <photon Boltzmann hierarchy>.