= Spherical harmonic addition theorem
{title2=$P_\ell(\hat{\mathbf n}\cdot\hat{\mathbf m})=\frac{4\pi}{2\ell+1}\sum_mY_{\ell m}(\hat{\mathbf n})Y_{\ell m}^*(\hat{\mathbf m})$}
For orthonormal complex <spherical harmonics>, $P_\ell(\hat{\mathbf n}\cdot\hat{\mathbf m})=4\pi\sum_{m=-\ell}^{\ell}Y_{\ell m}(\hat{\mathbf n})Y_{\ell m}^*(\hat{\mathbf m})/(2\ell+1)$. This converts an angle between two directions into a separable sum. Together with <Orthogonality of Legendre polynomials>, it projects rotationally invariant scattering kernels onto angular multipoles.
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