Rayleigh plane-wave expansion
= Rayleigh plane-wave expansion
{c}
The Rayleigh plane-wave expansion is
$$
e^{i\mathbf k\cdot\mathbf x}
=4\pi\sum_{\ell m}i^\ell j_\ell(kr)
Y_{\ell m}^*(\widehat{\mathbf k})Y_{\ell m}(\widehat{\mathbf x}),
$$
where $j_\ell$ is a spherical Bessel function.