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Spherical harmonic

{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.


Rayleigh plane-wave expansion

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Rayleigh plane-wave expansion

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Rayleigh plane-wave expansion

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