An O(M) algorithm evaluates azimuthal Fourier modes of the 3D Helmholtz Green's function and derivatives with cost independent of wavenumber and separation.
On the azimuthal fourier components of the green’s function for the helmholtz equation in three dimensions.Journal of Mathematical Physics, 36(9):5159–5169
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Fast Evaluation of the Azimuthal Fourier Modes of the 3D Helmholtz Green's Function and Their Derivatives
An O(M) algorithm evaluates azimuthal Fourier modes of the 3D Helmholtz Green's function and derivatives with cost independent of wavenumber and separation.