An O(M) algorithm evaluates azimuthal Fourier modes of the 3D Helmholtz Green's function and derivatives with cost independent of wavenumber and separation.
Ho and Leslie Greengard
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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.