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A new derivation of the plane wave expansion into spherical harmonics and related Fourier transforms

A new derivation of the plane wave expansion into spherical harmonics and related Fourier transforms

This article summarizes a new, direct approach to the determination of the expansion into spherical harmonics of the exponential e i(x|y) with x, y ∈ R d .It is elementary in the sense that it is based on direct computations with the canonical decomposition of homogeneous polynomials into harmonic components …