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To get the correct result for the 2D Fourier transform of a function which doesn't factor in Cartesian coordinates, it's usually necessary to give Mathematica some assistance as to the best choice of coordinates. In the circular case, that of course means we should use polar coordinates: Clear[k]; airy[k_] = 1/(2 Pi) Integrate[ r Exp[I k r ...


It does appear something might have been tinkered with, or my recollection / documentation is in error. InverseFourierSequenceTransform[cf, t, -n, FourierParameters -> {1, 1}, Assumptions -> 0 < p < 1] // PiecewiseExpand properly recovers the PDF (PMF) for the GeometricDistribution case.

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