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Nov 5, 2014 at 18:23 comment added chris tulane Note that the sech density is also self dual, and is not a stable density.
Jul 10, 2014 at 1:38 comment added Alex R. The generalized central limit theorem applies to stable distributions, which in general are not self dual.
Jul 10, 2014 at 1:23 comment added Alex R. The fact that the characteristic function is the same is "because" the Gaussian, along with Hermite polynomials are eigenfunctions of the Fourier transform: en.m.wikipedia.org/wiki/Fourier_transform#Eigenfunctions
Jul 10, 2014 at 0:51 history asked Ash Malyshev CC BY-SA 3.0