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let's suppose we are given a Gaussian function [tex]f(x)=Ae^{-ax^2}[/tex] (wherea,Aare real scalars andais positive)

Is it possible to (dis)prove that the following identity is true only for Gaussians?

[tex]\frac{\partial^2}{\partial x^2} log f(x) = const[/tex]

Thanks!

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# Unique properties of Gaussians

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