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A comment on Researchers thought this was a bug (Borwein integrals) [video]. Parent comment

Re:Researchers thought this was a bug (Borwein integrals) [v... by eutectic on Wednesday November 16, 2022 @09:03AM (#33623047)
I guess it's a Gaussian, by the central limit theorem.
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Re:Researchers thought this was a bug (Borwein integrals) [v... by gugagore on Wednesday November 16, 2022 @11:00AM (#33625308)
No, it can't be. This function has compact support, the Gaussian clearly does not.

You get a Gaussian by repeated convolution of the same function (and normalizing the width).

The equivalent question to what I asked is what's the pdf of X1 + X2/2 + X3/4 + ...

where Xi is iid unit uniform.

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