The graph of a function f( x) (black) and its generalized Weierstrass transforms for five width ( t) parameters. But if you want to avoid the function, the integral can be reduced to the Gaussian integral more directly by grixors answer. 1 which shows that is sub-Gaussian with parameter 1 as claimed. In mathematics, the Weierstrass transform of a function f : R → R, named after Karl Weierstrass, is a "smoothed" version of f( x) obtained by averaging the values of f, weighted with a Gaussian centered at x.
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