Weierstrass transform
![The graph of a function f(x) (gray) and its generalized Weierstrass transforms for t = 0.2 (red), t = 1 (green) and t = 3 (blue). The standard Weierstrass transform F(x) is given by the case t = 1, the green graph.](/Images/godic/202502/20/Weierstrass3035.png")
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.
Specifically, it is the function F defined by