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单词 Weierstrass transform
释义

Weierstrass transform

英语百科

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.

In mathematics, the Weierstrass transform of a function f : RR, 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

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