![]() The graph of a function f( x) (black) and its generalized Weierstrass transforms for five width ( t) parameters. Erf Gaussian Integral Download Wolfram Notebook The Gaussian integral, also called the probability integral and closely related to the erf function, is the integral of the one-dimensional Gaussian function over. Similarly, the Gaussian integral over the Hermitian matrices (Q r) FF is done by completing the square and shifting.The integral over (Q r) BB, however, is not Gaussian, as the domain is not R n but the SchäferWegner domain. Since the limits on s as y ± depend on the sign of x, it simplifies the calculation to use the fact that e x 2 is an even function, and, therefore, the integral over all real numbers is just twice the integral from zero to infinity. ![]() 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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