Gaussian function: Difference between revisions

Revision as of 17:50, 24 August 2025

Latest revision as of 18:01, 24 August 2025

Line 91:

<math display="block">\int_{-\infty}^\infty ae^{-(x-b)^2/2c^2}\,dx = a\sqrt{2\pi c^2}.</math>

== ThreeTwo-dimensional Gaussian function ==

[[File:Gaussian 2d surface.png|thumb|3d plot of a Gaussian function with a two-dimensional ___domain]]

Base form:

<math display="block">f(x,y) = \exp(-x^2-y^2)</math>

In threetwo dimensions, the power to which ''e'' is raised in the Gaussian function is any negative-definite quadratic form. Consequently, the [[level set]]s of the Gaussian will always be ellipses.

A particular example of a two-dimensional Gaussian function is