What is Gaussian function?

In mathematics, a Gaussian function, often simply referred to as a Gaussian, is a function of the base form

Gaussian functions are often used to represent the probability density function of a normally distributed random variable with expected value μ = b and variance σ = c. In this case, the Gaussian is of the form

Gaussian functions are widely used in statistics to describe the normal distributions, in signal processing to define Gaussian filters, in image processing where two-dimensional Gaussians are used for Gaussian blurs, and in mathematics to solve heat equations and diffusion equations and to define the Weierstrass transform.