Gaussian Function

In mathematics, a Gaussian function (named after Carl Friedrich Gauss) is a function of the form:

for some real constants a, b, c, and e ≈ 2.71828...(Euler's number).

The graph of a Gaussian is a characteristic symmetric "bell curve" shape that quickly falls off towards plus/minus infinity. The parameter a is the height of the curve's peak, b is the position of the centre of the peak, and c controls the width of the "bell".

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