For issues related to any of the uses of the Gaussian function. Don't forget to add additional tags to clarify the context.
The graph of a Gaussian is a characteristic symmetric "bell curve" shape that quickly falls off towards plus/minus infinity. The 1-D Gaussian is defined as (taken from wikipedia):
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".
In multiple dimensions, the Gaussian is defined as the product of 1D curves along each dimension.
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, in mathematics and physics where they are used to solve heat equations and diffusion equations, to formulate the propagation of optical beams (Gaussian beams), to from a basis set of wavefunctions, to define the Weierstrass transform, and many more.
