Gaussian functions are analytic, and their limit as x is 0.

Consequently, Gaussian functions are also associated with the vacuum state in quantum field theory.

Gaussian functions are used to define some types of artificial neural networks.

This was done using two-dimensional gaussian functions to represent the spots, as shown in Fig.

The original choice of is to use a multidimensional Gaussian function.

The Gaussian function has infinite range and it is impractical for implementation.

Outside these limits of integration , the Gaussian function is small enough to be ignored.

The weight is usually set to a Gaussian function of the distance between and p.

This gives an output pulse shaped like a Gaussian function.

It also frequently appears in various integrals involving Gaussian functions.