Gaussian function ($e-x^2$)

A Gaussian function has the form $A\exp [-a(x-b{)}^2]$ with $a>0$. Its integral and moments reduce by translation and scaling to the Gaussian integral.

The Gaussian function is a specific type of mathematical function that describes a symmetrical, bell-shaped curve. It is often used in statistics, probability, and various fields of science for modeling normal distributions, among other applications.