Gaussian function

A Gaussian function in red, with the area underneath (defined by a Gaussian integral) in blue).

A Gaussian function is a function in the form
$f(x) = a \exp{\left(- { \frac{(x-b)^2 }{ 2 c^2} } \right)}+d$
Where a, b, c, and d are constants. This graph takes on a bell curve shape, with a being the maximum height, b is the position of the centre, and c is the width of the "bell". The integral of a Gaussian function is a Gaussian integral.