In mathematics, a Gaussian function , often simply referred to as a
Gaussian , is a function of the base form
and with parametric extension for arbitrary real constants a, b and non-zero
c. It is named after the mathematician Carl Friedrich Gauss. The graph of a
Gaussian is a characteristic symmetric "bell curve" shape. The parameter a is
the height of the curve's peak, b is the position of the center of the peak,
and c (the standard deviation, sometimes called the Gaussian RMS width)
controls the width of the "bell".
Gaussian functions are often used to represent the probability density
function of a normally distributed random variable with expected value μ = b
and variance σ2 = c2.