### Gaussian function

(function producing the bell curve)

A **Gaussian function** is a function of this form:

f(x) = a e^{(-(x-b)²/2c²)}

for constants a, b, c, and Euler's number e, 2.71828...
The adjective **Gaussian** means "described by this function".
The function plots a **bell curve**,
and among its uses is that it is the
probability density function of **normal distributions** (i.e., **Gaussian distributions**),
which, as per the **central limit theorem**,
describe probability distributions
of summing a specific number of
independent random variables.
For example, errors in measurement are commonly
assumed to include a purely random element
and analyzed using a normal distribution
and thus a gaussian function.
When representing a normal distribution, *a* (per above)
has this relation with σ, the standard deviation:

a = 1 / ( σ √(2π) )

(*mathematics,statistics,probability*)
**Further reading:**

http://en.wikipedia.org/wiki/Gaussian_function

https://astronomy.swin.edu.au/cosmos/g/Gaussian+Function

http://hyperphysics.phy-astr.gsu.edu/hbase/Math/gaufcn.html

https://mathworld.wolfram.com/GaussianFunction.html

**Referenced by pages:**

full width at half maximum (FWHM)

line shape function

non-Gaussian (NG)

photon noise

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