Gaussian function
Noun
Meaning
Gaussian function (plural Gaussian functions)
(mathematics) A function of the form
f
(
x
)
=
a
⋅
exp
(
−
(
x
−
b
)
2
2
c
2
)
{\displaystyle f(x)=a\cdot \exp {\left(-{\frac {(x-b)^{2}}{2c^{2}}}\right)}}
for arbitrary real-number constants .mw-parser-output .texhtml{font-family:"Nimbus Roman No9 L","Times New Roman",Times,serif;font-size:118%;line-height:1;white-space:nowrap;font-feature-settings:"lnum","tnum","kern"0;font-variant-numeric:lining-nums tabular-nums;font-kerning:none}.mw-parser-output .texhtml .texhtml{font-size:100%}a, b and non-zero c; used in statistics, signal processing, etc.
Synonym: Gaussian
Related terms
Examples
This theorem is ultimately connected with the spectral characterization of as the eigenvalue associated with the Heisenberg uncertainty principle, and the fact that equality holds in the uncertainty principle only for the Gaussian function.
The terms Gaussian function and Gaussian bell curve are also ambiguous because they sometimes refer to multiples of the normal distribution that cannot be directly interpreted in terms of probabilities.