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Smoothness
Number of derivatives of a function (mathematics) / From Wikipedia, the free encyclopedia
"C infinity" redirects here. For the extended complex plane
, see Riemann sphere.
"C^n" redirects here. For
, see Complex coordinate space.
For smoothness in number theory, see smooth number.
In mathematical analysis, the smoothness of a function is a property measured by the number, called differentiability class, of continuous derivatives it has over its domain.[1]
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A function of class is a function of smoothness at least k; that is, a function of class
is a function that has a kth derivative that is continuous in its domain.
A function of class or
-function (pronounced C-infinity function) is an infinitely differentiable function, that is, a function that has derivatives of all orders (this implies that all these derivatives are continuous).
Generally, the term smooth function refers to a -function. However, it may also mean "sufficiently differentiable" for the problem under consideration.