"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.
A bump function is a smooth function with compact support.
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]
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.
^Weisstein, Eric W. "Smooth Function". mathworld.wolfram.com. Archived from the original on 2019-12-16. Retrieved 2019-12-13.
In mathematical analysis, the smoothness of a function is a property measured by the number, called differentiability class, of continuous derivatives...
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