Smoothness

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 of continuous derivatives (differentiability class) 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.

  1. ^ Weisstein, Eric W. "Smooth Function". mathworld.wolfram.com. Archived from the original on 2019-12-16. Retrieved 2019-12-13.