Smoothness

In mathematical analysis, the smoothness of a function is a property measured by the number of continuous derivatives it has over some domain, called differentiability class.[1] At the very minimum, a function could be considered smooth if it is differentiable everywhere (hence continuous).[2] At the other end, it might also possess derivatives of all orders in its domain, in which case it is said to be infinitely differentiable and referred to as a C-infinity function (or ${\displaystyle C^{\infty }}$ function).[3]

"C infinity" redirects here. For the extended complex plane ${\displaystyle \mathbb {C} _{\infty }}$, see Riemann sphere.

"C^n" redirects here. For ${\displaystyle \mathbb {C} ^{n}}$, see Complex coordinate space.