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. At the very minimum, a function could be considered smooth if it is differentiable everywhere (hence continuous). 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).

"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.