Entire

Analytic (holomorphic) at every point of the whole complex plane.

A function is entire if it is analytic at every single point of the complex plane, with no domain restriction at all. Entire functions form a comparatively small, well-behaved family: polynomials, $e^z$ , $\sin z$ , and $\cos z$ are all entire, while a function like $1/z$ is analytic everywhere except at its one bad point and so falls just short of entire.

Examples

Every polynomial in $z$ is entire.
$f(z)=1/z$ is analytic on $\mathbb{C}\setminus\{0\}$ but is not entire, since it fails to be defined -- let alone differentiable -- at $z=0$ .