entire function

An entire function is a function $f: \mathbb{C} \longrightarrow \mathbb{C}$ which is holomorphic everywhere on the complex domain $\mathbb{C}$ .

For example, a polynomial is holomorphic everywhere, as is the exponential function. The function $z\mapsto 1/z$ is not holomorphic at zero, so it is not entire; it is meromorphic.