Definition:Convergent Mapping/Complex Function

Definition
Let $f: \C \to \C$ be a complex function defined everywhere on $\C$ except possibly at $c$.

Let $f \left({z}\right)$ tend to the limit $L$ as $z$ tends to $c$.

Then $f$ converges to the limit $L$ as $z$ tends to $c$.

Also see

 * Definition:Divergent Function