Solution
= Solution
An <isolated singularity> at $a$ is a <removable singularity> when there is a <holomorphic function> $F$ on a full disc $B(a,r)$ agreeing with $f$ away from $a$. Equivalently,
$$
\boxed{\lim_{z\to a}f(z)=L\in\mathbb C,\qquad F(a)=L}.
$$
The <Riemann removable singularity theorem> also characterizes this by boundedness of $f$ on a sufficiently small punctured disc. A preassigned incorrect value at $a$ is replaced by $L$.