The question asks whether $z_0$ is an isolated singularity of $f(z)$ given that $f(z)$ is analytic in the punctured disk $0 < |z - z_0| < r$, and whether this implies that $f(z)$ has a Laurent series expansion in this domain.

In complex analysis, if $f(z)$ is analytic in the punctured neighborhood around $z_0$, then $z_0$ is indeed an isolated singularity. Additionally, any isolated singularity allows for a Laurent series expansion of $f(z)$ in $0 < |z - z_0| < r$.

Thus, the statement "has a Laurent series expansion" is correct. The answer should be:

• B. ✅ (Correct)

Would you like further details on Laurent series, types of singularities, or how to approach similar problems?

Here are some related questions for further exploration:

1. What are the different types of isolated singularities?
2. How does a Laurent series differ from a Taylor series?
3. What does it mean if the Laurent series of $f(z)$ around $z_0$ contains a principal part?
4. Can a singularity still be isolated if $f(z)$ is not analytic in the punctured disk?
5. What are the conditions for a singularity to be classified as essential?

Tip: To determine the type of singularity, analyze the terms in the Laurent series expansion around that point.