Definition 32.2.2 seems wrong about napkin

[vEnhance]

Re the first example, Def 32.2.2 has a second clause: there must be a Laurent series. So I think the example would not work here, because at 0 you cannot write a Laurent series with $m > 0$ and $c_{-m} \neq 0$ agreeing with the zero function near $z = 0$.

Perhaps the confusion is that Def 32.2.2 makes it look like the Laurent series is a conclusion, not part of the definition. I'll rewrite that now to say "the function $f$ is FURTHER REQUIRED TO ADMIT a Laurent series..." to eliminate that ambiguity.

Re essential singularity, my memory is that $e^{1/z}$ is not considered a meromorphic function on $\mathbb{C}$. See https://en.wikipedia.org/wiki/Meromorphic_function#Examples third example. So iirc this is intentional.

Abuse of Notation 32.2.4 goes into this more.

[vEnhance]

I addressed this in 2aa3078

Does that look right now?

[SamZhang3]

I addressed this in 2aa3078

Does that look right now?

That looks good to me, thank you!