I'm comfortable with the process of finding the Laurent series for a complex function, but in many of the answers from the textbook the first few terms will be expanded from it. Since I'm teaching myself this material I suspect it's something conceptual I'm missing.
For example this is an answer I got for a question
$$z^2sin(1/z^2)=\sum_{n=0}^\infty \frac{(-1)^n}{z^{4n}(2n+1)!},(0<|z|<\infty)$$
And this is the answer from the textbook
$$z^2sin(1/z^2)=1+\sum_{n=1}^\infty \frac{(-1)^n}{z^{4n}(2n+1)!},(0<|z|<\infty)$$
It seems to me that they are equal and the difference shouldn't matter, but this discrepancy is consistently coming up where the textbook's answers have a term or two expanded. So it feels like I'm missing something here.