This was an exam question and I was absolutely lost.
Find positive constants $a,b$ such that the function
$$ \frac{1}{z^2+a} + \frac{1}{z+b} $$
has three Laurent series, one for each of the domains $|z|<1, \,\, 1<|z|<4, \,\, |z|>4$.
2026-04-01 07:13:35.1775027615
Finding Laurent Series
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Try $a=1$ and $b=4$ or $a=16$ and $b=1$.