Proposition

Find the terms $c_nz^n$ in the Laurent series for $\frac{1}{\sin^2(z)}$ centered at $z = 0$ for $-4 \leq n \leq 4$.

Solution

Example 8.23 [A first course in complex analysis] has the Laurent series for $\frac{1}{\sin(z)}$. By simply squaring it, we obtain