Solution
= Solution
Uniqueness of Laurent coefficients applied to $f(z)=f(-z)$ gives
$$
\sum_na_nz^n=\sum_n(-1)^na_nz^n.
$$
\b[Hence $a_n=(-1)^na_n$, so every coefficient with odd $n$ vanishes.]
= Solution
Uniqueness of Laurent coefficients applied to $f(z)=f(-z)$ gives
$$
\sum_na_nz^n=\sum_n(-1)^na_nz^n.
$$
\b[Hence $a_n=(-1)^na_n$, so every coefficient with odd $n$ vanishes.]