Let $\theta \in \mathbb { R }$. Determine the power series expansion of the function $$x \mapsto \frac { 1 - x ^ { 2 } } { x ^ { 2 } - 2 x \cos \theta + 1 }$$ on an interval to be specified.
Let $\theta \in \mathbb { R }$. Determine the power series expansion of the function
$$x \mapsto \frac { 1 - x ^ { 2 } } { x ^ { 2 } - 2 x \cos \theta + 1 }$$
on an interval to be specified.