Hello,

If I have an expansion of a certain function- $\displaystyle f(z) = \sum_{n = 0}^\infty a_n z^n$, how do I derive the expantion of 1/f(z) ?

Namely, I am looking for a series $\displaystyle b_m$ such that:

$\displaystyle \sum_{m = -\infty}^\infty b_m z^m = \frac{1}{\sum_{n = 0}^\infty a_n z^n} $

And I'm looking to express it as a function of the given series of $\displaystyle a_n$

Thank you