If we have a function $f(s)$ with this form:
$ f(s) = \sum_{i=0}^{\infty} p_i s^i $
We also know that:
$ f(1) = 1 $
and
$ p_i \ge 0 \quad \text {for all $ i \ge 0$} $
Assume we can calculate $f(s)$ for any $s$, is it possible that with all the info we know, we would be able to get $p_n$ for any n?
(Actually $p_i$ is the probability that $[Z=i]$ where Z is a random variable.)