Section 1
Definition and Examples
Show that $b_{r, p}^{-} * b_{s, p}^{-}=b_{r+s, p}^{-}$for $r, s \in(0, \infty)$ and $p \in(0,1]$.
Give an example for two different probability generating functions that coincide at countably many points $x_{i} \in(0,1), i \in \mathbb{N}$. (That is, in Theorem $3.2$ (iii), the assumption $\psi(z)<\infty$ for some $z>1$ cannot be dropped.)