If $g(\theta)=\underset{k=0,1,2..}{\overset{\infty}{\sum}} a_k\theta^k$ is a Taylor series then, we can generate a probability distribution such that $$P(X=k)=\frac{a_k\theta^k}{g(\theta)}.$$ Then, $X$ is said to have a power series distribution.
Question: What is "$g$" called in relation to $X$? Is it the probability generating function?
$g$ is a normalizing constant. It is needed for sum of probabilities to be equal to $1$. The equation for $P(X=k)$ is okay if $a_k\ge0$ for all $k$.
[answered by @NCh in the comments section]