# How to obtain probability function from its probability generating function

For a discrete random variable $X$, we have known the exact expression of its PGF $G(z)=E[z^X]$.

The question is how can I get $Pr\{X>k\}$ from this PGF.

I want to have an explicit expression of the probability in terms of $G(z)$.

The Z-Transform is too complex to use. And an explicit expression is preferred rather than a upper bound. Is there some other way?

Thanks!

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