= Dirichlet probability generating function
{c}
{title2=$q_X(z)=\mathbb E[X^{-z}]$}
For a positive integer-valued <random variable> of finite support, this transform is a finite <Dirichlet series>. Its values encode ordinary moments, $q_X(-r)=\mathbb E[X^r]$, and its derivatives at zero encode logarithmic moments: $(-1)^rq_X^{(r)}(0)=\mathbb E[(\log X)^r]$. Positive support is essential to these definitions; the transform is distinct from the ordinary <probability generating function> $\mathbb E[s^X]$.
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