Similar to the case of polytopes with integer vertices, one defines the Ehrhart series for a rational polytope.
\operatorname{Ehr}_P(z) = \sum_{t\ge 0} L(P, t)z^t = \frac{\displaystyle\sum_{j=0}^{d(n+1)} h_j^\ast z^j}{\left(1 - z^d\right)^{n + 1}}, .