The Ehrhart function L(P,t) for real t >= 0 on a rational polytope is a quasi-polynomial whose coefficients are periodic piecewise polynomials (or periodic vanishing functions), with explicit vertex-based formulas when P is a simplex and reciprocity preserved.
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Ehrhart quasi-polynomials of rational polytopes by real dilations
The Ehrhart function L(P,t) for real t >= 0 on a rational polytope is a quasi-polynomial whose coefficients are periodic piecewise polynomials (or periodic vanishing functions), with explicit vertex-based formulas when P is a simplex and reciprocity preserved.