A degenerate version of Brion's formula

Carsten Peterson

Let $\mathfrak{p}\subset V$ be a polytope and $\xi \in V_{\mathbb{C}}^{\ast }$. We obtain an expression for $I(\mathfrak{p};\alpha ):={\int }_{\mathfrak{p}}{e}^{⟨\alpha ,x⟩}dx$ as a sum…