Editing Stanley's reciprocity theorem (section)

== Formulation ==
Stanley's reciprocity theorem states that for a rational cone as above, we have<ref>{{cite journal |first=Richard P. |last=Stanley |title=Combinatorial reciprocity theorems |journal=[[Advances in Mathematics]] |volume=14 |issue=2 |pages=194–253 |year=1974 |doi=10.1016/0001-8708(74)90030-9 |doi-access=free |url=http://math.mit.edu/~rstan/pubs/pubfiles/22.pdf}}</ref>

:<math>F(1/x_1,\dots,1/x_d)=(-1)^d F_{\rm int}(x_1,\dots,x_d).</math>

[[Matthias Beck]] and [[Mike Develin]] have shown how to prove this by using the [[methods of contour integration|calculus of residues]].<ref>{{cite arXiv |first1=M. |last1=Beck |first2=M. |last2=Develin |eprint=math.CO/0409562 |title=On Stanley's reciprocity theorem for rational cones |year=2004}}</ref>

Stanley's reciprocity theorem generalizes Ehrhart-Macdonald reciprocity for [[Ehrhart polynomials]] of rational [[Convex polytope|convex polytopes]].