An Euler-MacLaurin formula for polygonal sums
An Euler-MacLaurin formula for polygonal sums
We prove an Euler-Maclaurin formula for double polygonal sums and, as a corollary, we obtain approximate quadrature formulas for integrals of smooth functions over polygons with integer vertices. Our Euler-Maclaurin formula is in the spirit of Pickâs theorem on the number of integer points in an integer polygon and involves …