Numerical evaluation of multiple integrals. I

which are known for special regions (in n-dimensional euclidean space En) may be used to determine formulas for other regions. They also showed, in some cases, how the symmetry of a region may simplify the task of finding integration formulas for the region. To facilitate numerical integration over regions in higher dimensional spaces, we summarize the most important formulas (1) and review methods by which formulas for classes of regions may be obtained from them. These methods enable one to obtain formulas for regions which we consider too special to warrant particular formulas.