In mathematics, the BergmanâÂÂWeil formula is an integral representation for holomorphic functions of several variables generalizing the Cauchy integral formula. It was introduced by and .
A Weil domain is an analytic polyhedron with a domain U in C<sup>n</sup> defined by inequalities f<sub>j</sub>(z) < 1 for functions f<sub>j</sub> that are holomorphic on some neighborhood of the closure of U, such that the faces of the Weil domain (where one of the functions is 1 and the others are less than 1) all have dimension 2n − 1, and the intersections of k faces have codimension at least k.