# Bergman–Weil formula

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In mathematics, the Bergman–Weil formula is an integral representation for holomorphic functions of several variables generalizing the Cauchy integral formula. It was introduced by (Bergmann 1936) and (Weil 1935).

## Weil domains

A Weil domain (Weil 1935) is an analytic polyhedron with a domain U in Cn defined by inequalities fj(z) < 1 for functions fj 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.