Bochner–Martinelli formula


In mathematics, the Bochner–Martinelli formula is a generalization of the Cauchy integral formula to functions of several complex variables, introduced by and.

History

Bochner–Martinelli kernel

For, in ℂn the Bochner–Martinelli kernel is a differential form in of bidegree defined by
.
Suppose that is a continuously differentiable function on the closure of a domain in ℂn with piecewise smooth boundary. Then the Bochner–Martinelli formula states that if is in the domain then
In particular if is holomorphic the second term vanishes, so