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

Several complex variables

The theory of functions of several complex variables is the branch of mathematics dealing with functionson the space Cn of n-tuples of complex numbers...

, introduced by and .

Bochner–Martinelli kernel

For ζ, z in C ⁿ the Bochner–Martinelli kernel ω(ζ,z) is a differential form in ζ of bidegree (n,n−1) defined by

(where the term d_j is omitted).

Bochner–Martinelli formula

Suppose that f is a continuously differentiable function on the closure of a domain D in Cⁿ with piecewise smooth boundary ∂D. Then the Bochner–Martinelli formula states that if z is in the domain D then

In particular if f is holomorphic the second term vanishes, so