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  the Bochner–Martinelli kernel  is a differential form in  of bidegree  defined by

(where the term  is omitted). Suppose that  is a continuously differentiable function on the closure of a domain  in n 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

See also

Bergman–Weil formula

Notes

References

. . . . . . ,  (ebook). . The first paper where the now called Bochner-Martinelli formula is introduced and proved. . Available at the SEALS Portal . In this paper Martinelli gives a proof of Hartogs' extension theorem by using the Bochner-Martinelli formula. . The notes form a course, published by the Accademia Nazionale dei Lincei, held by Martinelli during his stay at the Accademia as "Professore Linceo". . In this article, Martinelli gives another form to the Martinelli–Bochner formula. Theorems in complex analysis
Several complex variables