A formula for the derivatives of holomorphic functions in C2 in terms of certain integrals taken on boundaries of analytic varieties

We derive a Cauchy–Fantappiè type formula which expresses the derivatives of holomorphic functions at a point on a given analytic variety, in terms of the values of the function in an arbitrarily small neighborhood of the curve which bounds the variety. The formula involves derivatives of functions defined by integrals taken on boundaries of nearby analytic varieties. We also apply these formulas to questions related to analytic functionals.  2003 Elsevier Science (USA). All rights reserved