generalized Cauchy integral formula
Let be a domain with boundary. Let be a function that is up to the boundary. Then for
Note that up to the boundary means that the function and the derivative extend to be continuous functions on the closure of The theorem follows from Stokes’ theorem. When is holomorphic, then the second term is zero and this is the classical Cauchy integral formula.
- 1 Lars Hörmander. , North-Holland Publishing Company, New York, New York, 1973.
- 2 Steven G. Krantz. , AMS Chelsea Publishing, Providence, Rhode Island, 1992.
|Title||generalized Cauchy integral formula|
|Date of creation||2013-03-22 17:46:41|
|Last modified on||2013-03-22 17:46:41|
|Last modified by||jirka (4157)|
|Synonym||generalized Cauchy formula|