generalized Cauchy integral formula


Let UC be a domain with C1 boundary. Let f:UC be a C1 function that is C1 up to the boundary. Then for zU,


Note that C1 up to the boundary means that the function and the derivativePlanetmathPlanetmath extend to be continuous functionsMathworldPlanetmathPlanetmath on the closure of U. The theorem follows from Stokes’ theorem. When f is holomorphic, then the second term is zero and this is the classical Cauchy integral formulaPlanetmathPlanetmath.


  • 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
Canonical name GeneralizedCauchyIntegralFormula
Date of creation 2013-03-22 17:46:41
Last modified on 2013-03-22 17:46:41
Owner jirka (4157)
Last modified by jirka (4157)
Numerical id 6
Author jirka (4157)
Entry type Theorem
Classification msc 30E20
Synonym generalized Cauchy formula