closed curve theorem

Let U be a simply connected domain, and suppose f:U is holomorphic. Then


for any smooth closed curveMathworldPlanetmath C in U.

More generally, if U is any domain, and C1 and C2 are two homotopicMathworldPlanetmath smooth closed curves in U, then


for any holomorphic function f:U.

Title closed curve theorem
Canonical name ClosedCurveTheorem
Date of creation 2013-03-22 12:04:43
Last modified on 2013-03-22 12:04:43
Owner djao (24)
Last modified by djao (24)
Numerical id 7
Author djao (24)
Entry type Theorem
Classification msc 30E20
Related topic CauchyIntegralTheorem