Applying this theorem to a space encompassing smaller contours containing poles allows one to arise at its namesake's residue theorem.
An extension of this theorem establishes the same result if the function in question can be determined by a rectifiable 1-cycle and an antidifferentiable function satisfying this theorem's result Â is guaranteed to to be holomorphic as per Morera's theorem. A proof of this theorem can be achieved by applying the generalized Stokes' theorem and then using the equality relations between the(*) partial derivatives of the real and imaginary parts of the function. Applying this theorem to a space encompassing smaller contours containing poles allows one to arise at its namesake's residue theorem. For 10 points, identify this theorem from complex analysis which states that the contour Â integral of a complex, analytic function is equal to zero and is named after a Frenchman.
An extension of this theorem establishes the same result if the function in question can be determined by a rectifiable 1-cycle and an antidifferentiable function satisfying this theorem's result
Cauchy integral theorem or Cauchy-Goursat theorem