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.
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