Generalization and Application of Cauchy Integral Formula

摘要

Cauchy integral theorem or Cauchy integral formula is the core knowledge of complex complex integral. However, when singular points exist on the integral path or these closed contours form finite or infinite self-intersections, Cauchy integral theorem or Cauchy integral formula can not be used. Aiming at this case, in combination with Holder condition and related knowledge on singular integral, Cauchy integral formula for singular points on the contour is summarized in this paper, what's more, in the paper, a conclusion is drawn that integral path C is a closed contour and the integral value is still zero when the selfintersection is finite or infinite.