Complex Analysis pp 123-143 | Cite as

# Cauchy’s Theorem, Second Part

Chapter

- 2.8k Downloads

## Abstract

We wish to give a general global criterion when the integral of a holo-morphic function along a closed path is 0. In practice, we meet two types of properties of paths: (1) properties of homotopy, and (2) properties having to do with integration, relating to the number of times a curve “winds” around a point, as we already saw when we evaluated the integral along a circle centered at z. These properties are of course related, but they also exist independently of each other, so we now consider those conditions on a closed path for all holomorphic functions

$$\int {\frac{1} {{\zeta - z}}d\zeta }$$

*y*when$$\int\limits_r {f = 0}$$

*f*, and also describe what the value of this integral may be if not 0.## Preview

Unable to display preview. Download preview PDF.

## Copyright information

© Springer Science+Business Media New York 1985