Abstract: Abstract Armed with Cauchy's theorem we can prove a host of striking results about holomorphic functions. These stem from the Cauchy formulae which we derive in this chapter. We are then able to prove the following, with relative ease.All this is in sharp contrast to the behaviour of real-valued functions on JR. The contrast is very welcome: the theorems are not hedged around with unmemorable technical restrictions.Cauchy's integral formula expresses the value of a holomorphic function at a point a in terms of a 'boundary value integral' taken round a contour encircling the point.In Cauchy's theorem, the orientation of the contour did not need to be specified. In Cauchy's integral formula, and all subsequent results giving formulae for integrals whose values are not in general zero, the contour is taken to be positively oriented.
Publication Year: 1992
Publication Date: 1992-03-19
Language: en
Type: book-chapter
Indexed In: ['crossref']
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