Cauchy型积分定理的证明

依据积分估值对Cauchy型积分F(z)在z平面上简单逐段光滑曲线C外任一区域D内的解析进行了证明 ,其方法是利用数学归纳法 .且在证明过程中作了一个以原点为心包含积分路线C及z0 ,z0 +Δz的圆盘 |z0 |≤R ,致使 |ζ -z0 |≤ 2R ,|ζ -z0 -Δz|≤ 2R ,最后 ,令Δz→ 0 ,获证

The proof of Cauchy integration theorem

In terms of the assessment value of integration, a proof of the analysis of Cauchy integration F(z) in the arbitrary area D that is out of the simple field by field smooth curve C on the plane z is given by applying the mathematical induction. A circle |Z 0|≤R is made, in which the origin is the center and the integral path C, Z 0 and Z 0+ΔZ are all contained, therefore |ξ Z 0|≤2R, |ξ Z 0 ΔZ |≤2R. At last, making ΔZ→0, the proof is tenable.