Beispiel.

Berechne die folgenden Kurvenintegrale.

  1. $ \mbox{$\displaystyle\int_{\partial B_3(0)} \frac{e^{-z}}{(z+2)^3}\,\text{d}z$}$ .
  2. $ \mbox{$\displaystyle\int_{\partial B_1(1)} \frac{z^n}{(z-1)^n} \,\text{d}z$}$ .
  3. $ \mbox{$\displaystyle\int_{\partial B_{1/2}(0)} \left(\cos\frac{\pi}{z+1}\right)\cdot \frac{1}{z^3} \,\text{d}z$}$ .
  4. $ \mbox{$\displaystyle\int_{\partial B_r(0)} (z-a)^{-m}(z-b)^{-n}\,\text{d}z$}$ , wobei $ \mbox{$\vert a\vert<r<\vert b\vert$}$ und $ \mbox{$m,n\in\mathbb{N}$}$ .