$\displaystyle \int_{|z|=1}^{nothing } \frac{1}{z}e^{\frac{1}{z}}$ in this integral there is no upper bound its around |z|=1 there are no poles here only singular significant what to do here when calclating the residium ??
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Originally Posted by transgalactic $\displaystyle \int_{|z|=1}^{nothing } \frac{1}{z}e^{\frac{1}{z}}$ in this integral there is no upper bound its around |z|=1 there are no poles here only singular significant what to do here when calclating the residium ?? $\displaystyle \frac1ze^{1/z}=\frac1z\left(1+\frac1z+\frac{1}{2z^2}+\cdots\ri ght) = \frac1z+\frac{1}{z^2}+\frac{1}{2z^3}+\cdots $ Thus $\displaystyle \text{Res}_{z=0}\left(\frac1ze^{1/z}\right)=1 $
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