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Question Number 145820 by Mrsof last updated on 08/Jul/21

$$findresideo{e}^{(z+1)/z}$$

Commented by Mrsof last updated on 08/Jul/21

$$helpmesirplease$$

Commented by Mrsof last updated on 08/Jul/21

$$?????$$

Commented by Mrsof last updated on 09/Jul/21

$$?????????$$

Answered by Olaf_Thorendsen last updated on 09/Jul/21

$$f\left(z\right)=e^{\frac{z+1}{z}}=e^{1+\frac{1}{z}}=e.e^{\frac{1}{z}}$$$$\mathrm{The}\mathrm{value}z=0\mathrm{is}\mathrm{an}\mathrm{essential}$$$$\mathrm{singularity}\mathrm{of}f.$$$$f\left(z\right)=e(1+\frac{1}{z}+\frac{1}{2z^2}+\frac{1}{6z^3}+...)$$$$\mathrm{The}\mathrm{coeff}.\mathrm{of}\frac{1}{z}\mathrm{is}e.$$$$\Rightarrow {\mathrm{Res}}_{0}f=e$$

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