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

f i n d r e s i d e o e^{(z + 1) / z}

Commented by Mrsof last updated on 08/Jul/21

h e l p m e s i r p l e a s e

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 (z) = e^{\frac{z + 1}{z}} = e^{1 + \frac{1}{z}} = e . e^{\frac{1}{z}}

The value z = 0 is an essential

singularity of f .

f (z) = e (1 + \frac{1}{z} + \frac{1}{2 z^{2}} + \frac{1}{6 z^{3}} + \dots)

The coeff . of \frac{1}{z} is e .

\Rightarrow {Res}_{0} f = e