9. Let Ω ⊆ C be open and a ∈ Ω. Suppose f is analytic on Ω except for a pole at a. Set g(z) = ef (z) for z ∈ Ω \ {a}. Show that g has an essential singularity at a. (Hint: Consider g,/g.)


9. Let Ω
⊆
C be open and
a

∈
Ω. Suppose
f
is analytic on Ω except for a pole at
a. Set



g(z) =
e
f

(z) for
z


∈

Ω
\


{
a
}. Show that
g

has an essential singularity at
a. (Hint:


Consider
g
,
/g.)





May 12, 2022
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