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Just when I thought I understood whatever there was to understand about Normal Families...

F(z) is analytic on the punctured disk and we define the sequence

f_{n}=f(z/n) for n \leq 1.

Trying (and failing) to show that {f_n} is a normal family on the punctured disk iff the singularity of f(z) at z=0 is removable or a pole

Any help is appreciated, thank you