True or false? Justify.

Let

be an isolated singularity of f(z) such that

. Then

is a removable singularity and thus

is analytic in a neighborhood of

.

Attempt: True. I know that if

is a removable singularity, then f can be extended to an analytic function by giving a value to

. Thus I also believe that f is bounded if its singularity is removable.

Though formally I don't know how to prove it. If

(I know I assume that f has a Laurent series representation, I'm not sure I can assume that) then I'm told that

. I'm not going far with this.

Any idea?