I have been asked to show that for that
I know since and
Converge uniformly on compact subsets of the unit disk that both of the infinite products converge to a holomorphic function of the open disk.
So here is my idea let
I would be sufficient to show that
My idea was to take the deriative and show that it is equal to
I cannot sum this series or show that it is equal to 0. Also if you see a different approach please let me know.