I'm supposed to evaluate where a function is a regular point, essential singularity, or a pole (and of what order) at a specific location. Problem here. Evaluated at (where else but) z=1. I know its not a regular point since it doesn't evaluate to a simple Taylor Series... likewise -- I know its not an essential singularity since its Lorentz series doesn't go on forever (unless I'm entirely wrong). I cannot tell what order the pole is though: Using l'Hopital's rule (0/0) would suggest that its a pole of order 1... but applying it directly which the textbooks seem to do would suggest its a pole of order 2. It would be easier if I could conform it to a Lorentz series but across 7 textbooks I have on the topic of Complex Analysis (not kidding -- I just bought one today -- 120$ -- only a dozen problems on the topic -- and no solutions nor even answers). "Arfken" -- good for reference -- but I really should have bought Boas.