I'm not too sure how easy this would be to prove, but I'm guessing that what you are saying is that the roots of are precisely those of for any . So how do you know that the RHS of (2) isn't the expansion for one of those? Well, assuming that you agree the RHS is the product for something of the form we must merely note that we arrived at it by evaluating . But, if this limit diverges and if the limit is zero. Can you use this fact to show that the RHS neither diverges nor is zero to conclude that and thus the RHS is the product for ?