Let be a polynomial. We're trying to show that we can write:
.
If has a root (and it does by the FTA) then we can write:
for some entire function .
Next, in my notes it says "Clearly,
I really don't see how that is "clear", could anyone help?
Thanks.
Since , wouldn't it make sense that deg(P(z))=k? Not sure how "n" fits into this. And I still think that would be too "handwavy" to say it follows thereafter. Regardless,
The reason why I asked about the z_i earlier was because it would follow nicely that if for each z_i, then
Otherwise, if this restriction on z_i isn't as above, then more will have to be done to bound the polynomial. Thoughts?