At infinity, the quotient for some constant c right?
That is, it becomes dominated by the higher-degree denominator. Then the ML-inequality says what about the limit:
where and are polynomials in
Prove , where integration is over a closed curve which encloses all poles of
I have been trying this for long - but really stuck up. Tried Cauchy, Laurent Expansion but not going anywhere. Request help please.
And with some work we get:
but so that:
with and therefore that's zero.
Maybe I should have said "convex hull" which is just a border containing all the poles. Outside this border, the quotient is analytic and therefore we can evaluate a contour integral outside the hull by taking the (single) residue at infinity which by definition is:
You'll go over that soon or just look it up.