The function f(z) and g(z) are both analytic in the region |z|>10.
These functions also satisfy |f(z)| < M and |g(z)| > E in this region,
with M and E positive real numbers. What additional constraints are needed on
the function g(z) in order to ensure
\int f(z)/ g(z) dz =0 by using on;y integral bounds anf Cauchy's theorem?
Assume these additional restrictions, show that this integral equals 0.
Be sure to indicate where the additional assumptions are used in your proof.
原本覺得 這題需要g(z) 在 |z| > 10 沒有 root，這樣f/g就沒有pole，
那整個積分就可以把積分半徑取大一點 然後用Cauchy's inequality 證明是0?
想著想著又覺得怪怪的 說不清楚...
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