Let-f-is-a-2-nd-degree-polynomial-1-2pii-z-2-z-f-z-f-z-dz-0-and-1-2pii-z-2-z-2-f-z-f-z-dz-2-If-f-0-2017-find-explicit-form-of-f-z-

Question Number 52499 by Joel578 last updated on 09/Jan/19

Let f is a 2^{nd} degree polynomial .

\frac{1}{2 π i} \int_{∣ z ∣= 2} \frac{z f^{'} (z)}{f (z)} d z = 0, and \frac{1}{2 π i} \int_{∣ z ∣= 2} \frac{z^{2} f^{'} (z)}{f (z)} d z = - 2

If f (0) = 2017, find explicit form of f (z)