Unformatted text preview: of the domain, then it is identically zero. Can it vanish on a set with a limit point in the domain and not be identically zero? 4. (20 pts) Suppose that f ( z ) has an essential singularity at z = a . Prove that there is a sequence of points z n tending to a such that ( z na ) n f ( z n ) tends to ∞ . 5. (10 pts) Does there exist a sequence of polynomials P n ( z ) which converges uniformly to 1 /z on { z :  z  = 1 } ? Explain. 6. (20 pts) Suppose that f is a continuous complex valued function on a domain Ω. Prove that if f 2 and f 3 are analytic on Ω, then f itself must be analytic....
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 Spring '09
 Polynomials, pts, 10 pts, 20 pts, Prof. Bell

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