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Subject: Complex Analysis 7. Suppose that f(z) is an entire function with the property f(z)Cz2 for all zR where C,R>0 are positive real constants. Prove

Subject: Complex Analysis
7. Suppose that f(z) is an entire function with the property f(z)Cz2 for all zR where C,R>0 are positive real constants. Prove that f(z) is a polynomial with degree at most 2. (Hint: show that f(3)(z0)=0 for all z0 C using Cauchy estimates. What can you say from there?)

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Subject: Complex Analysis 7. Suppose that f(z) is an entire function with the property f(z)Cz2 for all zR where C,R>0 are positive real constants. Prove

Subject: Complex Analysis 7. Suppose that f(z) is an entire function with the property f(z)Cz2 for all zR where C,R>0 are positive real constants. Prove that f(z) is a polynomial with degree at most 2. (Hint: show that f(3)(z0)=0 for all z0 C using Cauchy estimates. What can you say from there?)

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Subject: Complex Analysis
7. Suppose that f(z) is an entire function with the property f(z)Cz2 for all zR where C,R>0 are positive real constants. Prove that f(z) is a polynomial with degree at most 2. (Hint: show that f(3)(z0)=0 for all z0 C using Cauchy estimates. What can you say from there?)