Question

Asked Mar 7, 2019

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Suppose that f(z) is an entire function such that f(z)/z^{n} is bounded for |z|>= R. Show that f(z) is a polynomial of degree at most n.

Step 1

Let *f(z)* is an entire function such that *f(z)/z ^{n}* is bounded for |

Since *f *is an entire function, it has a power series about the origin which converges for all *z.*

Step 2

We will show that *f ^{(k)}(0) = 0* for

Consider a circle of radius *R, *then Cauchy\'s inequality says that

Step 3

Then by the hyp...

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