12. Let D = {2E C | 너く1} denote the open unit disc and let f : D → C be a holomorphic function. Suppose that for any integer n>1 we have that f(1/n)-1/n3. Show that f(z)3. 12. Let D = {2E C...

Question

Question

12. Let D = {2E C | 너く1} denote the open unit disc and let f : D → C be a holomorphic function. Suppose that for any integer

Answer 1

Answer #1

ANSWER :-

Let D = {z $\epsilon$ C| |z|<1}denote the open unit disc.

And also given that f : D $\rightarrow$ C be a homorphic function.

Let us suppose that for any integer n>1 we have that

f(1/n) =-1/㎡ .................................................................................(1)

Here we need to show that $f(z) = -z^3$ :-

From equation (1) we already know that

f(1/n) =-1/㎡

where f(1 ...........................................................(2)

Therefore $f(z) = -z^3$ .

Hence proved.

Thank you

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Answer 2

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