Let f : &DoubleLongLeftRightArrow; → &DoubleLongLeftRightArrow; be an entire function with f( 1 n ) = 1 n 2 for all n &in; &naturals;. Then which of the following statements is true?

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Mathematics · Complex Analysis

Let f : &DoubleLongLeftRightArrow; → &DoubleLongLeftRightArrow; be an entire function with f( 1 n ) = 1 n 2 for all n &in; &naturals;. Then which of the following statements is true?

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Correct answer

f(z) = z 2 for all z &in; &DoubleLongLeftRightArrow;

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Answer 1

No such f exists

Answer 2

Such an f is not unique

Answer 3

f(z) = z 2 for all z &in; &DoubleLongLeftRightArrow;

Answer 4

f need not be a polynomial function

Let f : &DoubleLongLeftRightArrow; → &DoubleLongLeftRightArrow; be an entire function with f( 1 n ) = 1 n 2 for all n &in; &naturals;. Then which of the following statements is true?

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Let f : &DoubleLongLeftRightArrow; &rarr; &DoubleLongLeftRightArrow; be an entire function with f( 1 n ) = 1 n 2 for all n &in; &naturals;. Then which of the following statements is true?

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Let f : &DoubleLongLeftRightArrow; → &DoubleLongLeftRightArrow; be an entire function with f( 1 n ) = 1 n 2 for all n &in; &naturals;. Then which of the following statements is true?