Mathematics · Complex Analysis
Let disc D = {z ∈ &complex; : |z| < 1} and f be a holomorphic function on D such that the function g(z) = e1/zf(z) on D &backslash; {0} is bounded. Which of the following statements is true?
Verified Solution4 OptionsUpdated: October 2026👁️1 View
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- 1There exists a nonzero constant c and a positive integer n such that f(z) = czne-1/z for all z ∈ D &backslash; {0}
- 2There exists a nonzero constant c such that f(z) = ce-1/z for all z ∈ D &backslash; {0}
- 3f(z) = 0 for all z ∈ D✓
- 4f(0) = 0 but f(z) may be non-zero for some z ∈ D
Correct answer
f(z) = 0 for all z ∈ D
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