Mathematics · Complex Analysis
Let f be an entire function on ℂ. Which of the following statements is true?
Verified Solution4 OptionsUpdated: October 2026👁️1 View
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- 1If f(z) = f(z + 1) for all z ∈ ℂ, then f must be bounded.
- 2If f(z) = f(z + 1) = f(z + i) for all z ∈ ℂ, then f is a constant function.✓
- 3If f(1/z) has a removable singularity at z = 0, then f is not bounded.
- 4If f is a non-constant function, then f(1/z) always has a pole at z = 0.
Correct answer
If f(z) = f(z + 1) = f(z + i) for all z ∈ ℂ, then f is a constant function.
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