non-constant entire function such that |f| = 1 on the unit circle and f(1) = 1. Let f be a Show that the function f has the form : f(z) = z" for some integer n. Hint: Note that in this case the set of zeros of f in the unit disc is non-empty and finite.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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Let f be a non-constant entire function such that |f| 1 on the unit circle and f(1) = 1.
Show that the function f has the form : f(z) = z" for some integer ʼn.
Hint: Note that in this case the set of zeros of f in the unit disc is non-empty and finite.
Transcribed Image Text:Let f be a non-constant entire function such that |f| 1 on the unit circle and f(1) = 1. Show that the function f has the form : f(z) = z" for some integer ʼn. Hint: Note that in this case the set of zeros of f in the unit disc is non-empty and finite.
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