3. Suppose that f: C→C is entire and that for all z € C, |z| ≥ 100 we have |S(z)| ≤ 100|z|". Prove that is a polynomial of degree
3. Suppose that f: C→C is entire and that for all z € C, |z| ≥ 100 we have |S(z)| ≤ 100|z|". Prove that is a polynomial of degree
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![3.
Suppose that f: C→C is entire and that for all z € C, |z| ≥ 100 we have
|S(z)| ≤ 100|z|".
Prove that is a polynomial of degree <n.
[Hint: study and adapt the proof of Louisville's theorem.]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb7d0892c-a19b-49d0-ac25-73d2c42d4d77%2F6236b128-645f-4820-afcb-e22e2de20340%2Fyyop2d9_processed.png&w=3840&q=75)
Transcribed Image Text:3.
Suppose that f: C→C is entire and that for all z € C, |z| ≥ 100 we have
|S(z)| ≤ 100|z|".
Prove that is a polynomial of degree <n.
[Hint: study and adapt the proof of Louisville's theorem.]
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