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Question :- Suppose that of | -f1z) | = | on |2|=1. When is entire function and That_fR²) = C. 2². pona

Question :- Suppose that of | -f1z) | = | on |2|=1. When is entire function and That_fR²) = C. 2². pona

Advanced Engineering Mathematics
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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Question:- Suppose that of is antive 121=1. y han pone |- f₁2)| = | Solt: The first- on analytic If of has Symmetry infinity. Zero function f is entire. We the paint Again Lam of (w) Now t in So fiz) | f₁₂) | = 1 Zero f would have using gymorely Henle Com which - prove ㅏ <\ {0}. Z on 2 Therfire only That t is a polynomial. at zo to This is n an. Z |2|=1. f(z) = am - 2², Z fonction and That f₁2²) = C. 2². 1 + (-1/2) So / have possiblity This then f is a polynomial. have at most Case it has to be by pole possible Sine meas So of has pole at But by |an| =! का is fo=o. That |an| = | 2 is ore distinct at z=0. The Criteric
Transcribed Image Text:Question:- Suppose that of is antive 121=1. y han pone |- f₁2)| = | Solt: The first- on analytic If of has Symmetry infinity. Zero function f is entire. We the paint Again Lam of (w) Now t in So fiz) | f₁₂) | = 1 Zero f would have using gymorely Henle Com which - prove ㅏ <\ {0}. Z on 2 Therfire only That t is a polynomial. at zo to This is n an. Z |2|=1. f(z) = am - 2², Z fonction and That f₁2²) = C. 2². 1 + (-1/2) So / have possiblity This then f is a polynomial. have at most Case it has to be by pole possible Sine meas So of has pole at But by |an| =! का is fo=o. That |an| = | 2 is ore distinct at z=0. The Criteric
Expert Solution
Step 1

Given that f is entire entire function and f(z) =1  on z =1.

To prove that f(z) = c·zn

steps

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