Question 4. Suppose that f is holomorphic on C and there exists C> 0 such that f(z)| ≤ C|2|2 for all z € C. Show that f(2)= cz² for some c E C such that c ≤ C. Another fact that is certainly not true of real differentiable functions (can you find a
Question 4. Suppose that f is holomorphic on C and there exists C> 0 such that f(z)| ≤ C|2|2 for all z € C. Show that f(2)= cz² for some c E C such that c ≤ C. Another fact that is certainly not true of real differentiable functions (can you find a
Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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![Question 4. Suppose that f is holomorphic on C and there exists C> 0 such that
f(z)| ≤ Cz|2 for all z € C.
Show that f(z) = cz² for some c E C such that c ≤ C.
Another fact that is certainly not true of real differentiable functions (can you find a
counter-example?). I recommend that you first establish that f is a polynomial of degree
at most 2, then deal with the remaining constant and linear terms separately. You may
use the result of workshop 8, question 4, and be guided by the accompanying comment
(although any use of the further information alluded to there must be justified).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F008f8cce-1e45-43a4-8b17-46721d7357f5%2F6915f337-7ca9-4dad-8907-5ab14780e066%2Fx0gzu8v_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Question 4. Suppose that f is holomorphic on C and there exists C> 0 such that
f(z)| ≤ Cz|2 for all z € C.
Show that f(z) = cz² for some c E C such that c ≤ C.
Another fact that is certainly not true of real differentiable functions (can you find a
counter-example?). I recommend that you first establish that f is a polynomial of degree
at most 2, then deal with the remaining constant and linear terms separately. You may
use the result of workshop 8, question 4, and be guided by the accompanying comment
(although any use of the further information alluded to there must be justified).
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