Let f be an entire function. Prove that f is constant if f satisfies one of the following conditions: (a) there is a disk B(a, ro) such that f(C)ND(a, ro) = 0; (b) there is an M>0 such that Re f(z)
Let f be an entire function. Prove that f is constant if f satisfies one of the following conditions: (a) there is a disk B(a, ro) such that f(C)ND(a, ro) = 0; (b) there is an M>0 such that Re f(z)
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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I need help with number 3
![2. Let f be an entire function. Prove that f is constant if ƒ satisfies one of the following conditions:
(a) there is a disk B(a, ro) such that f(C)ND(a, ro) = 0;
(b) there is an M>0 such that Re f(z) <M for z E C;
3. Let zn
1
ark = 1 and a2k–1 =1+
1
Can you find a function f analytic in a neighborhood of
2k – 1
O such that f(zj)=a; for j=1, 2, 3, ·.? Justify your answer.
%3D
...](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb5f8fb56-c519-448a-bccd-239824e4adff%2F99ddba23-8258-4561-94bf-d360cabeb17a%2Fvfuai5q_processed.jpeg&w=3840&q=75)
Transcribed Image Text:2. Let f be an entire function. Prove that f is constant if ƒ satisfies one of the following conditions:
(a) there is a disk B(a, ro) such that f(C)ND(a, ro) = 0;
(b) there is an M>0 such that Re f(z) <M for z E C;
3. Let zn
1
ark = 1 and a2k–1 =1+
1
Can you find a function f analytic in a neighborhood of
2k – 1
O such that f(zj)=a; for j=1, 2, 3, ·.? Justify your answer.
%3D
...
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