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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
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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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 ...
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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