3. (Analytic branches of multiple-valued functions) (a) Let w + Vw denote the principal branch. Describe the domain of analyticity of the function f(2) = Ve +I and find its derivative. (b) Let w+ Vw denote the principal branch. Describe the domain of analyticity of the function 9(2) = Vz2 – 4 and find its derivative. Is there a branch of vz2 – 4 which is analytic on C\[-2, 2]?
3. (Analytic branches of multiple-valued functions) (a) Let w + Vw denote the principal branch. Describe the domain of analyticity of the function f(2) = Ve +I and find its derivative. (b) Let w+ Vw denote the principal branch. Describe the domain of analyticity of the function 9(2) = Vz2 – 4 and find its derivative. Is there a branch of vz2 – 4 which is analytic on C\[-2, 2]?
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. (Analytic branches of multiple-valued functions)
(a) Let w + Vw denote the principal branch. Describe the domain of analyticity of the function
f(2) = Ve + I and find its derivative.
(b) Let w + Jw denote the principal branch. Describe the domain of analyticity of the function
g(2) = Vz2 – 4 and find its derivative. Is there a branch of vz² – 4 which is analytic on C\[-2, 2]?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F942d8395-ce39-44af-9e4d-fbdcfc13f43e%2F44be5366-9111-4fb0-a854-9923ba346ceb%2Fks3vbk_processed.jpeg&w=3840&q=75)
Transcribed Image Text:3. (Analytic branches of multiple-valued functions)
(a) Let w + Vw denote the principal branch. Describe the domain of analyticity of the function
f(2) = Ve + I and find its derivative.
(b) Let w + Jw denote the principal branch. Describe the domain of analyticity of the function
g(2) = Vz2 – 4 and find its derivative. Is there a branch of vz² – 4 which is analytic on C\[-2, 2]?
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