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Find all the singularities of the f(z). Are they isolated? sin z z3(z – 3i)² sin f(z) = Classify all the isolated singularities. Indicate the order of the singularity if it is a pole.

Find all the singularities of the f(z). Are they isolated? sin z z3(z – 3i)² sin f(z) = Classify all the isolated singularities. Indicate the order of the singularity if it is a pole.

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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Find all the singularities of the f(z). Are they isolated? sin z 23 (z – 3i)² sin – f(z) = Classify all the isolated singularities. Indicate the order of the singularity if it is a pole. Compute the residue Res(f; zo), where zo is the pole. Write down the Laurent expansion g(z) = e about z* = 0 as g(2) = E arz* k=-0 How many non-vanishing terms aj, do we have for k < 0? What does that imply?
Transcribed Image Text:Find all the singularities of the f(z). Are they isolated? sin z 23 (z – 3i)² sin – f(z) = Classify all the isolated singularities. Indicate the order of the singularity if it is a pole. Compute the residue Res(f; zo), where zo is the pole. Write down the Laurent expansion g(z) = e about z* = 0 as g(2) = E arz* k=-0 How many non-vanishing terms aj, do we have for k < 0? What does that imply?
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