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Consider the function sin(z) f(2) = z + 23 (a) Determine the domain of holomorphy of f. Identify all the singular points of f, and decide whether they are isolated or not. (b) Classify the isolated singular points from part (a), deciding, for each of them, whether they are removable, poles (of which order?) or essential singularities. (c) Compute the residues of f at each singular point.

Consider the function sin(z) f(2) = z + 23 (a) Determine the domain of holomorphy of f. Identify all the singular points of f, and decide whether they are isolated or not. (b) Classify the isolated singular points from part (a), deciding, for each of them, whether they are removable, poles (of which order?) or essential singularities. (c) Compute the residues of f at each singular point.

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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Consider the function sin(z) f(2) z + z3 (a) Determine the domain of holomorphy of f. Identify all the singular points of f, and decide whether they are isolated or not. (b) Classify the isolated singular points from part (a), deciding, for each of them, whether they are removable, poles (of which order?) or essential singularities. (c) Compute the residues of f at each singular point. (d) Compute sin(z) dz , z + z3 where +C2 is the circle centered at the origin with radius 2, traversed once counter- clockwise.
Transcribed Image Text:Consider the function sin(z) f(2) z + z3 (a) Determine the domain of holomorphy of f. Identify all the singular points of f, and decide whether they are isolated or not. (b) Classify the isolated singular points from part (a), deciding, for each of them, whether they are removable, poles (of which order?) or essential singularities. (c) Compute the residues of f at each singular point. (d) Compute sin(z) dz , z + z3 where +C2 is the circle centered at the origin with radius 2, traversed once counter- clockwise.
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