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Determine the nature of the singularities of each of the following functions and evaluate the residues (a > 0): ze+iz 2² + a² etiz (h) zetiz 2²+ a² 0

Determine the nature of the singularities of each of the following functions and evaluate the residues (a > 0): ze+iz 2² + a² etiz (h) zetiz 2²+ a² 0

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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Question: Determine the nature of the singularities of each of the following functions and evaluate the residues (a > 0): (e) zetiz 2² + a² etiz 22-a² (f) zetiz + a². -k (h) 2+1 Hint. For the point at infinity, use the transformation w = 1/2 for |2| → 0. For the residue, transform f(z) dz into g(w) dw and look at the behavior of g (w). 0 <k < 1. "
Transcribed Image Text:Question: Determine the nature of the singularities of each of the following functions and evaluate the residues (a > 0): (e) zetiz 2² + a² etiz 22-a² (f) zetiz + a². -k (h) 2+1 Hint. For the point at infinity, use the transformation w = 1/2 for |2| → 0. For the residue, transform f(z) dz into g(w) dw and look at the behavior of g (w). 0 <k < 1. "
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