25.1. Expand each of the following functions f(z) in a Laurent series on the indicated domain: 22-2z+5 1< |z| < 2, (b). , 1z- 1|> 1, (2-1) |2 - 1|> 1, (a). (-2)(2 +1)'
25.1. Expand each of the following functions f(z) in a Laurent series on the indicated domain: 22-2z+5 1< |z| < 2, (b). , 1z- 1|> 1, (2-1) |2 - 1|> 1, (a). (-2)(2 +1)'
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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![25.1. Expand each of the following functions f(z) in a Laurent series
on the indicated domain:
(2-1)
22
(a).
(z-2)(22 + 1)'
22-2z+5
1< lz| < 2, (b). , Iz- 1| > 1,
|z - 1|> 1,
2- (a
(c). Log
where b> a > 1 are real, |z| > b.
25.2. Find the Laurent series for the function 1/[z(z-1)] in the follow-
ing domains: (a). 0< 2| < 1, (b). 1< z, (c). 0< |z-1| < 1, (d). 1<
|z - 1, (e). 1< z-2 <2.
25.3. Find the Laurent series for the function z/[(2² + 1)(z² + 4)] in
the following domains (a). 0<lz| < 1, (b). 1< |2 < 2, (c). |2| > 2.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff70fc076-38b9-4b4a-bc5b-af99db489db8%2Faeb358fc-f3d0-413d-9b4e-9facba2a7390%2F57f4ct8_processed.jpeg&w=3840&q=75)
Transcribed Image Text:25.1. Expand each of the following functions f(z) in a Laurent series
on the indicated domain:
(2-1)
22
(a).
(z-2)(22 + 1)'
22-2z+5
1< lz| < 2, (b). , Iz- 1| > 1,
|z - 1|> 1,
2- (a
(c). Log
where b> a > 1 are real, |z| > b.
25.2. Find the Laurent series for the function 1/[z(z-1)] in the follow-
ing domains: (a). 0< 2| < 1, (b). 1< z, (c). 0< |z-1| < 1, (d). 1<
|z - 1, (e). 1< z-2 <2.
25.3. Find the Laurent series for the function z/[(2² + 1)(z² + 4)] in
the following domains (a). 0<lz| < 1, (b). 1< |2 < 2, (c). |2| > 2.
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