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25.1. Expand each of the following functions f(z) in a Laurent series on the indicated domain: (a). 2²-2z+5 (z-2)(2²+1)' (²=6 (c). Log 1<|z|<2, (b). (²−¹), |z−1|>1, where b>a> 1 are real, [2] > b.

25.1. Expand each of the following functions f(z) in a Laurent series on the indicated domain: (a). 2²-2z+5 (z-2)(2²+1)' (²=6 (c). Log 1<|z|<2, (b). (²−¹), |z−1|>1, where b>a> 1 are real, [2] > b.

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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25.1. Expand each of the following functions f(z) in a Laurent series on the indicated domain: (a). 2²-22+5 (2-2)(2²+1)¹ (c). Log (4) where b> a > 1 are real, [2] > b. 1<z <2, (b). -1), 2-1|>1, 25.2. Find the Laurent series for the function 1/[2(2-1)] in the follow- ing domains: (a). 0< |z| < 1, (b). 1</z/, (c). 0</2-1 <1, (d). 1< |z-1, (e). 1 < 2-2 < 2.
Transcribed Image Text:25.1. Expand each of the following functions f(z) in a Laurent series on the indicated domain: (a). 2²-22+5 (2-2)(2²+1)¹ (c). Log (4) where b> a > 1 are real, [2] > b. 1<z <2, (b). -1), 2-1|>1, 25.2. Find the Laurent series for the function 1/[2(2-1)] in the follow- ing domains: (a). 0< |z| < 1, (b). 1</z/, (c). 0</2-1 <1, (d). 1< |z-1, (e). 1 < 2-2 < 2.
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