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1. Determine the Laurent series expansions of f(2) = in the regions: z(1+2²)(4 – 2²) a) 0 < |z| < 1, b) 1<|z| < 2, c) |2| > 2.

1. Determine the Laurent series expansions of f(2) = in the regions: z(1+2²)(4 – 2²) a) 0 < |z| < 1, b) 1<|z| < 2, c) |2| > 2.

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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I) LAURENT SERIES EXPANSIONS AND ISOLATED SIN 1 a) f(z) = 1 +E(-1)"+1 + 1. 1 2n+1 4z 4n+2 n=0 (-1)" 1 22n-1 b) f(z) = 22n+3 n=0 4n+1 n=0 1 c) f(z) = 1 (-1)" – 4") 22n+3 n=0
Transcribed Image Text:I) LAURENT SERIES EXPANSIONS AND ISOLATED SIN 1 a) f(z) = 1 +E(-1)"+1 + 1. 1 2n+1 4z 4n+2 n=0 (-1)" 1 22n-1 b) f(z) = 22n+3 n=0 4n+1 n=0 1 c) f(z) = 1 (-1)" – 4") 22n+3 n=0
I) LAURENT SERIES EXPANSIONS AND ISOLATED SINGULARITIES (SESSION 10) 1. Determine the Laurent series expansions of f(z) = in the regions: z(1+2²)(4 – 2²) c) |z| > 2. a) 0 < |z| < 1, b) 1< |z| < 2,
Transcribed Image Text:I) LAURENT SERIES EXPANSIONS AND ISOLATED SINGULARITIES (SESSION 10) 1. Determine the Laurent series expansions of f(z) = in the regions: z(1+2²)(4 – 2²) c) |z| > 2. a) 0 < |z| < 1, b) 1< |z| < 2,
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