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3. Find the Laurent series of f(2) = Log ( ) for |2| > 1. %3D z+i.

3. Find the Laurent series of f(2) = Log ( ) for |2| > 1. %3D z+i.

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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Do just problem 3 and answer is attached so detail solution required

I) LAURENT SERIES EXPANSIONS AND ISOLATED SIN 1 1. a) f(z) = 4z 1 1 C((-1)"+1 + )n+1, 4n+2 n=0 1 b) f(z) = (-1)" 22n-1 1 22n+3 n=0 4n+1 n=0 1 c) f(2) =E(-1)" – 4")- 22n+3° n=0 (-i)" 1 n+1 2. f(2) = + (z – i)n+1 n=0 (-1)n+1 1 3. f(2) = 2i 2n +1 z2n+1 ° n=0
Transcribed Image Text:I) LAURENT SERIES EXPANSIONS AND ISOLATED SIN 1 1. a) f(z) = 4z 1 1 C((-1)"+1 + )n+1, 4n+2 n=0 1 b) f(z) = (-1)" 22n-1 1 22n+3 n=0 4n+1 n=0 1 c) f(2) =E(-1)" – 4")- 22n+3° n=0 (-i)" 1 n+1 2. f(2) = + (z – i)n+1 n=0 (-1)n+1 1 3. f(2) = 2i 2n +1 z2n+1 ° n=0
1 2. Expand f(z) = 22 + 2z in a Laurent series in the region 1< 3. Find the Laurent series of f(z) = Log| ( ) for |2| > 1. 4. Find the isolates singularities of the following functions, and removable, poles or essential.
Transcribed Image Text:1 2. Expand f(z) = 22 + 2z in a Laurent series in the region 1< 3. Find the Laurent series of f(z) = Log| ( ) for |2| > 1. 4. Find the isolates singularities of the following functions, and removable, poles or essential.
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