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Unformatted text preview: z + 1) + ( z + 1) 2 ) =-2 + ( z + 1) + 1 z + 1 . Simple pole at z =-1 . (c) sin z/z : Removable singularity at z = 0 . No singular (principal) part of the expansion. (d) cos z/z : Simple pole at z = 0 . Principal part is 1 /z. (e) 1 (2-z ) 3 =-1 ( z-2) 3 Already a Laurent series about pole of order 3 at z = 2 . #2: Answers given in book; expand numerator in (a), (b); diFerentiate it at z = 1 to get the residue in case (c). p. 248: #1: Answers given in book. #3: Answers given in book. (a): Singular points (simple poles) at z = 1; (b): Singular points (simple poles) at z = 1 , z = 3 i ;...
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This note was uploaded on 06/11/2010 for the course MA 513 taught by Professor Staff during the Spring '08 term at N.C. State.
- Spring '08