1. Consider the function 1 f(e) = Find all Laurent series (and their respective convergence regions) for f, centered at 20 = 2i.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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1. Consider the function
1
f(2) =
2 - iz +2°
Find all Laurent series (and their respective convergence regions) for f, centered at
20 = 2i.
2. Find the Laurent series for
19)=
centered at 0 which converges in the punctured disk 0 < |2| < 1. Hint: You have to
multiply two series and keep track of the coefficients.
Transcribed Image Text:1. Consider the function 1 f(2) = 2 - iz +2° Find all Laurent series (and their respective convergence regions) for f, centered at 20 = 2i. 2. Find the Laurent series for 19)= centered at 0 which converges in the punctured disk 0 < |2| < 1. Hint: You have to multiply two series and keep track of the coefficients.
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