3) Find the laurent series expansion for: a) z² sin 2, O D on i) 1 2 iii) D< /Z-11 <1 0<12/21 e) Let f(z) = √7²-3Z+2²₁ 1 <12/<<2. Does the laurent series expansion for f(z) exist? Justify your answer. 1-cosz (2-21)3 b) Z-7 Z²+Z-2 2+32 d) z ² + Z²

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.5: The Binomial Theorem
Problem 41E
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Hi I,need help with 3a) and d)

3) Find the laurent series expansion for:
a) z² sin 2,
O<IZI< R
c)
1Z-2711 > D
on i) 1</2/<2; ii) 1Z) > 2
iii) D< /Z-11 <1
0<12/21
e) Let f(z) = √7²-3Z+2²₁ 1 <12/<<2. Does the laurent series
expansion for f(z) exist? Justify your answer.
1-cosz
(2-21)3
b) Z-7
Z²+Z-2
2+32
d) z ² + Z²
Transcribed Image Text:3) Find the laurent series expansion for: a) z² sin 2, O<IZI< R c) 1Z-2711 > D on i) 1</2/<2; ii) 1Z) > 2 iii) D< /Z-11 <1 0<12/21 e) Let f(z) = √7²-3Z+2²₁ 1 <12/<<2. Does the laurent series expansion for f(z) exist? Justify your answer. 1-cosz (2-21)3 b) Z-7 Z²+Z-2 2+32 d) z ² + Z²
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