Find the following Laurent expansions (i.c., determine the coefficients bk). (a) The function f(2)=e² + e¹/² on the annulus {z € C: 0 < |z|<∞0}. (b) The function f(2)= (c) The function f(z) = on the annulus {z € C: 1 < |z − 1| <2}. on the annulus {z € C: 0 < |z − 1|<∞0}. (d) The function f(2)=+¹₁+¹₂ on {z € C: 0.

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter5: Inverse, Exponential, And Logarithmic Functions
Section5.2: Exponential Functions
Problem 71E
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Find the following Laurent expansions (i.c., determine the coefficients bk).
(a) The function f(2)=e² + e¹/² on the annulus {z € C: 0 < |z|<∞0}.
(b) The function f(2)=
(c) The function f(z) =
on the annulus {z € C: 1 < |z − 1| <2}.
on the annulus {z € C: 0 < |z − 1|<∞0}.
(d) The function f(2)=+¹₁+¹₂ on {z € C: 0</z< 1}.
(e) The function f(2)=+₁+₂
on {z € C: 1</2 <2}.
2.
Transcribed Image Text:Find the following Laurent expansions (i.c., determine the coefficients bk). (a) The function f(2)=e² + e¹/² on the annulus {z € C: 0 < |z|<∞0}. (b) The function f(2)= (c) The function f(z) = on the annulus {z € C: 1 < |z − 1| <2}. on the annulus {z € C: 0 < |z − 1|<∞0}. (d) The function f(2)=+¹₁+¹₂ on {z € C: 0</z< 1}. (e) The function f(2)=+₁+₂ on {z € C: 1</2 <2}. 2.
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