(c) Find the Laurent series expansion of f(z) in the domain D₁ in powers of z. (d) Let C be the positive oriented circle |z| = 2, and let n be an integer. Evaluate the integral 1 2πί f(z) -dz. 2n+1

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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question c and d

Let D₁ be the domain 1 < |z|< 3, and let D2 be the domain
|2|3. Consider the function
2z+1
(z+3)(z² + 1)
f(z) =
(a) Find the partial fraction decomposition of f.
(b) Find the Laurent series expansion of f(z) in the domain D₂ in powers of z.
(c) Find the Laurent series expansion of f(z) in the domain D₁ in powers of z.
(d) Let C be the positive oriented circle |z|
=
2, and let n be an integer. Evaluate the
integral
1
i bo
2πί
f(z)
dz.
2n+1
Transcribed Image Text:Let D₁ be the domain 1 < |z|< 3, and let D2 be the domain |2|3. Consider the function 2z+1 (z+3)(z² + 1) f(z) = (a) Find the partial fraction decomposition of f. (b) Find the Laurent series expansion of f(z) in the domain D₂ in powers of z. (c) Find the Laurent series expansion of f(z) in the domain D₁ in powers of z. (d) Let C be the positive oriented circle |z| = 2, and let n be an integer. Evaluate the integral 1 i bo 2πί f(z) dz. 2n+1
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