3. The Laurent series of f (z) about z = 0 is: z(z + 4 5 1 3 1 3 f(z) z? + 64 + ... 4 z² 4 z 16 16 (a) Determine the radius of convergence of the series. (b) Determine the value of the integral of f(z) over the contour of the unit circle |z| = 1 for counterclockwise integration. Hint for (b): Use the Laurent series. %3D

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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3z - 5
3. The Laurent series of f(z) =
z'(z
about z = 0 is:
+ 4)
5 1
3 1
f(z)
z? +
64
4 z²
4 z
16
16
(a) Determine the radius of convergence of the series. (b) Determine the value of the
integral of f(z) over the contour of the unit circle |z| = 1 for counterclockwise integration.
Hint for (b): Use the Laurent series.
Transcribed Image Text:3z - 5 3. The Laurent series of f(z) = z'(z about z = 0 is: + 4) 5 1 3 1 f(z) z? + 64 4 z² 4 z 16 16 (a) Determine the radius of convergence of the series. (b) Determine the value of the integral of f(z) over the contour of the unit circle |z| = 1 for counterclockwise integration. Hint for (b): Use the Laurent series.
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