1. Find the Taylor or Laurent series, whichever appropriate, of a) f(z) = e²-/(z - 2)² about z = 2, b) f(z) = z/(z² + 1) about z = 0 for |z| > 1. In each case, write explicitly at least the first three terms of the series. [You may find it useful to recall that the Maclaurin series of e? is E-o z"/n!.] Zn=0
1. Find the Taylor or Laurent series, whichever appropriate, of a) f(z) = e²-/(z - 2)² about z = 2, b) f(z) = z/(z² + 1) about z = 0 for |z| > 1. In each case, write explicitly at least the first three terms of the series. [You may find it useful to recall that the Maclaurin series of e? is E-o z"/n!.] Zn=0
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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![1. Find the Taylor or Laurent series, whichever appropriate, of
a) f(z) = e?-1/(z – 2)? about z = 2,
b) f(z) = z/(z? + 1) about z = 0 for |z| > 1.
In each case, write explicitly at least the first three terms of the series.
[You may find it useful to recall that the Maclaurin series of e? is E=o z" /n!.]
n%3D0](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ffb665f96-8ef0-4ccd-80eb-2aa2625dc822%2F747eedc0-ede2-43c3-942b-e0972cfd21dd%2Fswgnq4r_processed.png&w=3840&q=75)
Transcribed Image Text:1. Find the Taylor or Laurent series, whichever appropriate, of
a) f(z) = e?-1/(z – 2)? about z = 2,
b) f(z) = z/(z? + 1) about z = 0 for |z| > 1.
In each case, write explicitly at least the first three terms of the series.
[You may find it useful to recall that the Maclaurin series of e? is E=o z" /n!.]
n%3D0
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