Show that the functions below are meromorphic; that is, the only singu- larities in the finite z plane are poles. Determine the location, order and strength of the poles. (d) (a) e² Z z4+2 z4 (b) tan z 1 2πi (c) Z sin² z w dw (e) fc (w² - 2) (w - z) C is the unit circle centered at the origin. First find the function for |z| < 1, then analytically continue the function to [z] ≥ 1.
Show that the functions below are meromorphic; that is, the only singu- larities in the finite z plane are poles. Determine the location, order and strength of the poles. (d) (a) e² Z z4+2 z4 (b) tan z 1 2πi (c) Z sin² z w dw (e) fc (w² - 2) (w - z) C is the unit circle centered at the origin. First find the function for |z| < 1, then analytically continue the function to [z] ≥ 1.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
![3. Show that the functions below are meromorphic; that is, the only singu-
larities in the finite z plane are poles. Determine the location, order and
strength of the poles.
(a)
e²
(d)
Z
z4+2
1
z4
(b) tan z
1
(e)
Z
sin² z
dw
$c (w² -2)(w - z)
2лi
(c)
C is the unit circle centered at the origin. First find the function for |z| < 1,
then analytically continue the function to |z| ≥ 1.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd9cdd9f8-87ce-45c4-aa3a-6df6b1b26c96%2F6b017755-d0e7-411c-ac98-a052f2e9b781%2Fxbdpyq4_processed.png&w=3840&q=75)
Transcribed Image Text:3. Show that the functions below are meromorphic; that is, the only singu-
larities in the finite z plane are poles. Determine the location, order and
strength of the poles.
(a)
e²
(d)
Z
z4+2
1
z4
(b) tan z
1
(e)
Z
sin² z
dw
$c (w² -2)(w - z)
2лi
(c)
C is the unit circle centered at the origin. First find the function for |z| < 1,
then analytically continue the function to |z| ≥ 1.
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Step 1: Analysis and Introduction
VIEWStep 2: Examine the singularity of first function
VIEWStep 3: Examine the singularity of second function
VIEWStep 4: Examine the singularity of third function
VIEWStep 5: Examine the singularity of fourth function
VIEWStep 6: Find the function from the integral.
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