EX: Find all residues of f(Z) = Sol: f(z)= 50 Z x₁ = [ -=520- 7/42-7] 2-4 (Z+4)(Z-1)² 12= L 11 d 10 m [1/12 (22 200 25 507 Z +41 = 8, ^^ 50 Z Z³+2Z²²-7Z+4 there are simple pole at Z=-- double pole at Z=1 = -8 (Z+4) (50)-50Z* A im. (Z+4)² How did he get the value inside the circle

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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EX: Find all residues of f(z) =
Sol:
there are
f(z)= 50 Z
(Z+4)(Z-1)²
12- L
=
r₁ = [ 350
71
32²² +42-7 Z-4
50 Z
Z→1
200
25
507
Z +4
= 8.
↑ ₁
Z³+2Z²²-7Z+4
-8
50Z
_im.
simple pole at Z=-L
double pole at Z=1
(2+4) (50)-50Z* A
(Z+4)(50)
(2+4)²
How did he get the
value inside the circle
Transcribed Image Text:EX: Find all residues of f(z) = Sol: there are f(z)= 50 Z (Z+4)(Z-1)² 12- L = r₁ = [ 350 71 32²² +42-7 Z-4 50 Z Z→1 200 25 507 Z +4 = 8. ↑ ₁ Z³+2Z²²-7Z+4 -8 50Z _im. simple pole at Z=-L double pole at Z=1 (2+4) (50)-50Z* A (Z+4)(50) (2+4)² How did he get the value inside the circle
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