Let Find с S = 2=-t P(2) q(z) be the 2²-1 Sinz poles inside the circle By residue theorem 250i/Res 22-1 Sinz = dz __2²_1 circle Sinz + Res 2²-1 Z=0 Sinz |z 2Ji = 2,5 i (1- JT ³² -1 + 1 - JT ²) - (2 ST - 4st ³) (₂ 3 Анд ore + residue → _p(2) 9'(2) at z =- J, 0, JT Res 2=J ((-³) -1 + = +*+ ² =1) Z²-1 Sinz cosz
Let Find с S = 2=-t P(2) q(z) be the 2²-1 Sinz poles inside the circle By residue theorem 250i/Res 22-1 Sinz = dz __2²_1 circle Sinz + Res 2²-1 Z=0 Sinz |z 2Ji = 2,5 i (1- JT ³² -1 + 1 - JT ²) - (2 ST - 4st ³) (₂ 3 Анд ore + residue → _p(2) 9'(2) at z =- J, 0, JT Res 2=J ((-³) -1 + = +*+ ² =1) Z²-1 Sinz cosz
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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Transcribed Image Text:Let
Find
с
S
P(2)
q(z)
be the
2²-1
Sinz
=
poles inside the circle
By residue theorem
250i/Resz
Z=-t
2-1
Sinz
__2²_1
dz
Sinz
circle
+ Res 2²-1
Z=0
Sinz
|z
ore
2Ji
((-3) -1 + =
+
= 2,5T (1-JT ³² - 1 + 1 - JT ²)
- (2 st - 4st ³) (₂
3
Анд
+
residue → _p(2)
9'(2)
at 2 = -Jt₂0, JT
Res
2=J
+ 3+² -1)
2
Z²--1
Sinz
cosz
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