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Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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TRANSCRIBE THE FOLLOWING TEXT IN DIGITAL FORMAT

Transcribed Image Text:Let
I =
where is the square with vertices -1-i, 1-i, ¹+í¸‚-¹ + i
if
now,
S
r
since Z=0
:: by residue theorem
S
here
&
dz
here
73
dz
73
where
-iti
-1-i
f(²)=
f(²)=
we know that
4 (4)
(2-20)h+1
lies in a square
dz
Z3
r
= 2πi Res f(2)
2-0
1
f (²) = 273
73
Res f(²)=
2= 0
140
dz
N
i-i
(2) is analytic function with $ (20) #0
23
then Res f(2)=
2=20
&"(0)
2!
using this value in D, we get.
επί (0) = ο
(Z)
=
دره - 2)
3
=
Ⓡ
O
2!
;. $(4) = 1
<=0
4 (20)
n!
(:. 4² (²) = 4" (2₁) = 0)
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