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 6
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z
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z
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3
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n
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6
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42
2
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zz
z
mm
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==
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1
==
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3
1
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m
n

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2
3
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m
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3
2
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m
Imπ
=

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1
,
ch
sh
th π?
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z
kz
z
z
zzf
k
1 B)? ( )",1,0 ±=k 0=k
H i
2
0
π
=z 
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00
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2
i
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π
π =
==

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C
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2
1
+= kz
k

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2
1
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π
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2
1
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z
z
?
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1
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k
C
zdz f z zππ π
π

==



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=

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11
12
11(1)
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nn
n
n
za
dn
fza z a
ndx zazbnab

21
)!
n


=?=

12
111
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nn
n
n
za
dn
fzb z b
ndx zazbnba


=?=

2n
b
#s1 0
? ||
Hs"1||a<<
1
22
(1) (2 2)!
[( 1)!] ( )
n
n
n
nab
1?


10
? z =∞
^/
òf
¥
I
1 ?$i p ∞¥
=
b
1
2
1
z
e  2 cos  3sinz? z
2
2
3
z
z+
b
3 1 V ? ?  ¥
=
1
,b∞
2
1
() ( ) ( )
t
tfzf e
t
= ==
2
221
1
00
1
() ( ) ( ) ( 1) ( 1)
(2 )! (2 1)!
nn
nn
nn
zz
tfzf
tn
+∞∞
+
==
===
+
∑∑
# z =∞
z
1f
¥'? ? ?? ?
??ˉ
ü
3# ¥
=
1
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3
224
2239
(1 )
3
z
zz zz
=?++
+
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a[#1 V ? ?
=
1
1
2c
=
22
11 2
Res[ ( ),] Res[ ( ),0] Res[,0] 2
(1 3 )
fz f
zz z z
∞= = =
+
b
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1
1
)(
2
=
z
e
zf
z

2
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1
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4
+
=
zzz
zf
3 
1
1
)(
2
=
z
e
zf
z

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=
1
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1
lim
1
lim1,Res1,Res,Res
11
+
==∞
→→
z
e
z
e
zfzfzf
z
z
z
z
= 1sh
22
1
=+?
ee

2 ()
()()41
1
4
+
=
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zf [ 1B)?0=z 1?=z 1
1)? 4=z 1B)?¨μK ?
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9
V?
t
PB??¨°¤ ∞=z ¥?ì×
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=Z 7
1
μ)
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()
()()

+?
=
+
=
zz
zz
zzz
zf
4
1z
1
1
1
41
1
4
4
4
=
+
=

+
zz
z
zz
z
4
1
1
·
1
1
11
4
1
1
1
1
4
6
4
6
=?
+++?
++?,..
164
1...
11

1
2
4
26
zzzzz
An#,0
1
=
c ()[]0,Res =∞zf,
?9 V ?¨5 IVb
129
/
 òs C1 ?_?? b
1
15
224 3
,:| | 3
(1)(2)
C
z
dz C z
zz
=
++
∫v
 2
13
1
z
C
z
edz
z+
∫v
 2|:| =zC 
3
2
1
n
n
C
z
dz
z+
∫v

1B ?
 n,| | 1Cz r= > b
3 1f
15
224
(1)(2)
z
zz++
3
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15
224 3 2
22 43
11
2iRes[(),] 2iRes[(),0]
(1)(2)
1
2 i Res[,0] 2 i
(1 ) (1 2 )
C
z
dz f z f
zz zz
zz z
ππ
ππ
=? ∞ =
++
==
++
∫v
2 ()
z
e
z
z
zf
1
3
1+
= μ ? 1?=z  0=z 1?=z 1B)? 7 0=z 1'? ?  +∞<< ||2 z
=Z
7 5 ()zf
()
zz
e
z
z
e
z
z
z
zf
1
2
1
3
·
1
1
1
1?
+
=
+
= =?
+++?
+?,..
!2
11
1...
11
1
22
2
zzzz
z
=?
+++?
+?,..
!2
11
1...
11
1
22
2
zzzz
zz,..
1
3
1
!2
1
2
+?+=
z
z
¤,
3
1
1
=?
c#es () ici ππ
3
2
2
1
==
,
3?
H1n =
2
2iRes[(),1] 2i
1
C
z
dz f z
z
π π=?
+
∫v
= ? 1n ≠
H
2
2
11 1
(1 ) 1
11
nn
nn
nn nn n
zz
zz
zz zz z
==?++=?++
++
""
? #
1
0c
=
2
0
1
n
n
C
z
dz
z
=
+
∫v
b
139
/
 s
1)
2
0
1
53sin
d
π
θ
θ+

 2
2
2
0
sin
cos
d
ab
π
θ
θ
θ+

 3(ab>>0)
22
1
(1 )
dx
x
+∞

+


- 6 -
4
2
4
0
1
x
dx
x
+∞
+

 5
2
cos
45
x
dx
xx
+∞

++

 6
2
sin
1
x x
dx
x
+∞

+

b
3 ??$f
¥s
 53sinθ+  02θ π≤ ≤
=?1
,y7sμilb
2 2
||1 ||1
i
3
12
2iRes[(),]
1 i310i3
53
2i
2
2i
6 +10i 2
zz
z
dz
Idz
z zzz
z
z
π
π
π
==
=?
=
+?
+
==
∫∫vv
i
3
fz?

??$f
¥s
 cosab θ+  02θ π≤≤
=?1
,y7sμilb
2
2
22 22
2 22
||1 ||1
1
()
i( 1)
2i
2 i{Re [ ( ),0] Res[ ( ),]}
1 i2(2)
2
zz
z
dz z a a b
z
Idsfz
z z z bz az b b
ab
z
π
==

=+
+ ++
+
∫∫vv
+?

?
22 2
22 2
0
(1 )( 3 (3 )) i
Res[ ( ),0]
(2 )
z
z a az bz z a
fz
bazbz b
=
+ + + +
++

22
22 2 2 22
22
i( 1) i
Res[ ( ),]
4( 3 2 ) aab
z
b
aab z ab
fz
bzbab?+?
=
+
==
++

#
22
2
2
()I aab
b
π
=b
 f
22
1
()
(1 )
fz
z
=
+

?
ü
=oμ 2)? i O
2
23
ii
12
Res[ ( ),i] lim ( i) ( ) lim
(i) (2i) 4
zz
dd
fz z fz
dz dz z
→→
=?= =?=
+
i

#
22
1
(1 )
dx
x
+∞

+

" 2iRes[(),i]
2
fz
π
π = b
4?i?$ f
1
}f

22
44
0
1
121
xx
I dx dx
+∞ +∞

==
++
∫∫
f
2
4
()
1
z
fz
z
=
+

?
ü
=oμB)?
i3i
44
,ee
π π
 O
i
4
2
3
i1i
Res[ ( ),]
44
42
ze
z
fz
z
π
π
=
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