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fMD 53s
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fMD,i¨°V￥ZE ?￡2T,
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2
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3 (1) & ()
ii
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|
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- 1 -
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(6) & ()
00
cosh
2
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st st
ee
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& ()
0
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∫ 2
11
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s
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t
tf sin
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5
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6
( ) tttf 2cos32sin5?=
- 4 -
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7
8() tetf
t
6sin
2?
=
( )
4
cos 4
t
f te
= t
9
10()
tn
ettf
α
= ( ) ( )53?= tutf
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t
eutf
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t
e
tf
t3
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3
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1
1
>
+Γ
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α
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s
t
& & &()[]=tf
2
32tt++=
2
3t+
&
3
2
2t
+
&[]1
32
232
sss
= ++
2 & & & &()[]=tf []=?
t
te1 []?1 [ ]
t
te
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s
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11
1
11
=
=
ssss
e
t
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2
(1)
t
te=
2
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t
tte +=
2
2
d
ds
&[ 2]
t
e
d
ds
&[ &[] ]
t
e
t
e
2
3
45
(1)
ss
s
+
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a
at
a
t
2
1
sin
2
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ds
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a2
1
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22 22
1
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as
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[
()[]=tf
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ds
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[ ]
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22
22 22
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ss
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4
310
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4
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s
s
s
s
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2
2
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t
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s
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10 3E ? ()
<
>
=?
3
5
3
5
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53
t
t
tu
& ()[]=tf & ()[]()
∫
+∞
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5353 dtetutu
st
∫
∞+
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=
=
==
3
5
3
5
3
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s
e
s
e
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s
t
st
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tu
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3
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0,01
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1
te
te
eu
t
t
t
[
& ()[] ()
∫∫
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+∞
===
00
1
s
dtedtetftf
stst
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2
1
2
1
2
1
2
1
ss
t
π
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3
3
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s
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s
fat F
aa
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00
11
[()] () () () ()
s
at
st
a
s
f at f at e dt f at e d at F
aa
+∞ +∞
== =
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a
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ü
()
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n
Fs= &[( Re b+ Y &[( ) ( )]
n
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t
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9
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T
1
['()]Fs
3
() sin2
t
f tte
= t p
()Fs
3
0
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t
t
f tte td
=
∫
t p ()Fs
1
() ln
1
s
Fs
s
+
=
p ()f t
3
0
() sin2
t
t
f tte t
=
∫
d p b ()Fs
3
()
()
n
Fs=
n
n
d
ds
&[()]f t
00 0
() [ () ] ( ) ()
nn
st st n st
dd
f te dt fte dt t fte dt
ds ds
+∞ +∞ +∞
== =?
∫∫ ∫
- 6 -
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" &[( Re b ) ( )]
n
tft? ( )s> c
1 ?¨
T & ( )[] ()sFttf '?=
& &()[]=tf
3
sin 2
t
d
te t
ds
=?
&
3
[sin2]
t
et
222
2
24(
(3)2
(3)4
s
s
s
+
=? ′=
++
++
3)
2?s ?é
&
s
de
t
1
2sin
0
3
=
∫
ττ
τ
&[ ]
()43
21
2sin
2
3
++
=
ss
te
t
?^f
￥±s
T
& ()[]=tf &
()
++
=
∫
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2
2sin
2
0
3
ssds
d
det
t
ττ
τ
( )
()[]
2
22
2
43
131232
++
++
=
ss
ss
3
2
11
'( ) ln ' 2
s
Fs
ss
+
==?=
&
2
inh]tt
t
[s ?
2
() sinhf tt
t
=
4 & &()[]=tf
3
0
1
sin 2
t
t
te tdt
s
=
∫
&[ ]tte
t
2sin
3?
( )
()[]
2
2
43
34
++
+
=
ss
s
4 ? &[()] ()f tFs= ￡
ü &
()
()
s
ft
Fsds
t
∞
=
∫
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()
s
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∞
∫
bi ? ¨N
2
9
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T
sin
()
kt
ft
t
= p
()Fs
3
sin 2
()
t
et
ft
t
= p ()Fs
2
()
(1)
s
Fs
s
=
2
p ()f t
3
0
sin 2
()
t
t
et
f tdt
t
=
∫
()Fs p b
3
00 0
()
() () ()
st st st
ss s
ft
F s ds f t e dtds f t e dsdt e dt
t
∞ ∞ +∞ +∞ ∞ +∞
====
∫∫∫ ∫ ∫
&
()f t
t
&()=sF
sin
s
kt
t
∞
=
∫
&
[ ]
sin kt du
22
arctan
|
ss
ku
du
uk k
∞ ∞
==
+
∫
arctan
2
s
k
π
=? arccot
s
k
=
2 &()=sF
∫
∞
=
s
t
t
te 2sin
3
&[]dute
t
2sin
3?
()
∫
∞ ∞
+
=
++
=
s s
u
du
u
|
2
3
arctan
43
2
2
2
3
arctan
2
+
=
sπ
2
3
cotarc
+
=
s
3 &() ttf =
()
1
2
2
1
s
u
du t
u
∞
=
∫
&
∞
s
u 1
1
2
1
2
1
t= & ()
tt
eet
ss
=
+
4
1
1
1
4
1
1
1
4
1
1
t
t
sh
2
=
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4 &()=sF
s
d
e
t
12sin
0
3
=
∫
τ
τ
τ
τ
&
t
te 2sin
3τ
∫
∞
=
s
s
1
&[ ]
∫
∞
++
==
s
t
du
us
dute
4)3(
21
2sin
2
3
2
3
cotarc
1
2
3
arctan
1
|
+
=
+
=
∞
=
s
s
u
s
su
59
/
s
(1)
∫
+∞
0
2
.dt
t
ee
tt
(2)
∫
+∞
0
cos1
dte
t
t
t
(3)
∫
+∞
0
coscos
dt
t
ntebte
mtat
(4) (5) (6),2cos
0
3
∫
+∞
tdte
t
.
0
2
∫
+∞
dtte
t
.2sin
0
3
∫
+∞
tdtte
t
(7),
sinsh
0
2
∫
∞+
dt
t
tte
t
(8),
sin
0
2
∫
+∞
dt
t
te
t
(9),sin
0
3
∫
+∞
tdtet
t
(10)
∫
+∞
0
2
2
sin
dt
t
t
,(11)
0
erf,
t
et
+∞
∫
dt (12)
0
0
J(),tdt
+∞
∫
?
2
0
2
erf
t
u
te
π
=
∫
d?1μf
2
0
2
0
(1)
J()
(!) 2
k
k
k
t
t
k
+∞
=
=
∑
?1
,¨ ?,(Bessel)f
b
3 (1)?
T
( )
∫∫
+∞ ∞
=
00
dt
t
tf
& ¤ ()[]dstf
∫∫
+∞ ∞
=
00
2
dt
t
ee
tt
&[] ds
ss
dsee
tt
∫
∞
+
+
=?
0
2
2
1
1
1
2ln
2
1
ln
|
0
=
+
+
=
∞
s
s
(2)
∫∫
+∞ ∞
=
00
cos1
t
e
t
& ()[]dste
t
cos1?
()
∫
∞
++
+
+
=
0
2
11
1
1
1
ds
s
s
s
()
2ln
2
1
11
1
ln
|
02
=
++
+
=
∞
s
s
(3)
+∞ ∞
=
coscos
dt
t
ntebte
mtat
&[ ]dsntebte
mtat
coscos
() ()
ds
nms
ms
bas
as
∫
∞
++
+
++
+
=
0
2222
()
()
|
0
22
22
ln
2
1
∞
=
++
++
=
s
nms
bas
22
22
ln
2
1
ba
nm
+
+
=
(4)X? &[]
∫
+∞
+
=?=
0
2
4
2cos2cos
s
s
dtett
st
yN
∫
+∞
=
=
+
=
0
3
2
3
13
3
4
2cos
s
t
s
s
tdte
(5) &[]
∫
+∞
=
0
2
dtte
t
4
11
2
2
2
==
=
=
s
s
s
t
(6)X? &[]
4
2
2sin
2
+
=
s
t ?±s?é &[]
()
2
2
2
4
4
4
2
2sin
+
=′?
+
=
s
s
s
tt
¤
()
∫
+∞
=
=
+
=
0
32
2
3
169
12
4
4
2sin
s
t
s
s
tdtte
()
∫∫
∞∞+
=
00
2
sinsh
7 dt
t
tte
t
& dst
ee
e
tt
t
sin
2
2
∫
∞
=
0
2
1
&
( ) ( )
[ ]dstete
tt
sinsin
1212 +
()()
ds
ss
∫
∞
+++
+?+
=
0
22
112
1
112
1
2
1
( ) ()
+++=
∞∞
||
00
12arctan12arctan
2
1
ss
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() ( )[]12arctan12arctan
2
1
+=
8
1arctan
2
1 π
==
(8)
∫∫
+∞ +∞
=
00
2
sin
dt
t
te
t
&[]
∫
∞
=
0
2
2
1
sin dste
t
& ( )[ ]dste
t
2cos1?
()
()
|
020
2
41
1
ln
2
1
41
1
1
1
2
1
∞∞
++
+
=
++
+
+
=
∫
s
s
ds
s
s
s
5ln
4
1
=
(9)X? &[],
1
1
sin
2
+
=
s
t ?¨±s?é &[]
()
4
2
3
2
3
4
2424
1
1
sin
+
=″′?
+
=
s
ss
s
tt
∫
+∞
=
0
3
sin tdtet
t
&[]
()
0
4
2424
sin
1
4
2
3
1
3
=
+
=
=
=
s
s
s
ss
tt
(10)
∫∫
+∞ +∞
′?
=
00
2
2
2
1
sin
sin
dt
t
tdt
t
t
∫∫
+∞ +∞∞
=+?=
000
2
2sin2sinsin
|
dt
t
t
dt
t
t
t
t
∫
∞
=
0
&[]
∫
∞
+
=
0
4
2
2sin ds
s
dst
22
arctan
|
0
π
==
∞
s
(11)
0
erf
t
etdt
+∞
=
∫
&
1
1
12
erf( )
2
1
s
s
t
ss
=
=
==
+
(12) &
[]
0
0
J()tdt
+∞
=
∫
0
0 2
0
1
J() 1
1
s
s
t
s
=
=
==
+
6 p/
f
￥ ?
f
IMD,
1 (),
4
1
2
+
=
s
sF
2 (),
1
4
s
sF =
3 ()
()
.
1
1
4
+
=
s
sF
4 (),
3
1
+
=
s
sF
5 (),
9
32
2
+
+
=
s
s
sF
6 ()
()()
.
31
3
+
+
=
ss
s
sF
7 (),
6
1
2
+
+
=
ss
s
sF
8 (),
134
52
2
++
+
=
ss
s
sF
3
1 &()=tf ()[]
2
1
1
=
sF & t
s
2sin
2
1
4
2
2
1
=
+
2 &()=tf
!3
11
4
1
=
s
&
3
13
1
6
1!3
t
s
=
+
3? &
3
4
1
6
11
t
s
=
#êM?é & ( )[ ] ( )tfeasF
at
=?
1
¤
()=tf & ( )[ ]=
sF
1
&
()
t
et
s
=
+
3
4
1
6
1
1
1
4 &()=tf ( )[]=
sF
1
&
t
e
s
31
3
1
=
+
5 &()=tf ( )[]2
1
=
sF & +
+
9
2
1
s
s
& tt
s
3sin3cos2
9
3
2
1
+=
+
- 9 -
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6 & &()=tf ()[]=
sF
1
()()
+
+
31
3
1
ss
s
=&
2
3
1
1
3
3
2
1
1
=
+
ss
&
2
1
3-s
1
1
&
+
1
1
1
s
tt
ee
=
2
1
2
3
3
7 & &()=tf ()[]=
sF
1
=
+
+
6
1
2
1
ss
s
&
+
+
3
2
2
3
5
1
1
ss
5
3
= &
5
2
2
1
1
+
s
&
tt
ee
s
321
5
2
5
3
3
1
+=
+
8 & &()=tf ()[]=
sF
1
=
++
+
134
52
2
1
ss
s
&
( )
()
++
++
22
1
32
122
s
s
2= &
()
() 3
1
32
2
22
1
+
++
+
s
s
&
()
++
22
1
32
3
s
()
222
11
2cos3 sin3 6cos3sin3
33
ttt
etete t
=+= +t
7 p/
ò m
Uf
()f t ￥ ?
fMD,
()ft
A
A?
τo
2τ 3τ
4τ
t
o
t
()ft
2
4
6
τ
3τ 5τ
(1) (2)
o
t
()ft
2
4
6
8
2
o
t
()ft
1
2
3
τ
2τ 3τ
4
(3) (4)
(1) ?m^?,
^?
ù1()tf 2τ ￥?
ùf
, B??
ù
=
- 10 -
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()
,0
,2
At
ft
At
τ
τ τ
≤ <
=
≤<
?
T
& () ()
2
2
0
1
st
s
A
f tftedt
e
τ
τ
=
∫
()
( )
2
2
0
1
1
st st
s
A
edt edt
e
ττ
τ
τ
=+?
∫∫
2
0
2
1
||
st st
tt
s
ee
A
ess
ττ
τ
τ
==
=?
2
2
1
1
s ss
s
Aeee
es
τ ττ
τ
+?
=?
()
2
2
1
tanh
12
s
s
e
AA
se s
τ
τ
sτ
=? =
(2) ?m^?
0
() 2[ ( ) ( 3 ) ( 5 ) ] 2 ( (2 1) )
k
f t ut ut ut ut kτ ττ
∞
=
=?+?+?+=?+
∑
"τ
?
H &Re( ) 0s > ()
(2 1)
2
0
22
1sin
s
ks
s
k
e
ft e
ss
τ
τ
τ
1
hsτ
∞
+
=
==?=
∑
(3) ?m^? () 8 () 2 ( 2)f t ut ut=?
H Re( ) 0s >
& ()
2
2
0
1822
(4 )
s
ks s
k
e
f te e
ssss
τ
∞
=
==?=
∑
(4)?m^?
0
()[()( )(2) ] (
k
)f tutut ut utkτ ττ
∞
=
=+?+?+=?
∑
"( ) 0s >? Re
H
&
()
0
1111
(1 coth )
12
ks
s
k
s
ft e
sses
τ
τ
2
τ
∞
=
==?=+
∑
5 ?
!
1
()f t
2
()f t (
@ ?
fMDi ? ?￥Hq
?
ì￥9é·
(1 c O
&
11
[()] ()f tFs= &
22
[()] ()f tFs= 5e
12
() ()f tft? ￥ ?
fMDB?i O
&
[]
j
12 12
j
1
() () ( ) ( )
2j
f tft FqFsqdq
β
β
π
+∞
∞
=?
∫
? cβ > Re( )scβ>+ b
￡ ?? (
@ ?
fMDi ? ? ￥Hq[# 9é·
( 1 ?e() ()tftf
21
,
0
c () ( )tftf
21
9B
?
@ ?
f MDi ￥ ? ?￥Hq O9é·
1 ? ?
f i ? ?￥ ￡
ü?.2
0
c
0
c>β
H
& () () () ()
12 12
0
st
f tft ftftedt
+∞
=
∫
0
Re cs +≥ β
i OBá
l ?,??
() ()
i
11
i
1
2i
qt
f tFq
β
β
π
+∞
∞
=
∫
edq
7 & () () () ()
12 12
0
st
f tft ftftedt
+∞
=
∫
() ()
i
12
0i
1
2i
qt st
Fqedqf te dt
β
β
π
+∞ + ∞
∞
=
∫∫
- 11 -
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() ()
i
()
12
i0
1
2i
sq
Fq f te dtdq
β
β
π
+∞ +∞
∞
=
∫∫
() ( )
i
12
i
1
2i
FqFs qdq
β
β
π
+∞
∞
=?
∫
p/
f
￥ ?
f
IMD
^ef
i¨
6B?ZEF[￡,
1 (),
1
22
as
sF
+
=
2 ()
()()
.
bsas
s
sF
=
3 ()
()()
2
bsas
cs
sF
++
+
=
4 ()
()
2
22
22
2
as
as
sF
+
+
=
5 ()
()
.
1
322
sas
sF
+
=
6 ()
()()bsass
sF
++
=
1
7 (),
1
44
as
sF
=
8 ()
()
2
2
1
12
+
=
ss
ss
sF
9 ()
()
.
1
1
22
=
ss
sF
10 ()
()()41
22
++
=
ss
s
sF
1 3E ()=tf & &()[]=
sF
1
+
22
1
1
as
a
a a
1
= &
a
at
as
a sin
22
1
=
+
3E ()
+
+
+
= i,Resi,Res
2222
a
as
e
a
as
e
tf
stst
a
at
a
e
a
e
atat
sin
i2i2
ii
=?=
3E ()=tf & =
+
22
1
1
as
&
+
i
1
i
1
i2
1
1
asasa
i2
1
a
=
&?
i
1
1
as
&
+
i
1
1
as
()
a
at
ee
a
atat
sin
i2
1
ii
=?=
2 3E ( )=tf & &()[]=
sF
1
()()
bsas
s
1
()() ()()
+
= b
bsas
se
a
bsas
se
stst
,Res,Res
()
btat
btat
beae
baab
be
ba
ae
=
+
=
1
3E ( )=tf & &()[]=
sF
1
()()
bsas
s
1
=&
bs
b
as
a
ba
1
1
ba?
=
1
&
a b
as
1
1
&
bs
1
1
()
btat
beae
ba
=
1
3 3E ( )=tf & ()[]sF
1?
( )
()()
( )
()()?
++
+
+
++
+
= b
bsas
ecs
a
bsas
ecs
stst
,Res,Res
22
()
()
bs
st
at
e
as
cs
ds
d
ab
eac
=
+
+
+
=
2
() ()
btbtat
e
ba
ca
te
ba
bc
e
ba
ac
+
+
=
22
3E &()=tf ( )[]=
sF
1
&
()()
++
+
2
1
bsas
cs
=&
() () ()
+
+
+
+
+
222
1
111
bs
ba
bc
bs
ba
ca
as
ba
ac
()
2
ba
ac
=
&
()
2
1
1
ba
ca
as?
+
+
&
ba
ac
bs?
+
+
1
1
&
()?
+
2
1
1
bs
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() ()
btbtat
te
ba
bc
e
ba
ca
e
ba
ac
+
+
=
22
4 3E & &()=tf ()[]=
sF
1
()?
+
+
2
22
22
1
2
as
as
=&
+
+
+
'
2222
1
2
1
2
3
as
s
as
a
a
a2
3
= &
2
1
22
1
+
+
as
a
&
+
'
22
1
as
s
attat
a
cos
2
1
sin
2
3
=
3E ()=tf & ()[]sF
1?
() ()?
+
+
+
+
+
= i,
2
Resi,
2
Res
2
22
22
2
22
22
ae
as
as
ae
as
as
stst
() ()
i
2
22
i
2
22
i
2
i
2
as
st
as
st
e
as
as
ds
d
e
as
as
ds
d
==
+
+
+
+
= tatatata
tee
a
tee
a
iiii
4
1
i4
3
4
1
i4
3
=
attat
a
cos
2
1
sin
2
3
=
5 3E ( )=tf &
()
2322
1
11
asas
=
+
&
()
+
223
1
11
asss
(
1
2
a
= &?
3
1
1
s
&
()
)
1
22
1
+
ass
∫
=
t
t
a
0
3
2
2
1
(
1
& )
1
22
1
dt
as
+
3
2
0
11 1
sin
22
t
ta
aa
=?
∫
td
()
3
24
11
1cos
2
ta
aa
=t
3E &()=tf
()
+
322
1
1
sas
() () ()
+
+
+
+
+
= i,Resi,Res0,Res
322322322
a
sas
e
a
sas
e
sas
e
ststst
() ()
3
i
3
i
0
222
2
ii2ii22
1
aa
e
aa
e
as
e
ds
d
tata
s
st
+
+
=
=
()at
a
t
a
cos1
1
2
1
4
2
2
=
6 3E ()=tf &
()()
+
bsass
1
1
=&
() ()
+
+
+?
bsbabasbaasab
111111
1
=
ab
1
&
()baas?
+
11
1
&
()babas?
1
+
1
1
&
+
bs
1
1
() ()
btat
e
bab
e
baaab
+=
111
3E &()=tf
()()
++
bsass
1
1
()() ()() ()()
++
+
++
+
++
= b
bsass
e
a
bsass
e
bsass
e
ststst
,Res,Res0,Res
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() ()
btat
e
bab
e
baaab
+=
111
3E ()=tf &
44
1
1
as
=&
+
+
2233
1
2
111
4
1
as
a
aasasa
() at
a
ee
a
atat
sin
2
1
4
1
33
=
()atat
a
sinsh
2
1
3
=
3E ()=tf &
44
1
1
as
+
+
+
= i,Resi,Res,Res,Res
44444444
a
as
e
a
as
e
a
as
e
a
as
e
stststst
() ()
3
i
3
i
33
i4i444 a
e
a
e
a
e
a
e
tataatst
++?=
()atat
a
sinsh
2
1
3
=
8 3E ()=tf &
()
=
+
2
2
1
1
12
ss
ss
&
()
+
+?
2
1
1
2
1
21
s
ss
=& +
s
1
1
& +
1
2
1
s
&
()
2
1
1
2
s
tt
tee 221 ++?=
3E ()=tf &
()
+
2
2
1
1
12
ss
ss
() ()
+
+
+
= 1,
1
12
Res0,
1
12
Res
2
2
2
2
stst
e
ss
ss
e
ss
ss
1
2
12
1
=
+
+?=
s
st
e
s
ss
ds
d
tt
tee 221 ++?=
9 3E ()=tf & &()[]=
sF
1
()
1
1
22
1
ss
=& ()tee
sss
tt
=
+
2
11
1
1
1
1
2
1
2
1
tsht?=
3E ()
() () ()
+
+
= 1,
1
Res1,
1
Res0,
1
Res
222222
ss
e
ss
e
ss
e
tf
ststst
tt
ee
s
e
ds
d
tt
s
st
=?+
=
=
sh
221
0
2
103E ( )=tf &
()()
++
41
22
1
ss
s
=&
+
+
413
1
22
1
s
s
s
s
(
3
1
= &?
+
1
2
1
s
s
& ()tt
s
s
2coscos
3
1
)
4
2
1
=
+
3E &=)(tf
()()
++
41
22
1
ss
s
()() ()() ()() ()()
++
+
++
+
++
+
++
= i2,
41
Resi2,
41
Resi,
41
Resi,
41
Res
22222222
ss
se
ss
se
ss
se
ss
se
stststst
() ()()()()i41i4
i2
i41i4
i2
4ii2
i
4ii2
i
2
i2
2
i2
2
i
2
i
+
+
+
+
+?
+
+
=
tttt
eeee
6666
i2i2ii tttt
eeee
+++= ()tt 2coscos
3
1
=
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3. p/
f
￥ ?
f
IMD,
1 ()
()
2
2
4
1
+
=
s
sF
2 ()
2+
=
s
s
sF
3 ()
()()21
12
++
+
=
sss
s
sF
4 ()
45
1
24
++
=
ss
sF
5 ()
569
1
2
++
+
=
ss
s
sF
6 ()
2
2
1
ln
s
s
sF
=
7 ()
()
.
54
2
2
2
++
+
=
ss
s
sF
8 ()
()
.
22
1
2
2
++
=
ss
sF
9 ()
()
2
2
2
134
44
++
++
=
ss
ss
sF
10 (),
6116
52
23
2
+++
++
=
sss
ss
sF
11 ()
463
3
23
+++
+
=
sss
s
sF
12 ()
()()
3
2
31
332
++
++
=
ss
ss
sF
13 ()
2
2
1
s
e
sF
s?
+
=
3
1 &
()
=
+
2
2
1
4
1
s
&
′?
+
+
+
48
1
4
2
16
1
22
1
s
s
s 16
1
= &
8
1
4
2
2
1
+
+
s
&
′?
+
4
2
1
s
s
ttt 2cos
8
1
2sin
16
1
=
2 &()=tf =
+
2
1
s
s
&
+
2
2
1
1
s
=& []?
1
1
& ()
t
et
s
21
2
2
2
=
+
δ
3 &()=tf
()()
++
+
21
12
1
sss
s ()
()()
( )
()()
()
()()
++
+
+
++
+
+
++
+
= 2,
21
12
Res1,
21
12
Res0,
21
12
Res
sss
es
sss
es
sss
es
ststst
()
()()
()
()
( )
()1
12
lim
2
12
lim
21
12
lim
210
+
+
+
+
+
+
++
+
=
→?→→
ss
es
ss
es
ss
es
st
s
st
s
st
s
tt
ee
2
2
3
2
1
+=
4 &()=tf =
++
45
1
24
1
ss
&
()()
=&
1
22
11 12
3164ss
+ +
++
41
1
22
1
ss
1
3
= &
6
1
1
1
2
1
+
s
&
+
4
2
2
1
s
tt 2sin
6
1
sin
3
1
=
5 &()=tf =
++
+
569
1
2
1
ss
s
&
+?
+
+
4
3
1
9
1
2
1
s
s
9
1
= &
+?
+
+
+?
+
+
2222
1
3
2
3
1
3
2
3
2
3
1
3
1
ss
s
+?=
tt
etet
3
1
3
1
3
2
sin
3
2
cos
9
1
t
ett
3
1
3
2
cos
3
2
sin
9
1
+=
6 &()=tf
ts
s 11
ln
2
2
1
=
&
1?
′
2
2
1
ln
s
s
t
1
= &
tss
s 12
1
2
2
1
=
&
+
+
sss
2
1
1
1
1
1
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()()t
t
ee
t
tt
ch1
2
2
1
=?+?=
&()=tf
()
=
++
+
2
2
1
54
2
ss
s
&
()[]
++
+
2
2
1
12
2
s
s
=&
() 2
1
12
1
2
1
2
1
=
′
++
s
&
()
′
++
12
1
2
1
s
()t=
2
1
&
()
tteet
t
s
tt
sin
2
1
sin
212
1
22
2
1
=?=
++
&()=tf
()
=
++
2
2
1
22
1
ss
&
()[]
++
2
2
1
11
1
s
2
1
= &
() ()?
′
++
+
+
++
11
1
11
1
22
1
s
s
s
(
2
1
= &
()
+
++
11
1
2
1
s
&
()
′
++
+
11
1
2
1
s
s
tte
t
=
sin(
2
1
&
()
++
+
11
1
2
1
s
s
()ttete
tt
cossin
2
1
= ()ttte
t
cossin
2
1
=
&()=tf
()
=
++
++
2
2
2
1
134
44
ss
ss
&
()
()[]
++
+
2
2
2
1
92
2
s
s
=&
()
()[]
++
++
2
2
2
1
92
9
92
1
s
s
=&
() ()
′
++
+
++
2222
1
32
2
2
1
32
3
6
1
s
s
s
tte
t
2
1
3sin
6
1
2
+=
&
()
++
+
22
1
32
2
s
s
ttete
tt
3cos
2
1
3sin
6
1
22
+= ()ttte
t
3cos33sin
6
1
2
+=
10 &()=tf =
+++
++
6116
52
23
2
1
sss
ss
&
()()()
+++
++
321
52
2
1
sss
ss
()
()()()
( )
()()()
( )
()()()
+++
++
+
+++
++
+
+++
++
= 3,
321
52
Res2,
321
52
Res1,
321
52
Res
222
sss
ess
sss
ess
sss
ess
ststst
()() ()() ()()
st
ss
st
s
e
ss
ss
ss
ss
e
ss
ss
21
52
lim
31
52
lim
32
52
lim
2
3
2
2
2
1
++
++
+
++
++
+
++
++
=
→?→?→
ttt
eee
32
10113
+?=
11 &()=tf =
+++
+
463
3
23
1
sss
s
&
()()
+++
+
131
3
3
1
ss
s
=&
() () ()
+++
+
++
1]31[
2
31
1
22
1
sss
=&
() ()
++
+
+
+
++ 31
1
3
2
1
1
3
2
31
1
22
1
s
s
ss
3
1
= &
()()
3
2
31
3
2
2
1
+
++
&
s
3
2
1
1
1
+
s
&
()()
++
+
2
2
1
31
1
s
s
teete
ttt
3cos
3
2
3
2
3sin
3
1
+= ( )tte
t
3sin33cos22
3
1
+?=
(12) &()=tf
()()
++
++
3
2
1
31
332
ss
ss
=&
() ()
+
+
+
+
+
32
1
3
1
6
3
1
2
3
3
1
4
1
1
1
4
1
ssss
4
1
= &
4
1
1
1
1
+
s
&
2
3
3
1
1
+
+
s
&
()
6
3
1
2
1
+
s
&
()
+
3
1
3
1
s
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tttt
etteee
3233
2
3
2
3
4
1
4
1
+?=
(13) &()=tf =
+
2
2
1
1
s
e
s
& +
2
1
1
s
&
2
2
1
s
e
s
()()
()
≥?
<≤
=+=
2,12
20,
22
tt
tt
tutt
5
1
p/
b
1
2.11? tt?
3
4 (.,* 1??
nmtt
nm
)
t
)
t
et?
5
6,cossin tt?,sin*sin ktkt
7,
8 sinh *sinht *sinh,at at
9
10()(.*u tfat? ( ) ( ).* tfat?δ
3 ? l,
() () () ( )
∫
=
t
dtfftftf
0
2121
* τττ
1
∫
=?=
t
td
0
111*1 τ
2 t ()
∫∫∫
=?=
ttt
ddtdtt
000
2
* τττττττ
333
6
1
3
1
2
1
ttt =?=
3 ()
∫∫
∑
=?=
=
ι
ττττττ
00
0
)1(*
t
n
k
kknk
n
kmnmnm
dtCdttt
() ()
∑
∫
∑
==
+++?
++
=?=
n
k
t
n
k
nmk
n
kkmknk
n
k
t
km
CdtC
0
0
0
1
1
1
11 ττ
()
()()( )
∑
=
++++
++++
=
++
=
n
k
nmk
n
k
nm
t
nmmm
n
C
km
t
0
11
1...21
!
1
1
()
1
!!
1!
mn
mn
t
mn
++
=
++
4 =
∫∫
==
tt
ttt
deedeet
00
* ττττ
ττ
1
00
|
=
+?
∫
tedeee
t
tt
t
ττ
ττ
5 () ()
∫∫∫
+=?=?
tt
dttddttt
000
2sin
2
1
sin
2
1
cossincossin ττττττ
() ttttt
t
sin
2
1
2cos
4
1
sin
2
1
|
0
==
=τ
τ
6 ()
∫
=
t
dtkkktkt
0
sinsinsin*sin τττ ()
∫∫
=
tt
ktddktk
00
cos
2
1
2cos
2
1
τττ
kttkt
k
cos
2
1
sin
2
1
=
7 ()
( )
00
*sinh sinh
2
tt
tt
ee
tt td d
ττ
τ ττ τ τ
=?=
∫∫ ∫∫
=
tt
tt
de
e
de
e
00
22
ττττ
ττ
() ()
+?=
||
00
1
2
1
2
t
t
t
t
e
e
e
e
ττ
ττ
sinh tt=?
8
()
0
sinh sinh sinh sinh
t
at at a a t dτ ττ?=?
∫
( )()
∫
=
t
tataaa
d
eeee
0
22
τ
ττττ
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+=
∫∫∫∫
t
at
t
aat
t
aat
t
at
dedeedeede
00
2
0
2
0
4
1
ττττ
ττ
11
cosh sinh
22
tat
a
=?at
9 ()() ()()
∫
=?
t
dtfautfatu
0
* τττ
? at <
H
( ) 0=?au τ
N
H ()()0* =? tfatu
?
H ta ≤≤0
()() ()() ()()
∫∫
+=?
at
a
dtfaudafautfatu
0
* ττττττ
()
∫
=
t
a
dtf ττ
yN
()()
()
≤≤?
<
=?
∫
tadtf
at
tfatu
t
a
0,
,0
*
ττ
10 ()() ()()
∫
=?
t
dtfatfat
0
* τττδδ
? at <
H ()0=?aτδ,N
H
( ) ( ) 0= tfatδ
?
H ta ≤≤0
()() ()() ()() ()()
∫∫∫
+
+
++=?
aa
a
t
a
dtfadtfadtfatfat
0
* τττδτττδτττδδ
()()
∫
+
++=
a
a
dtfa 00 τττδ ()()aft dδ ττ
+∞
∞
=
∫
τ
)
() (atftf
a
=?=
=τ
τ
yN ()()
() ta
at
atf
tfat
≤≤
<
=?
0,
,0
*δ
2 ?¨ ? ?￡
ü &
0
()
()
t
Fs
ftdt
s
=
∫
b
￡
() 1
()
Fs
Fs
ss
=?=&[(
00
)*()] ()( ) ()
tt
f tut f ut d ftdtτττ=?=
∫∫
3 ?¨ ? ?￡
ü &
()
at
a
t
as
s
sin
2
2
22
1
=
+
b
￡
! () ()
222221
1
,
as
a
a
sF
as
s
sF
+
=
+
=
?
^ & ()=tf
1
()[] atsF cos
1
1
=
()=tf
2
& ()[]
a
at
sF
sin
2
1
=
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PH &=
()
=
+
2
22
1
as
s
& () ( )[]sFsF
21
1
() () ()[]τττ dtaa
a
tftf
t
∫
==
0
21
sincos
1
*
()[]ττ aataat
a
t
∫
=
0
2sinsin
2
1
()
=
=
|
0
2cos
2
1
sin
2
1
t
ata
a
att
a
τ
τ == att
a
sin
2
1
·H
4 ?¨ ? ?￡
ü
&
()
∫
=
t
t
dee
ss
0
1
22
1
1
τ
π
τ
i p &,
1
1
1
+
ss
￡
! () (),
1
1
,
1
21
==
s
sF
s
sF ?
^
()=tf
1
& ( )[]=
sF
1
1
&
tt
s
111
2
1
11
2
1
1
=?
Γ
=
π
()=tf
2
& ( )[]=
sF
2
1
&
t
e
s
=
1
1
1
PH &=
()
=
1
1
1
ss
& ( ) ( )[]sFsF
21
1
() () () ( )τττ dtfftftf
t
==
∫
2
0
121
*
∫∫
=?=
tt
tt
deede
00
1111
τ
τπ
τ
τπ
ττ
∫
==
=
t
xt
x
dxee
0
2
2
2
π
τ
·H
! ()
()
,
1
1
=
ss
sF -
X￡ & ()[]
∫
=
t
t
deesF
0
1
22
τ
π
τ
?
& =
+
1
1
1
ss
& ( )[ ]
t
esF
=+1
1
& ()[] τ
π
τ
desF
t
∫
=
0
1
22
￡
ü
@FE￥s
￥
p
123 1213
()*[ () ()] ()* () ()* ()f tftft ftftftft+ =+
￡
123 12 3
0
()*[ () ()] ( )[ ( ) ( )]
t
f tftft f ft ft dτ ττ+=?+?
∫
τ
12 13 1 2 1 3
00
() ( ) () ( ) ()* () ()* ()
tt
f ft d f ft d ftft ftftττττττ=?+?=+
∫∫
￡
ü
@2
p
123 123
()*[ ()* ()] [ ()* ()]* ()f t ftft ftft ft=
￡
123 1 2 3
00
()*[ ()* ()] ( ) ( ) ( )
tts
f tftft fs fts fddsτ ττ
=
∫∫
312 12
00
() () ( ) [ ()* ()]* ()
tt
3
f dfsftsdsftftf
τ
ττ τ
=
∫∫
t
5?
p/
± sZ?
T#Z?F￥3,
1
() ( )'' 4 ' 3,0 ' 0 1
t
yyye y y
++= = =,
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2,''' 3 '' 3 ' 1,(0) '(0) ''(0) 0yyyy y y y+++= = = =
3 ( ) ( )'' 3 ' 2 ( 1),0 0,' 0 1yyyut y y++=? = =,
4 ( ) ( )'' 4sin 5cos2,0 1,' 0 2yy t t y y?= + =? =?,
5 ( ) ( )'' 2 ' 2 2 cos,0 ' 0 0
t
yyyet y y?+= = =
6
( ) ( )
1212
'' 4 ' 5 ( ),0,' 0,(,)yyyFt y cy ccc++= = = 1è
7 () ( )
2
''' ',0 ' 0 ''(0) 0
t
yye y y y+= = = =
8 ( ) ( ) ( )''' 3 '' 3 ' 6,0 ' 0 '' 0 0.
t
yyyye y y y
+++= = = =
9 ()
(4)
2 '' 0,0 '(0) '''(0) 0,''(0) 1.yyy yy y y++= = = = =
10
( )
() ( ) ( ) ( )
4
''' cos,0 ' 0 ''' 0 0,'' 0yy t y y y y+= = = = =c
1.
è
11 () ()
',
00
3'22,
t
t
xxye
xy
xy y e
+?=
= =
+? =
12
()
() () () ()
'2',
0'0 0'0
'' '' 0,
yzFt
yy zz
yzz
=
0.= ===
+=
13
()()( ) ( )
( )( ) () ()
2'' '9 ' '3 0,0 '0 1,
2'' '7 ' '5 0,0 '0 0.
xx x yy y x x
xx x yy y y y
+? ++ = = =?
+++ = = =
14
() () () () () ()
'' 0,
'' 0,0 1,0 0 ' 0 ' 0 ' 0 0.
'' 0,
xxyz
xy yz x y z x y z
xyz z
++=?
+?+= = = = = = =
++?=
3
1Z ?
H | ?
fMDi I
n?
SHq¤
() () ()
2
1
14 43
1
sY s s sY s Y s
s
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+
? ?a3 ( )Ys¤
()
()()
()()
2
15
13
31
s
Ys
ss
ss
+
=+
+ +
++
() 1
1
4
7
3
1
4
3
1
1
2
1
2
+
+
+
+
=
sss
| ?
f
IMD¤ 31
()yt=& ( )
1
Ys
2
1
= &
() 4
3
1
1
2
1
+
s
&
4
7
3
1
1
+
+
s
&
+
1
1
1
s
3
137
244
ttt
te e e
=?+ ()
3
1
27 3
4
tt
tee
=+?
2Z?
H | ?
fMDi I
n?
SHq¤
- 20 -
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() () ()
32
1
33 ()sY s sY s sY s Y s
s
+ ++=
? ?a3 ( )Ys¤
()
32
11
(331)(1)
Ys
ss s s ss
==
+++ +
3
23
11 1 1
1( 1) ( 1)ss s s
=
++ +
| ?
f
IMD¤ 31
()yt=& &()
1
Ys
=
1
1
s
&
1
1
1s
+
&
()
1
2
1
1s
+
&
1
3
1
(1)s
+
22
11(
22
tt t
tt
ete e te
= =? ++)
t?
3Z?
H | ?
fMDi} ?
SHq¤
()
2
1
13()2()
s
sY s Y s Y s e
s
+ + =
3 ¤ (),Ys
()
1
(1)(2) (1)(2
s
e
Ys
ss sss
=+
)+ +++
1111 1
1 2 2 1 2( 2)
s
e
ss ss s
=?+?+
++ + +
| ?
f
IMD¤
()yt
( )yt=& ()
1
Ys
2 ( 1) 2( 1)
11
(1)
22
tt t t
ee e e ut
=?+? + +?
4Z?
H | ?
fMDi} ?
SHq¤
() ()
2
22
45
2
14
s
sY s s Y s
ss
++? = +
+ +
? ?a¤
()
()()()()
222 22
45
111 14
ss
Ys
sss ss
+
=+?
41
2
22
+
+
=
s
s
s
+?+
| ?
f
IMD¤
()yt=& &()
1
2Ys
=
+
1
1
2
1
s
&
+
4
2
1
s
s
tt 2cossin2=
5Z?
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SHq¤
() () ()
2
2
1
222
(1)
s
sYs sYs Ys
s 1
+=
+
- 21 -
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3
()
:Ys
()
22
2( 1)
(( 1) 1)
s
Ys
s
=
+
| ?
f
IMD¤?eZ?3
()
yt=& ()
1
Ys
=&
1
2
1
'si
(1)1
t
te t
s
=
+
n
6Z?
H | ?
fMD¤
() ()Fs ft1 ￥ ?
fMD
() ( ) ( )
2
12 1
445sY s cs c sY s c Y s F s+?+ =()
? ?¤
()
( )
12
22
4
45 45
Fs
cs c c
Ys
ss ss
++
=+
1
+ +++
()
() () ()12
2
12
2
12
2
12
2
1
2
++
+
+
++
+
+
++
=
s
cc
s
s
c
s
sF
| ?
f
IMDi ?¨ ? ?¤
()yt=&
()
()?
++
12
1
2
1
s
sF
1
c+ &
()
()
12
2
1
2
12
2
cc
s
s
++
++
+
&
()?
++
12
1
2
1
s
() ( )
22 2
121
*sin cos 2 sin
tt t
Ft e t ce t c c e t
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() ( )
22
121
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tt
Ft e t e c t c c t
+
7Z?
H | ?
fMD¤
() ()
3
1
2
sY s sY s
s
+=
()
()()
2
1
21
Ys
sss
=
+
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T
()()
22
1
2121
ABCsD
ssssss
+
=++
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¨??"
E¤
112
,,,
10 2 5 5
AB CD==?==?
1
yN
()yt=& " &()
1
Ys
()()
1
2
1
21sss
+
1
10
= &
1
11
22s
&
1
12
5s
+
&
5
1
1
2
1
+
s
s
&
+
1
1
2
1
s
- 22 -
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2
112 1
cos sin
10 2 5 5
t
et=?+?t
8Z?
H | ?
fMD O} ?
SHq¤
() () ()
32
1
3()3 6
1
sY s sY s sY s Y s
s
+++=
+
3 ():Ys
()
4
6
(1)
Ys
s
=
| ?
f
IMD¤?eZ?3
()yt=& ( )
1
Ys
=&
13
1
'''
1
t
te
s
=
9Z?
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SHq¤
( ) ( )
42
2()sY s s sY s Y s 0? ++=
3
():Ys
()
22
(1)
s
Ys
s
=
+
| ?
f
IMD¤?eZ?3
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1
Ys
=&
1
2
11 1
'si
212
tt
s
=
+
n
10Z?
H | ?
fMD,¤
() ()
43
2
1
s
sY s cs sY s c
s
+?=
+
3 ():Ys
()
()()
3 22
1
11
c
Ys
s ss s
=+
+ +
&
()() ()() ()()
++
+
++
=
++
1,
11
Res0,
11
Res
11
1
222222
1
sss
e
sss
e
sss
stst
+
()() ()()
++
+
++
i,
11
Resi,
11
Res
2222
sss
e
sss
e
stst
()() () ()() ()()i1
lim
i1
lim
1
lim
11
lim
2
i
2
i
22
1
2
0
+
+
++
+
+
+′
++
=
→→?→→
sss
e
sss
e
ss
e
ss
e
st
s
st
s
st
s
st
s
()ttet
t
sincos
2
1
2
1
1?++?=
yNeZ?￥31
( )yt=& ()
1
Ys
c
= &
1
3
1
s
+ &
()()
++
11
1
22
1
sss
- 23 -
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()
2
11
1cos
222
t
c
tt e t t
=+?+ +?in
(11)Z?F
H | ?
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SHq,¤
() () ()
() () ()
=+
=?+?
1
1
2213
1
1
1
s
sYssYsX
s
sYsXssX
? ?a,¤
( ) () ()
() ( )()
+
=?+
=?+
1
1
23
1
1
s
s
sYssX
s
s
sYsXs
3-¤
()
()
=
=
1
1
1
1
s
sY
s
sX
| ?
f
IMD¤?eZ?F￥31
( )
()
t
t
x te
yt e
=
=
(12)Z?F
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fMDi} ?
SHq,
!
( )
Ys= & () ( ),yt Zs=
& ( ) ( ),zt Fs
=& ( ),Ft
¤
( ) ( ) ( )
() () ()
=+?
=?
0
2
22
sZsZssYs
sFssZssY
? ?a,3-¤
()
( ) ( )
()
()
+
=
+
=
1
1
2
2
2
s
ssF
sZ
s
ssF
s
sF
sY
| ?
f
IMD¤?eZ?F￥31
()=ty &
()[]& () 2
1
1
sF
s
& ()
+
sF
s
s
1
2
1
sY
1
=
( ) ( ) ( )(1* 2cos * 1 2cos *Ft t Ft t Ft=? =? )
()=tz & &()[]?=
sZ
1
()
+
sF
s
s
1
2
1
( )cos *tFt=?
'31
( ) ( ) ( )
() ()
12cos *
cos *
yt t Ft
zt t Ft
=
=?
(13)Z?F?
?Z?
H | ?
fMD,¤
- 24 -
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()( ) ( ) ( )
()() ()()
+=+++
+=++?+?
ssYsssXss
ssYsssXss
23572
21392
22
22
? ?¤
() ()
() ()
=+
+
+
=?
1
1
4
22
2
2
s
sYsX
s
s
sYsX
3-¤
()
()?
+
+
+
=
+
+
+
+
=
4
2
3
1
43
2
1
1
3
2
4
2
3
1
43
2
1
1
3
1
22
22
ss
s
s
sY
ss
s
s
sX
| ?
f
IMD¤? 31
()
()
12 1
cos 2 sin 2
33 3
22 1
cos 2 sin 2
33 3
t
t
x te t
yt e t t
=+ +
=
t
(14)Z?F?òZ?
H | ?
fMD,¤
()( ) ( )
() ()() ()
() () ()()
=?++
=+?+
=++?
01
01
)(1
2
2
2
sZssYsX
sZsYssX
ssZsYsXs
?a
?Z?¤ () () () ( )sYssXsZsY
2
==,} ??B?Z?3¤
()
()()
() ()
+
+
==
+
+
=
+
=
13
1
23
1
13
1
23
2
21
22
2222
3
s
s
s
s
sZsY
s
s
s
s
ss
s
sX
| ?
f
IMD¤ 31
()
() ()
21
cosh 2 cos
33
11
cosh 2 cos
33
xt t t
yt zt t t
=+
==? +
2 p3s Z?
() () ( )
0
sin,
t
f tat f t dτ ττ=+?
∫
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fMDi ?¨ ? ?
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sin
t
f tdτ ττ
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22
1
1
a
Fs
ss
=+?
+
? ?a¤
()
24
11
Fs a
ss
=+
| ?
f
IMD¤?eZ?￥3
- 25 -
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()
3
1
6
f tat t
=+
3.
! e)é
1 m ￥B é?
H 0t = xZ_
s?
? ( )tkδ ￥T¨ ? k 1è
L?é?￥
1
, p ?
p,
3
! t
H Yé?1 x à?Z_
? ( )tx )?5ié??￥
§W
1,F
1
O
[é?￥?
p
@±sZ?
()tx'
()tx′′ () () 00'0 == xx
() ( ) ( ) ( ) 00'0,'' === xxtktmx δ
13
￥±s|Z?
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fMDi} ?
SHq¤
( ),
2
ksXms =
'
()
2
1
sm
k
sX?=
| ?
f
IMD¤é?￥?
p1
()=tx & ()[]
m
k
sX =
1
&,
1
2
1
t
m
k
s
=
!μ ?m
U￥ 3 -1 óè
^
0
tt=
H|è
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°
@è÷ & pè
^ ?￥è
@ ()it
?m
U ￥è
^
H¤ ?°
@è÷ & pí
^?è
@ 0t = ()it
6.
"d￥,?f
(),
1
K
Gs
Ts
=
+
p? ? ( ) tAtx ωsin=
H￥"dY? y(t),
3 ?"d ￥.?f
()
1
K
Gs
Ts
=
+
^?"d￥
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&
1
1
1
t
T
KK
e
Ts T
=
+
?
^? ? () tAtx ωsin=
H￥"dY?1
() () ( )()()**yt gt xt xt gt==
00
sin sin
tt
tt
TT
KAK
Aede e
TT
ττ
T
dωττ ωτ
==?
∫∫
τ
=
2
2
0
11
sin cos
1
t
t
TT
AK
ee
T
τ
τ
τ
ωτ ω ωτ
ω
=
=
+
()
22
sin cos
1
t
T
AK
tT t Te
T
ωωω ω
ω
=?+
+
()
22
22
sin arctan
1
1
t
T
AK AKT
tT
T
T
ω
ωω
ω
ω
e
=?+
+
+
- 26 -
本文件是从网上收集，严禁用于商业用途！
?
fMD 53s
5B
1 p/
f
￥ ?
fMD,i¨°V￥ZE ?￡2T,
(1) () sin
2
t
ft= (2) ()
2t
f te
= (3) ( )
2
f tt= (4) () sin cosf tt= t
(5) () sinhf t= kt (6) () coshf tk= t (7) ( )
2
cosf t= t; (10) ()
2
cosf tt=,
3 (1) & ()
ii
22
00
()
sin
22i
tt
st
st
tee
f t e dt dt
+∞ +∞
==
∫∫
ii
() ()
22
0
1
2i
st st
eedt
+∞+
=?
∫
ii
() ()
22
00
1
ii
2i
22
||
st st
ee
ss
++∞+∞
=?
+
ii
11 1 1
22
ii
ii2i 2i
22
22
ss
ss
ss
+?+
=?=
+
+
()
2
2
1
2
2
Re 0
1
41
4
s
s
s
== >
+
+
(2) & ()
2(2)
00
tst st
f teede
+∞ +∞
+
==
∫∫
d ()
(2)
0
1
Re 2
(2) 2
|
st
e
s
ss
+∞
+
= =>
+ +
(3) & ()
22
0
1
2
|
st
st st
e
f ttedtt tedt
ss
+∞ +∞+∞
==+
22
0 0
22
|
st st
te e dt
ss
+∞+∞
=? +
∫
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32
0
22
Re 0
|
st
t
es
ss
+∞
=
=? = >
(4) &
()
00
1
sin cos sin 2
2
st st
f t t te dt te dt
+∞ +∞
==
∫∫
(2i) (2i)
0
1
4i
st st
ee dt
+∞
+
=?
∫
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+?
=
+∞
+?
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i2i2i4
1
||
0
i)2(
0
i)2(
s
e
s
e
tsts
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4
1
i2
1
i2
1
i4
1
2
>
+
=?
+
= s
sss
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()
00
sinh
2
kt kt
st st
ee
f tktedt edt
+∞ +∞
==
∫∫ ( )
() ()
00
1
2
skt skt
ed ed
+∞ +∞
+
=?
∫∫
() ()
00
1
2( ) ( )
||
skt skt
ee
sk sk
+∞ +∞
+
=?
+
()
22
11 1
Re max{,}
2
k
sk
sk sk s k
=?= >?
+?
k
- 1 -
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(6) & ()
00
cosh
2
kt kt
st st
ee
f tktedt edt
+∞ +∞
+
==
∫∫ ( )
() ()
00
1
2
skt skt
ed ed
+∞ +∞
+
=+
∫∫
() ()
00
1
2( ) ( )
||
skt skt
ee
sk sk
+∞ +∞
+
=+
+
()
22
11 1
Re max{,}
2
s
sk
sk sk s k
=+= >?
+?
k
(7)& () ()
2
00
1
cos 1 cos 2
2
st st
f t tedt tedt
+∞ +∞
=?=+
∫∫
+=
∫∫
+∞
+∞
dtetdte
stst
00
2cos
2
1
()0Re
)4(
2
4
1
2
1
2
2
2
>
+
+
=?
+
+= s
ss
s
s
s
s
(8)& () ()
2
00
1
sin 1 cos 2
2
st st
f ttedt t
+∞ +∞
=?=
∫∫
edt
( )
00
1
cos 2
2
st st
edt tedt
+∞ +∞
=
∫∫
()
22
11 2
Re 0
24(4)
s
s
ss ss
=?= >
++
2 p/
f
￥ ?
fMD,
(1) ; (2) ()()
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42
20
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≥
<≤
<≤
=
t
t
t
tf
.
2
2
,cos
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π
π
>
<
=
t
t
t
tf
(3) ; (4) () ().5
2
tetf
t
δ+= ( ) ( ) ( ),sincos ttutttf?=δ
3
1 & ()[] ()
∫∫∫
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==
4
20
2
0
3 dtedtedtetftf
ststst
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1
33
42
4
2
2
0
||
ss
stst
ee
ss
e
s
e
+?=+
=
2 & ()[] ()
∫∫∫
∞+
∞+
+==
2
2
00
cos3
π
st
π
stst
dtetdtedtetftf
∫
∞+
=
+
+
=
2
ii
2
0
2
3
| π
π
dte
ee
e
s
st
tt
t
st
∫
∞+
+
++?=
2
i)(i)(
2
)(
2
133
π
π
dteee
ss
tsts
s
+?
+
+?=
+∞
=
+?
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=
i)(i)(2
133
||
2
i)(
2
i)(
2
s
e
s
e
e
ss
t
ts
t
ts
s
πππ
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+
ii2
133
2
i)(
2
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s
e
s
e
e
ss
ss
s
ππ
π
2
2
2
1
133
ss
e
s
e
ss
ππ
+
=
3 & ()[] [] () dtetdteedtetetf
ststtstt?
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∫∫∫
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00
2
0
2
5)(5 δδ
()
2
95
5
2
1
5
2
1
|
0
=+
=+
=
=
+∞
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∫
s
s
e
s
dtet
s
t
stst
δ
4 &
() ()
0
cos sin
st st
f t t t e dt te dtδ
+∞ +∞
∞
=
∫∫
11
1
1
1
1
cos
2
2
22
0
|
+
=
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s
sF =
3 ()
()
.
1
1
4
+
=
s
sF
4 (),
3
1
+
=
s
sF
5 (),
9
32
2
+
+
=
s
s
sF
6 ()
()()
.
31
3
+
+
=
ss
s
sF
7 (),
6
1
2
+
+
=
ss
s
sF
8 (),
134
52
2
++
+
=
ss
s
sF
3
1 &()=tf ()[]
2
1
1
=
sF & t
s
2sin
2
1
4
2
2
1
=
+
2 &()=tf
!3
11
4
1
=
s
&
3
13
1
6
1!3
t
s
=
+
3? &
3
4
1
6
11
t
s
=
#êM?é & ( )[ ] ( )tfeasF
at
=?
1
¤
()=tf & ( )[ ]=
sF
1
&
()
t
et
s
=
+
3
4
1
6
1
1
1
4 &()=tf ( )[]=
sF
1
&
t
e
s
31
3
1
=
+
5 &()=tf ( )[]2
1
=
sF & +
+
9
2
1
s
s
& tt
s
3sin3cos2
9
3
2
1
+=
+
- 9 -
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6 & &()=tf ()[]=
sF
1
()()
+
+
31
3
1
ss
s
=&
2
3
1
1
3
3
2
1
1
=
+
ss
&
2
1
3-s
1
1
&
+
1
1
1
s
tt
ee
=
2
1
2
3
3
7 & &()=tf ()[]=
sF
1
=
+
+
6
1
2
1
ss
s
&
+
+
3
2
2
3
5
1
1
ss
5
3
= &
5
2
2
1
1
+
s
&
tt
ee
s
321
5
2
5
3
3
1
+=
+
8 & &()=tf ()[]=
sF
1
=
++
+
134
52
2
1
ss
s
&
( )
()
++
++
22
1
32
122
s
s
2= &
()
() 3
1
32
2
22
1
+
++
+
s
s
&
()
++
22
1
32
3
s
()
222
11
2cos3 sin3 6cos3sin3
33
ttt
etete t
=+= +t
7 p/
ò m
Uf
()f t ￥ ?
fMD,
()ft
A
A?
τo
2τ 3τ
4τ
t
o
t
()ft
2
4
6
τ
3τ 5τ
(1) (2)
o
t
()ft
2
4
6
8
2
o
t
()ft
1
2
3
τ
2τ 3τ
4
(3) (4)
(1) ?m^?,
^?
ù1()tf 2τ ￥?
ùf
, B??
ù
=
- 10 -
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()
,0
,2
At
ft
At
τ
τ τ
≤ <
=
≤<
?
T
& () ()
2
2
0
1
st
s
A
f tftedt
e
τ
τ
=
∫
()
( )
2
2
0
1
1
st st
s
A
edt edt
e
ττ
τ
τ
=+?
∫∫
2
0
2
1
||
st st
tt
s
ee
A
ess
ττ
τ
τ
==
=?
2
2
1
1
s ss
s
Aeee
es
τ ττ
τ
+?
=?
()
2
2
1
tanh
12
s
s
e
AA
se s
τ
τ
sτ
=? =
(2) ?m^?
0
() 2[ ( ) ( 3 ) ( 5 ) ] 2 ( (2 1) )
k
f t ut ut ut ut kτ ττ
∞
=
=?+?+?+=?+
∑
"τ
?
H &Re( ) 0s > ()
(2 1)
2
0
22
1sin
s
ks
s
k
e
ft e
ss
τ
τ
τ
1
hsτ
∞
+
=
==?=
∑
(3) ?m^? () 8 () 2 ( 2)f t ut ut=?
H Re( ) 0s >
& ()
2
2
0
1822
(4 )
s
ks s
k
e
f te e
ssss
τ
∞
=
==?=
∑
(4)?m^?
0
()[()( )(2) ] (
k
)f tutut ut utkτ ττ
∞
=
=+?+?+=?
∑
"( ) 0s >? Re
H
&
()
0
1111
(1 coth )
12
ks
s
k
s
ft e
sses
τ
τ
2
τ
∞
=
==?=+
∑
5 ?
!
1
()f t
2
()f t (
@ ?
fMDi ? ?￥Hq
?
ì￥9é·
(1 c O
&
11
[()] ()f tFs= &
22
[()] ()f tFs= 5e
12
() ()f tft? ￥ ?
fMDB?i O
&
[]
j
12 12
j
1
() () ( ) ( )
2j
f tft FqFsqdq
β
β
π
+∞
∞
=?
∫
? cβ > Re( )scβ>+ b
￡ ?? (
@ ?
fMDi ? ? ￥Hq[# 9é·
( 1 ?e() ()tftf
21
,
0
c () ( )tftf
21
9B
?
@ ?
f MDi ￥ ? ?￥Hq O9é·
1 ? ?
f i ? ?￥ ￡
ü?.2
0
c
0
c>β
H
& () () () ()
12 12
0
st
f tft ftftedt
+∞
=
∫
0
Re cs +≥ β
i OBá
l ?,??
() ()
i
11
i
1
2i
qt
f tFq
β
β
π
+∞
∞
=
∫
edq
7 & () () () ()
12 12
0
st
f tft ftftedt
+∞
=
∫
() ()
i
12
0i
1
2i
qt st
Fqedqf te dt
β
β
π
+∞ + ∞
∞
=
∫∫
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() ()
i
()
12
i0
1
2i
sq
Fq f te dtdq
β
β
π
+∞ +∞
∞
=
∫∫
() ( )
i
12
i
1
2i
FqFs qdq
β
β
π
+∞
∞
=?
∫
p/
f
￥ ?
f
IMD
^ef
i¨
6B?ZEF[￡,
1 (),
1
22
as
sF
+
=
2 ()
()()
.
bsas
s
sF
=
3 ()
()()
2
bsas
cs
sF
++
+
=
4 ()
()
2
22
22
2
as
as
sF
+
+
=
5 ()
()
.
1
322
sas
sF
+
=
6 ()
()()bsass
sF
++
=
1
7 (),
1
44
as
sF
=
8 ()
()
2
2
1
12
+
=
ss
ss
sF
9 ()
()
.
1
1
22
=
ss
sF
10 ()
()()41
22
++
=
ss
s
sF
1 3E ()=tf & &()[]=
sF
1
+
22
1
1
as
a
a a
1
= &
a
at
as
a sin
22
1
=
+
3E ()
+
+
+
= i,Resi,Res
2222
a
as
e
a
as
e
tf
stst
a
at
a
e
a
e
atat
sin
i2i2
ii
=?=
3E ()=tf & =
+
22
1
1
as
&
+
i
1
i
1
i2
1
1
asasa
i2
1
a
=
&?
i
1
1
as
&
+
i
1
1
as
()
a
at
ee
a
atat
sin
i2
1
ii
=?=
2 3E ( )=tf & &()[]=
sF
1
()()
bsas
s
1
()() ()()
+
= b
bsas
se
a
bsas
se
stst
,Res,Res
()
btat
btat
beae
baab
be
ba
ae
=
+
=
1
3E ( )=tf & &()[]=
sF
1
()()
bsas
s
1
=&
bs
b
as
a
ba
1
1
ba?
=
1
&
a b
as
1
1
&
bs
1
1
()
btat
beae
ba
=
1
3 3E ( )=tf & ()[]sF
1?
( )
()()
( )
()()?
++
+
+
++
+
= b
bsas
ecs
a
bsas
ecs
stst
,Res,Res
22
()
()
bs
st
at
e
as
cs
ds
d
ab
eac
=
+
+
+
=
2
() ()
btbtat
e
ba
ca
te
ba
bc
e
ba
ac
+
+
=
22
3E &()=tf ( )[]=
sF
1
&
()()
++
+
2
1
bsas
cs
=&
() () ()
+
+
+
+
+
222
1
111
bs
ba
bc
bs
ba
ca
as
ba
ac
()
2
ba
ac
=
&
()
2
1
1
ba
ca
as?
+
+
&
ba
ac
bs?
+
+
1
1
&
()?
+
2
1
1
bs
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() ()
btbtat
te
ba
bc
e
ba
ca
e
ba
ac
+
+
=
22
4 3E & &()=tf ()[]=
sF
1
()?
+
+
2
22
22
1
2
as
as
=&
+
+
+
'
2222
1
2
1
2
3
as
s
as
a
a
a2
3
= &
2
1
22
1
+
+
as
a
&
+
'
22
1
as
s
attat
a
cos
2
1
sin
2
3
=
3E ()=tf & ()[]sF
1?
() ()?
+
+
+
+
+
= i,
2
Resi,
2
Res
2
22
22
2
22
22
ae
as
as
ae
as
as
stst
() ()
i
2
22
i
2
22
i
2
i
2
as
st
as
st
e
as
as
ds
d
e
as
as
ds
d
==
+
+
+
+
= tatatata
tee
a
tee
a
iiii
4
1
i4
3
4
1
i4
3
=
attat
a
cos
2
1
sin
2
3
=
5 3E ( )=tf &
()
2322
1
11
asas
=
+
&
()
+
223
1
11
asss
(
1
2
a
= &?
3
1
1
s
&
()
)
1
22
1
+
ass
∫
=
t
t
a
0
3
2
2
1
(
1
& )
1
22
1
dt
as
+
3
2
0
11 1
sin
22
t
ta
aa
=?
∫
td
()
3
24
11
1cos
2
ta
aa
=t
3E &()=tf
()
+
322
1
1
sas
() () ()
+
+
+
+
+
= i,Resi,Res0,Res
322322322
a
sas
e
a
sas
e
sas
e
ststst
() ()
3
i
3
i
0
222
2
ii2ii22
1
aa
e
aa
e
as
e
ds
d
tata
s
st
+
+
=
=
()at
a
t
a
cos1
1
2
1
4
2
2
=
6 3E ()=tf &
()()
+
bsass
1
1
=&
() ()
+
+
+?
bsbabasbaasab
111111
1
=
ab
1
&
()baas?
+
11
1
&
()babas?
1
+
1
1
&
+
bs
1
1
() ()
btat
e
bab
e
baaab
+=
111
3E &()=tf
()()
++
bsass
1
1
()() ()() ()()
++
+
++
+
++
= b
bsass
e
a
bsass
e
bsass
e
ststst
,Res,Res0,Res
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() ()
btat
e
bab
e
baaab
+=
111
3E ()=tf &
44
1
1
as
=&
+
+
2233
1
2
111
4
1
as
a
aasasa
() at
a
ee
a
atat
sin
2
1
4
1
33
=
()atat
a
sinsh
2
1
3
=
3E ()=tf &
44
1
1
as
+
+
+
= i,Resi,Res,Res,Res
44444444
a
as
e
a
as
e
a
as
e
a
as
e
stststst
() ()
3
i
3
i
33
i4i444 a
e
a
e
a
e
a
e
tataatst
++?=
()atat
a
sinsh
2
1
3
=
8 3E ()=tf &
()
=
+
2
2
1
1
12
ss
ss
&
()
+
+?
2
1
1
2
1
21
s
ss
=& +
s
1
1
& +
1
2
1
s
&
()
2
1
1
2
s
tt
tee 221 ++?=
3E ()=tf &
()
+
2
2
1
1
12
ss
ss
() ()
+
+
+
= 1,
1
12
Res0,
1
12
Res
2
2
2
2
stst
e
ss
ss
e
ss
ss
1
2
12
1
=
+
+?=
s
st
e
s
ss
ds
d
tt
tee 221 ++?=
9 3E ()=tf & &()[]=
sF
1
()
1
1
22
1
ss
=& ()tee
sss
tt
=
+
2
11
1
1
1
1
2
1
2
1
tsht?=
3E ()
() () ()
+
+
= 1,
1
Res1,
1
Res0,
1
Res
222222
ss
e
ss
e
ss
e
tf
ststst
tt
ee
s
e
ds
d
tt
s
st
=?+
=
=
sh
221
0
2
103E ( )=tf &
()()
++
41
22
1
ss
s
=&
+
+
413
1
22
1
s
s
s
s
(
3
1
= &?
+
1
2
1
s
s
& ()tt
s
s
2coscos
3
1
)
4
2
1
=
+
3E &=)(tf
()()
++
41
22
1
ss
s
()() ()() ()() ()()
++
+
++
+
++
+
++
= i2,
41
Resi2,
41
Resi,
41
Resi,
41
Res
22222222
ss
se
ss
se
ss
se
ss
se
stststst
() ()()()()i41i4
i2
i41i4
i2
4ii2
i
4ii2
i
2
i2
2
i2
2
i
2
i
+
+
+
+
+?
+
+
=
tttt
eeee
6666
i2i2ii tttt
eeee
+++= ()tt 2coscos
3
1
=
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3. p/
f
￥ ?
f
IMD,
1 ()
()
2
2
4
1
+
=
s
sF
2 ()
2+
=
s
s
sF
3 ()
()()21
12
++
+
=
sss
s
sF
4 ()
45
1
24
++
=
ss
sF
5 ()
569
1
2
++
+
=
ss
s
sF
6 ()
2
2
1
ln
s
s
sF
=
7 ()
()
.
54
2
2
2
++
+
=
ss
s
sF
8 ()
()
.
22
1
2
2
++
=
ss
sF
9 ()
()
2
2
2
134
44
++
++
=
ss
ss
sF
10 (),
6116
52
23
2
+++
++
=
sss
ss
sF
11 ()
463
3
23
+++
+
=
sss
s
sF
12 ()
()()
3
2
31
332
++
++
=
ss
ss
sF
13 ()
2
2
1
s
e
sF
s?
+
=
3
1 &
()
=
+
2
2
1
4
1
s
&
′?
+
+
+
48
1
4
2
16
1
22
1
s
s
s 16
1
= &
8
1
4
2
2
1
+
+
s
&
′?
+
4
2
1
s
s
ttt 2cos
8
1
2sin
16
1
=
2 &()=tf =
+
2
1
s
s
&
+
2
2
1
1
s
=& []?
1
1
& ()
t
et
s
21
2
2
2
=
+
δ
3 &()=tf
()()
++
+
21
12
1
sss
s ()
()()
( )
()()
()
()()
++
+
+
++
+
+
++
+
= 2,
21
12
Res1,
21
12
Res0,
21
12
Res
sss
es
sss
es
sss
es
ststst
()
()()
()
()
( )
()1
12
lim
2
12
lim
21
12
lim
210
+
+
+
+
+
+
++
+
=
→?→→
ss
es
ss
es
ss
es
st
s
st
s
st
s
tt
ee
2
2
3
2
1
+=
4 &()=tf =
++
45
1
24
1
ss
&
()()
=&
1
22
11 12
3164ss
+ +
++
41
1
22
1
ss
1
3
= &
6
1
1
1
2
1
+
s
&
+
4
2
2
1
s
tt 2sin
6
1
sin
3
1
=
5 &()=tf =
++
+
569
1
2
1
ss
s
&
+?
+
+
4
3
1
9
1
2
1
s
s
9
1
= &
+?
+
+
+?
+
+
2222
1
3
2
3
1
3
2
3
2
3
1
3
1
ss
s
+?=
tt
etet
3
1
3
1
3
2
sin
3
2
cos
9
1
t
ett
3
1
3
2
cos
3
2
sin
9
1
+=
6 &()=tf
ts
s 11
ln
2
2
1
=
&
1?
′
2
2
1
ln
s
s
t
1
= &
tss
s 12
1
2
2
1
=
&
+
+
sss
2
1
1
1
1
1
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()()t
t
ee
t
tt
ch1
2
2
1
=?+?=
&()=tf
()
=
++
+
2
2
1
54
2
ss
s
&
()[]
++
+
2
2
1
12
2
s
s
=&
() 2
1
12
1
2
1
2
1
=
′
++
s
&
()
′
++
12
1
2
1
s
()t=
2
1
&
()
tteet
t
s
tt
sin
2
1
sin
212
1
22
2
1
=?=
++
&()=tf
()
=
++
2
2
1
22
1
ss
&
()[]
++
2
2
1
11
1
s
2
1
= &
() ()?
′
++
+
+
++
11
1
11
1
22
1
s
s
s
(
2
1
= &
()
+
++
11
1
2
1
s
&
()
′
++
+
11
1
2
1
s
s
tte
t
=
sin(
2
1
&
()
++
+
11
1
2
1
s
s
()ttete
tt
cossin
2
1
= ()ttte
t
cossin
2
1
=
&()=tf
()
=
++
++
2
2
2
1
134
44
ss
ss
&
()
()[]
++
+
2
2
2
1
92
2
s
s
=&
()
()[]
++
++
2
2
2
1
92
9
92
1
s
s
=&
() ()
′
++
+
++
2222
1
32
2
2
1
32
3
6
1
s
s
s
tte
t
2
1
3sin
6
1
2
+=
&
()
++
+
22
1
32
2
s
s
ttete
tt
3cos
2
1
3sin
6
1
22
+= ()ttte
t
3cos33sin
6
1
2
+=
10 &()=tf =
+++
++
6116
52
23
2
1
sss
ss
&
()()()
+++
++
321
52
2
1
sss
ss
()
()()()
( )
()()()
( )
()()()
+++
++
+
+++
++
+
+++
++
= 3,
321
52
Res2,
321
52
Res1,
321
52
Res
222
sss
ess
sss
ess
sss
ess
ststst
()() ()() ()()
st
ss
st
s
e
ss
ss
ss
ss
e
ss
ss
21
52
lim
31
52
lim
32
52
lim
2
3
2
2
2
1
++
++
+
++
++
+
++
++
=
→?→?→
ttt
eee
32
10113
+?=
11 &()=tf =
+++
+
463
3
23
1
sss
s
&
()()
+++
+
131
3
3
1
ss
s
=&
() () ()
+++
+
++
1]31[
2
31
1
22
1
sss
=&
() ()
++
+
+
+
++ 31
1
3
2
1
1
3
2
31
1
22
1
s
s
ss
3
1
= &
()()
3
2
31
3
2
2
1
+
++
&
s
3
2
1
1
1
+
s
&
()()
++
+
2
2
1
31
1
s
s
teete
ttt
3cos
3
2
3
2
3sin
3
1
+= ( )tte
t
3sin33cos22
3
1
+?=
(12) &()=tf
()()
++
++
3
2
1
31
332
ss
ss
=&
() ()
+
+
+
+
+
32
1
3
1
6
3
1
2
3
3
1
4
1
1
1
4
1
ssss
4
1
= &
4
1
1
1
1
+
s
&
2
3
3
1
1
+
+
s
&
()
6
3
1
2
1
+
s
&
()
+
3
1
3
1
s
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tttt
etteee
3233
2
3
2
3
4
1
4
1
+?=
(13) &()=tf =
+
2
2
1
1
s
e
s
& +
2
1
1
s
&
2
2
1
s
e
s
()()
()
≥?
<≤
=+=
2,12
20,
22
tt
tt
tutt
5
1
p/
b
1
2.11? tt?
3
4 (.,* 1??
nmtt
nm
)
t
)
t
et?
5
6,cossin tt?,sin*sin ktkt
7,
8 sinh *sinht *sinh,at at
9
10()(.*u tfat? ( ) ( ).* tfat?δ
3 ? l,
() () () ( )
∫
=
t
dtfftftf
0
2121
* τττ
1
∫
=?=
t
td
0
111*1 τ
2 t ()
∫∫∫
=?=
ttt
ddtdtt
000
2
* τττττττ
333
6
1
3
1
2
1
ttt =?=
3 ()
∫∫
∑
=?=
=
ι
ττττττ
00
0
)1(*
t
n
k
kknk
n
kmnmnm
dtCdttt
() ()
∑
∫
∑
==
+++?
++
=?=
n
k
t
n
k
nmk
n
kkmknk
n
k
t
km
CdtC
0
0
0
1
1
1
11 ττ
()
()()( )
∑
=
++++
++++
=
++
=
n
k
nmk
n
k
nm
t
nmmm
n
C
km
t
0
11
1...21
!
1
1
()
1
!!
1!
mn
mn
t
mn
++
=
++
4 =
∫∫
==
tt
ttt
deedeet
00
* ττττ
ττ
1
00
|
=
+?
∫
tedeee
t
tt
t
ττ
ττ
5 () ()
∫∫∫
+=?=?
tt
dttddttt
000
2sin
2
1
sin
2
1
cossincossin ττττττ
() ttttt
t
sin
2
1
2cos
4
1
sin
2
1
|
0
==
=τ
τ
6 ()
∫
=
t
dtkkktkt
0
sinsinsin*sin τττ ()
∫∫
=
tt
ktddktk
00
cos
2
1
2cos
2
1
τττ
kttkt
k
cos
2
1
sin
2
1
=
7 ()
( )
00
*sinh sinh
2
tt
tt
ee
tt td d
ττ
τ ττ τ τ
=?=
∫∫ ∫∫
=
tt
tt
de
e
de
e
00
22
ττττ
ττ
() ()
+?=
||
00
1
2
1
2
t
t
t
t
e
e
e
e
ττ
ττ
sinh tt=?
8
()
0
sinh sinh sinh sinh
t
at at a a t dτ ττ?=?
∫
( )()
∫
=
t
tataaa
d
eeee
0
22
τ
ττττ
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+=
∫∫∫∫
t
at
t
aat
t
aat
t
at
dedeedeede
00
2
0
2
0
4
1
ττττ
ττ
11
cosh sinh
22
tat
a
=?at
9 ()() ()()
∫
=?
t
dtfautfatu
0
* τττ
? at <
H
( ) 0=?au τ
N
H ()()0* =? tfatu
?
H ta ≤≤0
()() ()() ()()
∫∫
+=?
at
a
dtfaudafautfatu
0
* ττττττ
()
∫
=
t
a
dtf ττ
yN
()()
()
≤≤?
<
=?
∫
tadtf
at
tfatu
t
a
0,
,0
*
ττ
10 ()() ()()
∫
=?
t
dtfatfat
0
* τττδδ
? at <
H ()0=?aτδ,N
H
( ) ( ) 0= tfatδ
?
H ta ≤≤0
()() ()() ()() ()()
∫∫∫
+
+
++=?
aa
a
t
a
dtfadtfadtfatfat
0
* τττδτττδτττδδ
()()
∫
+
++=
a
a
dtfa 00 τττδ ()()aft dδ ττ
+∞
∞
=
∫
τ
)
() (atftf
a
=?=
=τ
τ
yN ()()
() ta
at
atf
tfat
≤≤
<
=?
0,
,0
*δ
2 ?¨ ? ?￡
ü &
0
()
()
t
Fs
ftdt
s
=
∫
b
￡
() 1
()
Fs
Fs
ss
=?=&[(
00
)*()] ()( ) ()
tt
f tut f ut d ftdtτττ=?=
∫∫
3 ?¨ ? ?￡
ü &
()
at
a
t
as
s
sin
2
2
22
1
=
+
b
￡
! () ()
222221
1
,
as
a
a
sF
as
s
sF
+
=
+
=
?
^ & ()=tf
1
()[] atsF cos
1
1
=
()=tf
2
& ()[]
a
at
sF
sin
2
1
=
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PH &=
()
=
+
2
22
1
as
s
& () ( )[]sFsF
21
1
() () ()[]τττ dtaa
a
tftf
t
∫
==
0
21
sincos
1
*
()[]ττ aataat
a
t
∫
=
0
2sinsin
2
1
()
=
=
|
0
2cos
2
1
sin
2
1
t
ata
a
att
a
τ
τ == att
a
sin
2
1
·H
4 ?¨ ? ?￡
ü
&
()
∫
=
t
t
dee
ss
0
1
22
1
1
τ
π
τ
i p &,
1
1
1
+
ss
￡
! () (),
1
1
,
1
21
==
s
sF
s
sF ?
^
()=tf
1
& ( )[]=
sF
1
1
&
tt
s
111
2
1
11
2
1
1
=?
Γ
=
π
()=tf
2
& ( )[]=
sF
2
1
&
t
e
s
=
1
1
1
PH &=
()
=
1
1
1
ss
& ( ) ( )[]sFsF
21
1
() () () ( )τττ dtfftftf
t
==
∫
2
0
121
*
∫∫
=?=
tt
tt
deede
00
1111
τ
τπ
τ
τπ
ττ
∫
==
=
t
xt
x
dxee
0
2
2
2
π
τ
·H
! ()
()
,
1
1
=
ss
sF -
X￡ & ()[]
∫
=
t
t
deesF
0
1
22
τ
π
τ
?
& =
+
1
1
1
ss
& ( )[ ]
t
esF
=+1
1
& ()[] τ
π
τ
desF
t
∫
=
0
1
22
￡
ü
@FE￥s
￥
p
123 1213
()*[ () ()] ()* () ()* ()f tftft ftftftft+ =+
￡
123 12 3
0
()*[ () ()] ( )[ ( ) ( )]
t
f tftft f ft ft dτ ττ+=?+?
∫
τ
12 13 1 2 1 3
00
() ( ) () ( ) ()* () ()* ()
tt
f ft d f ft d ftft ftftττττττ=?+?=+
∫∫
￡
ü
@2
p
123 123
()*[ ()* ()] [ ()* ()]* ()f t ftft ftft ft=
￡
123 1 2 3
00
()*[ ()* ()] ( ) ( ) ( )
tts
f tftft fs fts fddsτ ττ
=
∫∫
312 12
00
() () ( ) [ ()* ()]* ()
tt
3
f dfsftsdsftftf
τ
ττ τ
=
∫∫
t
5?
p/
± sZ?
T#Z?F￥3,
1
() ( )'' 4 ' 3,0 ' 0 1
t
yyye y y
++= = =,
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2,''' 3 '' 3 ' 1,(0) '(0) ''(0) 0yyyy y y y+++= = = =
3 ( ) ( )'' 3 ' 2 ( 1),0 0,' 0 1yyyut y y++=? = =,
4 ( ) ( )'' 4sin 5cos2,0 1,' 0 2yy t t y y?= + =? =?,
5 ( ) ( )'' 2 ' 2 2 cos,0 ' 0 0
t
yyyet y y?+= = =
6
( ) ( )
1212
'' 4 ' 5 ( ),0,' 0,(,)yyyFt y cy ccc++= = = 1è
7 () ( )
2
''' ',0 ' 0 ''(0) 0
t
yye y y y+= = = =
8 ( ) ( ) ( )''' 3 '' 3 ' 6,0 ' 0 '' 0 0.
t
yyyye y y y
+++= = = =
9 ()
(4)
2 '' 0,0 '(0) '''(0) 0,''(0) 1.yyy yy y y++= = = = =
10
( )
() ( ) ( ) ( )
4
''' cos,0 ' 0 ''' 0 0,'' 0yy t y y y y+= = = = =c
1.
è
11 () ()
',
00
3'22,
t
t
xxye
xy
xy y e
+?=
= =
+? =
12
()
() () () ()
'2',
0'0 0'0
'' '' 0,
yzFt
yy zz
yzz
=
0.= ===
+=
13
()()( ) ( )
( )( ) () ()
2'' '9 ' '3 0,0 '0 1,
2'' '7 ' '5 0,0 '0 0.
xx x yy y x x
xx x yy y y y
+? ++ = = =?
+++ = = =
14
() () () () () ()
'' 0,
'' 0,0 1,0 0 ' 0 ' 0 ' 0 0.
'' 0,
xxyz
xy yz x y z x y z
xyz z
++=?
+?+= = = = = = =
++?=
3
1Z ?
H | ?
fMDi I
n?
SHq¤
() () ()
2
1
14 43
1
sY s s sY s Y s
s
+?+ =
+
? ?a3 ( )Ys¤
()
()()
()()
2
15
13
31
s
Ys
ss
ss
+
=+
+ +
++
() 1
1
4
7
3
1
4
3
1
1
2
1
2
+
+
+
+
=
sss
| ?
f
IMD¤ 31
()yt=& ( )
1
Ys
2
1
= &
() 4
3
1
1
2
1
+
s
&
4
7
3
1
1
+
+
s
&
+
1
1
1
s
3
137
244
ttt
te e e
=?+ ()
3
1
27 3
4
tt
tee
=+?
2Z?
H | ?
fMDi I
n?
SHq¤
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() () ()
32
1
33 ()sY s sY s sY s Y s
s
+ ++=
? ?a3 ( )Ys¤
()
32
11
(331)(1)
Ys
ss s s ss
==
+++ +
3
23
11 1 1
1( 1) ( 1)ss s s
=
++ +
| ?
f
IMD¤ 31
()yt=& &()
1
Ys
=
1
1
s
&
1
1
1s
+
&
()
1
2
1
1s
+
&
1
3
1
(1)s
+
22
11(
22
tt t
tt
ete e te
= =? ++)
t?
3Z?
H | ?
fMDi} ?
SHq¤
()
2
1
13()2()
s
sY s Y s Y s e
s
+ + =
3 ¤ (),Ys
()
1
(1)(2) (1)(2
s
e
Ys
ss sss
=+
)+ +++
1111 1
1 2 2 1 2( 2)
s
e
ss ss s
=?+?+
++ + +
| ?
f
IMD¤
()yt
( )yt=& ()
1
Ys
2 ( 1) 2( 1)
11
(1)
22
tt t t
ee e e ut
=?+? + +?
4Z?
H | ?
fMDi} ?
SHq¤
() ()
2
22
45
2
14
s
sY s s Y s
ss
++? = +
+ +
? ?a¤
()
()()()()
222 22
45
111 14
ss
Ys
sss ss
+
=+?
41
2
22
+
+
=
s
s
s
+?+
| ?
f
IMD¤
()yt=& &()
1
2Ys
=
+
1
1
2
1
s
&
+
4
2
1
s
s
tt 2cossin2=
5Z?
H | ?
fMD O} ?
SHq¤
() () ()
2
2
1
222
(1)
s
sYs sYs Ys
s 1
+=
+
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3
()
:Ys
()
22
2( 1)
(( 1) 1)
s
Ys
s
=
+
| ?
f
IMD¤?eZ?3
()
yt=& ()
1
Ys
=&
1
2
1
'si
(1)1
t
te t
s
=
+
n
6Z?
H | ?
fMD¤
() ()Fs ft1 ￥ ?
fMD
() ( ) ( )
2
12 1
445sY s cs c sY s c Y s F s+?+ =()
? ?¤
()
( )
12
22
4
45 45
Fs
cs c c
Ys
ss ss
++
=+
1
+ +++
()
() () ()12
2
12
2
12
2
12
2
1
2
++
+
+
++
+
+
++
=
s
cc
s
s
c
s
sF
| ?
f
IMDi ?¨ ? ?¤
()yt=&
()
()?
++
12
1
2
1
s
sF
1
c+ &
()
()
12
2
1
2
12
2
cc
s
s
++
++
+
&
()?
++
12
1
2
1
s
() ( )
22 2
121
*sin cos 2 sin
tt t
Ft e t ce t c c e t
=+
() ( )
22
121
*sin cos 2sin
tt
Ft e t e c t c c t
+
7Z?
H | ?
fMD¤
() ()
3
1
2
sY s sY s
s
+=
()
()()
2
1
21
Ys
sss
=
+
?ss
T
()()
22
1
2121
ABCsD
ssssss
+
=++
+?+
¨??"
E¤
112
,,,
10 2 5 5
AB CD==?==?
1
yN
()yt=& " &()
1
Ys
()()
1
2
1
21sss
+
1
10
= &
1
11
22s
&
1
12
5s
+
&
5
1
1
2
1
+
s
s
&
+
1
1
2
1
s
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2
112 1
cos sin
10 2 5 5
t
et=?+?t
8Z?
H | ?
fMD O} ?
SHq¤
() () ()
32
1
3()3 6
1
sY s sY s sY s Y s
s
+++=
+
3 ():Ys
()
4
6
(1)
Ys
s
=
| ?
f
IMD¤?eZ?3
()yt=& ( )
1
Ys
=&
13
1
'''
1
t
te
s
=
9Z?
H | ?
fMD O} ?
SHq¤
( ) ( )
42
2()sY s s sY s Y s 0? ++=
3
():Ys
()
22
(1)
s
Ys
s
=
+
| ?
f
IMD¤?eZ?3
( )yt=& ()
1
Ys
=&
1
2
11 1
'si
212
tt
s
=
+
n
10Z?
H | ?
fMD,¤
() ()
43
2
1
s
sY s cs sY s c
s
+?=
+
3 ():Ys
()
()()
3 22
1
11
c
Ys
s ss s
=+
+ +
&
()() ()() ()()
++
+
++
=
++
1,
11
Res0,
11
Res
11
1
222222
1
sss
e
sss
e
sss
stst
+
()() ()()
++
+
++
i,
11
Resi,
11
Res
2222
sss
e
sss
e
stst
()() () ()() ()()i1
lim
i1
lim
1
lim
11
lim
2
i
2
i
22
1
2
0
+
+
++
+
+
+′
++
=
→→?→→
sss
e
sss
e
ss
e
ss
e
st
s
st
s
st
s
st
s
()ttet
t
sincos
2
1
2
1
1?++?=
yNeZ?￥31
( )yt=& ()
1
Ys
c
= &
1
3
1
s
+ &
()()
++
11
1
22
1
sss
- 23 -
我要答案网 www.51daan.net
本文件是从网上收集，严禁用于商业用途！
()
2
11
1cos
222
t
c
tt e t t
=+?+ +?in
(11)Z?F
H | ?
fMDi} ?
SHq,¤
() () ()
() () ()
=+
=?+?
1
1
2213
1
1
1
s
sYssYsX
s
sYsXssX
? ?a,¤
( ) () ()
() ( )()
+
=?+
=?+
1
1
23
1
1
s
s
sYssX
s
s
sYsXs
3-¤
()
()
=
=
1
1
1
1
s
sY
s
sX
| ?
f
IMD¤?eZ?F￥31
( )
()
t
t
x te
yt e
=
=
(12)Z?F
H | ?
fMDi} ?
SHq,
!
( )
Ys= & () ( ),yt Zs=
& ( ) ( ),zt Fs
=& ( ),Ft
¤
( ) ( ) ( )
() () ()
=+?
=?
0
2
22
sZsZssYs
sFssZssY
? ?a,3-¤
()
( ) ( )
()
()
+
=
+
=
1
1
2
2
2
s
ssF
sZ
s
ssF
s
sF
sY
| ?
f
IMD¤?eZ?F￥31
()=ty &
()[]& () 2
1
1
sF
s
& ()
+
sF
s
s
1
2
1
sY
1
=
( ) ( ) ( )(1* 2cos * 1 2cos *Ft t Ft t Ft=? =? )
()=tz & &()[]?=
sZ
1
()
+
sF
s
s
1
2
1
( )cos *tFt=?
'31
( ) ( ) ( )
() ()
12cos *
cos *
yt t Ft
zt t Ft
=
=?
(13)Z?F?
?Z?
H | ?
fMD,¤
- 24 -
我要答案网 www.51daan.net
本文件是从网上收集，严禁用于商业用途！
()( ) ( ) ( )
()() ()()
+=+++
+=++?+?
ssYsssXss
ssYsssXss
23572
21392
22
22
? ?¤
() ()
() ()
=+
+
+
=?
1
1
4
22
2
2
s
sYsX
s
s
sYsX
3-¤
()
()?
+
+
+
=
+
+
+
+
=
4
2
3
1
43
2
1
1
3
2
4
2
3
1
43
2
1
1
3
1
22
22
ss
s
s
sY
ss
s
s
sX
| ?
f
IMD¤? 31
()
()
12 1
cos 2 sin 2
33 3
22 1
cos 2 sin 2
33 3
t
t
x te t
yt e t t
=+ +
=
t
(14)Z?F?òZ?
H | ?
fMD,¤
()( ) ( )
() ()() ()
() () ()()
=?++
=+?+
=++?
01
01
)(1
2
2
2
sZssYsX
sZsYssX
ssZsYsXs
?a
?Z?¤ () () () ( )sYssXsZsY
2
==,} ??B?Z?3¤
()
()()
() ()
+
+
==
+
+
=
+
=
13
1
23
1
13
1
23
2
21
22
2222
3
s
s
s
s
sZsY
s
s
s
s
ss
s
sX
| ?
f
IMD¤ 31
()
() ()
21
cosh 2 cos
33
11
cosh 2 cos
33
xt t t
yt zt t t
=+
==? +
2 p3s Z?
() () ( )
0
sin,
t
f tat f t dτ ττ=+?
∫
3 |s Z? | ?
fMDi ?¨ ? ?
! ( )=sY & ( )[ ]ty
()Fs=&[]+at & () ( )
0
sin
t
f tdτ ττ
∫
()
22
1
1
a
Fs
ss
=+?
+
? ?a¤
()
24
11
Fs a
ss
=+
| ?
f
IMD¤?eZ?￥3
- 25 -
我要答案网 www.51daan.net
本文件是从网上收集，严禁用于商业用途！
()
3
1
6
f tat t
=+
3.
! e)é
1 m ￥B é?
H 0t = xZ_
s?
? ( )tkδ ￥T¨ ? k 1è
L?é?￥
1
, p ?
p,
3
! t
H Yé?1 x à?Z_
? ( )tx )?5ié??￥
§W
1,F
1
O
[é?￥?
p
@±sZ?
()tx'
()tx′′ () () 00'0 == xx
() ( ) ( ) ( ) 00'0,'' === xxtktmx δ
13
￥±s|Z?
H | ?
fMDi} ?
SHq¤
( ),
2
ksXms =
'
()
2
1
sm
k
sX?=
| ?
f
IMD¤é?￥?
p1
()=tx & ()[]
m
k
sX =
1
&,
1
2
1
t
m
k
s
=
!μ ?m
U￥ 3 -1 óè
^
0
tt=
H|è
^¤
°
@è÷ & pè
^ ?￥è
@ ()it
?m
U ￥è
^
H¤ ?°
@è÷ & pí
^?è
@ 0t = ()it
6.
"d￥,?f
(),
1
K
Gs
Ts
=
+
p? ? ( ) tAtx ωsin=
H￥"dY? y(t),
3 ?"d ￥.?f
()
1
K
Gs
Ts
=
+
^?"d￥
Y?f
()gt=& ( )
1
Gs
=
&
1
1
1
t
T
KK
e
Ts T
=
+
?
^? ? () tAtx ωsin=
H￥"dY?1
() () ( )()()**yt gt xt xt gt==
00
sin sin
tt
tt
TT
KAK
Aede e
TT
ττ
T
dωττ ωτ
==?
∫∫
τ
=
2
2
0
11
sin cos
1
t
t
TT
AK
ee
T
τ
τ
τ
ωτ ω ωτ
ω
=
=
+
()
22
sin cos
1
t
T
AK
tT t Te
T
ωωω ω
ω
=?+
+
()
22
22
sin arctan
1
1
t
T
AK AKT
tT
T
T
ω
ωω
ω
ω
e
=?+
+
+
- 26 -
