Slide 7
Slide 7 text
ݪཧɿෳԁܗεϐʔΧΞϨΠΛ༻͍ͨ࣍ݩԻ੍ޚ
֎෦Իͷٿ໘ௐల։
ෳԁܗΞϨΠʹΑΔԻ
ෳԁܗΞϨΠͷۦಈ৴߸ɿٿ໘ௐεϖΫτϧͷۮͷΈ
ैདྷ๏ɿݪͷԻݯʹΑΔԻΛ૬ࡴ͢Δํࣜ
ݪʹஔͨ͠ԻݯʹΑΔԻ
ෳԁܗΞϨΠͷۦಈ৴߸
1SFWJPVTGPSNVMBUJPO
S(r, ✓, ) =
1
X
n=0
n
X
m= n
ˇ
Bm
n
hn(kr)Y m
n
(✓, )
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
ˇ
Bm
n
+ 2⇡jk
Q
X
q=1
˚
Dm,qjn(krq)P|m|
n
(0) = 0
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
˚
D
even
m
=
1
2⇡jk
⇣
UT
|m|
U|m|
⌘ 1
UT
|m|
ˇ
Beven
m
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
S0(r, ✓, ) = D0G(r, r0 = 0) = D0
0
X
n=0
n
X
m= n
jk
p
4⇡
hn(kr)Y m
n
(✓, ) = D0
ejkr
4⇡r
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
ˇ
Beven
0
=
jk
p
4⇡
, 0, · · · , 0
T
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
˚
D0 = D =
1
8⇡2
⇣
UT
0
U0
⌘ 1
J0
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
J0 = [j0(kr1), j0(kr2), · · · , j0(krQ)]T
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
ɿ࣮
ɿ௨ৗෳૉ
S1(r, ✓, ) =
Q
X
q=1
Z 2⇡
0
D(rq, 0) G(r, rq)|
✓0=0
d 0 =
1
X
n=0
n
X
m= n
2⇡jk
Q
X
q=1
˚
Dm,q
P|m|
n
(0)jn(krq)hn(kr)Y m
n
(✓, )
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