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( µω)
n′+ 1 n+ 1 iρ
{ ( ) ( ) [ ][ ]
2 2
* k sen ϕ * 2
sθ
iθ
= ′ − − − π ′ −τ ′ τ + π
2 2 n n n n n n n n
∑
H H E E i i e b a
2ρ
n′+ 1 n+
1
() i ( i) [ n′ n′
][ bn n an n]}
− − π +τ τ + π
2 2
* ⎛ k ⎞ sen ϕ * n+ 1 n′
+ 1
* *
sθ
sθ
=
2 n n′ ( − ) ( ) [ nτ n + nπn]
⎡
n′ τ n′ + n′ πn′
∑
H H ⎜ ⎟ E E i i b a
⎣
b a ⎤
µω ρ
⎦
⎝ ⎠
2 2
* k cos ϕ * n ′
{( ) + 1 n
() + 1
′ − 2 i ρ
* *
iϕ
sϕ
= [ π −τ ] ⎡
′ π ′ − ′ τ
2 2 n n n n n n n n′
H H E E i i e
2ρ
⎣
b a
( µω)
∑
n
( ) + 1 n′
( ) + 1 * *
i i [ n n] ⎡bn ′ n′ an′ n′
⎤}
− − π +τ
⎣
π + τ
⎦
⎤
⎦
( µω)
n
{( ) + 1 n′
( ) + 1
[ ][ ]
2 2
* k cos ϕ *
sϕ
iϕ
= ′ − π + τ π ′ −τ
2 2 n n n n n n n n′
∑
H H E E i i b a
2ρ
n
( ) + 1 n′
( ) + 1
i i [ bn n an n][ n′ n′
]}
− − π + τ π −τ
2 2
* ⎛ k ⎞ cos ϕ * n n
* * * *
sϕ
sϕ
=
2 n n′ − nπ n + nτn n′ π n′ + n′ τn′
∑
+ 1 ′ + 1
{( ) ( ) [ ] ⎡
⎤}
H H ⎜ ⎟ E E i i b a
⎣
b a
µω ρ
⎦
⎝ ⎠
então dessa forma, ficamos com:
n′+ 1 n+ 1 iρ
{{ ( ) ( ) [ ][ ]}
2π
2
* * * π k
2
∫ ( HH θ θ HH ϕ ϕ)
d ∑ EE n n′ i i e
2 2
n′ n′
bn n an n bn n an n
2ρ 0
( µω)
+ ϕ= − − − π −τ τ + π − π − τ −
n
{() + 1 n′
() + 1 − 2 i ρ
* * * *
i i e [ n n]
⎡bn ′ n′ an′ n′ bn′ n′ an′ n′
⎤}
π −τ
⎣
τ + π − π − τ
⎦
−
n
{( ) + 1 n′
( ) + 1
i i [ n′ n′
][ bn n an n bn n an n]
}
− π +τ π + τ + τ + π −
n
() + 1 n′
( ) + 1 * * * *
{ i −i [ π n +τn]
⎡bn ′ π n′ + an′ τ n′
+ bn′ n′ an′ n′
⎤}
⎣
τ + π
⎦
+
n
{ ( ) + 1 n′
( ) + 1 * * * *
2 −i i {[ bnτ n+ anπn]
⎡
′ τ ′ + ′ π ′
⎤} + { ⎡
′ π ′ + ′ τ ′
⎤
⎣
bn n an n ⎦ ⎣
bn n an n ⎦[ bnπ n+ anτn]
}}
tal que as integrais ficam,
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