Faça o download da tese completa na versão em PDF - A Biblioteca ...

⎧ τn
n+ 1 iρ n+
1 −iρ n iρ n −iρ
⎫
Eiϕ
= ∑ En⎨−senϕ ⎡ ( − i) e + ( i) e ⎤ + isenϕπn
⎡ ( − i) e + ( i)
e ⎤ ⎬=
⎩ 2ρ ⎣ ⎦ ⎣ ⎦ ⎭
senϕ
∑
n+ 1 iρ n+ 1 −iρ n+ 1 iρ n+
1 −iρ
E ⎡
n
−( −i) e τn −( i) e τn −( −i) e π
n
+ ( i)
e π ⎤
n
=
2ρ ⎣
⎦
n+ {() 1 −ρ i
n+
[ ] ( ) 1 iρ
π −τ − − [ π +τ ]}
senϕ
∑ E i e i e
2ρ n n n n n
cosϕ
n iρ
n+
1 iρ
Es θ
= ∑ En{ ianτn( −i) e −bn( −i)
π
ne
} =
ρ
+
{( ) 1 ρ
[ ]}
cosϕ
n i
= ∑ E −i e a τ + b π
ρ
n n n n n
senϕ
n iρ
n+
1 iρ
Es ϕ
= ∑ En{ −ianπn( − i) e + bn( −i)
τ
ne
} =
ρ
+
{( ) 1 ρ
[ ]}
senϕ
n i
= ∑ E −i e a π + b τ
ρ
n n n n n
⎛cos
2ρ
assim, ficamos com as combinações:
2
⎛cos
ϕ ⎞
⎜ 2 ⎟
⎝ 2ρ
⎠
ϕ ⎞
n+ 1
{() −ρ i
n+
1
iρ
[ ] ( ) [ ] }
* ⎡cosϕ
⎤
EE
iθ
sθ
= ⎢ ∑ En i e πn −τ
n
+ −i π
n
+τ
n
e ⎥×
⎣ 2ρ
⎦
∑
⎡cosϕ
⎢
⎣ ρ
∑
n′ { () −ρ i
n′+
1 −ρ i
() }
* * *
⎤
En′ −ian′ τn′ i e −bn′ τn′ i π
n′
e ⎥ =
⎦
n
{ () + 1 n′ () + 1 − iρ n′
[ ] () + 1 n
() + 1 − iρ
[ ]
EE −a i i e τ π −τ −b i i e π π −τ −
* * 2 * 2
n n′ n′ n′ n n n′ n′
n n
n
( ) + 1 * n′ ( ) + 1 n ′
[ ] () + 1 * n
( ) + 1
i an′ i
n′ n n
i bn′ i
n′
[ n n]}
− τ π +τ − − π π +τ =
n+ 1 n′ + 1 − iρ
n′
+ 1 n+
1
{ −() () [ π −τ ] ⎡ τ + π ⎤−() ( − ) [ π +τ ] ⎡ τ + π ⎤}
2
⎜
* 2 * * * *
2 ⎟ EE
n n′ i i e
n n ⎣an′ n′ bn′ n′ ⎦ i i
n n ⎣an′ n′ bn′ n′
⎦
∑ ⎝ ⎠
* ⎡cosϕ
n
i
( ) ρ
( )
+ 1 n+
1 iρ
{ }
⎤
Es θEiθ
= ⎢ ∑ En − −i anτne −bn −i π
ne
⎥×
⎣ ρ
⎦
⎡cosϕ
⎢
⎣ 2ρ
∑
n′ {( ) + 1 iρ
n′
[ ] () + 1
−iρ
[ ] }
*
⎤
En′ −i e πn′ −τ
n′ + i π
n′ +τ
n′
e ⎥ =
⎦
231