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Use the boundary condition
u
(1
,θ
)=
∞
X
n
=1
a
n
cos (2
n
−
1)
θ
=
f
(
θ
)
This is a Fourier cosine series of
f
(
θ
), thus the coeﬃcients are given by
a
n
=
2
π/
2
Z
π/
2
0
f
(
θ
)cos(2
n
−
1)
θdθ
Remark: Since there is no constant term in this Fourier cosine
series, we should have
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This note was uploaded on 12/22/2011 for the course MAP 2302 taught by Professor Bell,d during the Fall '08 term at UNF.
 Fall '08
 BELL,D

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