文档介绍:జǔ ʓސ 2+1
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1 a + (a cosnx + b sin nx)
2 0 ∑n=1 n n
ඪ1cos(nx) sin(nx)
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ππ
cos nx cos mxdx = 0 sin nx mxdx 0sin n ≠= m
∫−π∫−π
π
cos nxsin mxdx = 0
∫−π
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2
f(x ) 34Ӎ156
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1 π 1 π
an = f (x)cos nxdx, bn = f (x)sin nxdx
π∫−ππ∫−π
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an = 0, bn = f ( )sin nxdxx
π∫0
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2 π
an = f (x) cos nxdx, bn = 0
π∫0
ab
( 2)
32
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Sgn(x) (4/ ) (si n x + sin3x/3 + sin5x/5 + …)
X 2 (sin x − sin2x/2 + sin3x/3 − sin4x/4 + sin5x/5 + …)
|x| /2 −(4/ )(cos x + cos3x/3 2 + cos5x/5 2 +…)
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+π/ 4, 0 < x < +π
f (x) =
−π/ 4, −π< x < 0
m sin(2n −1)x
S m (x) = ∑
n=1 2n −1
lim Sm (x) = (xf )
m→∞
f S2
-3 -2 -1 1 2 3 -3 -2 -1 1 2 3
- -
-
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S1 S3
1
-3 -2 -1 1 2 3 -3 -2 -1 1 2 3
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-1
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S6 S24
-3 -2 -1 1 2 3 -3 -2 -1 1 2 3
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S12 f
-3 -2 -1 1 2 3 -3 -2 -1 1 2 3
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f(t)
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∞
f (t) = 1 a + (a cos nπ t + b sin nπ t )
2 0 ∑n=1 n L n L
1 L nπ t
an = f (t)cos dt,
L ∫− L L
L