Serie de Fourier Funci´ on f (t) −π < t < π f (t) = t Serie 2 ∞ X (−1)n+1 n=1 f (t) = |t| −π < t < π n sen nt ∞
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Serie de Fourier Funci´ on f (t) −π < t < π
f (t) = t
Serie 2
∞ X (−1)n+1 n=1
f (t) = |t|
−π < t < π
n
sen nt
∞ π 4 X cos (2n − 1)t − 2 π (2n − 1)2 n=1
f (t) = π − t
0 < t < 2π
2
∞ X sen nt n=1
( f (t) =
0
−π < t < 0
t
0 | Im(z) | Re(s + ω) > | Im(z) |
f 0 (t)
sF (s) − f (0)
f (n (t)
sn F (s) − sn−1 f (0) − sn−2 f 0 (0) − · · · − f (n−1 (0)
tn f (t)
(−1)n F (n (s)
eat f (t)
F (s − a)
a∈C
f (t − a)
e−as F (s)
a≥0
f (at) f (t) sen ωt f (t) cos ωt
1 s F a>0 a a 1 F (s − iω) − F (s + iω) 2i 1 F (s − iω) + F (s + iω) 2