Find the trigonometric Fourier series for the function f(x): [-T, T] → R given by the expression: sin x if x = [-T, 0] f(x) = { 0 if z € (0, π] O FS(x) = - +n=2 (n²-1) π O FS (x) = 1 +n-2 FS(x) = - (-1)" cos (nx) - sinx. O FS(x) = 2 + 1+(-1)^ n-2 (n²+1) cos(nx) - sin x. 1+(-1)" cos(nx) + sinx. + En-2 (n²-1) T 1-(-1)" Zn-2 (n²-1) -sin(nx) — sin r. 1+(-1)^ -cos(nx) + sinx. O FS(x) = - +Σn=2 (n-1)π 2п
Find the trigonometric Fourier series for the function f(x): [-T, T] → R given by the expression: sin x if x = [-T, 0] f(x) = { 0 if z € (0, π] O FS(x) = - +n=2 (n²-1) π O FS (x) = 1 +n-2 FS(x) = - (-1)" cos (nx) - sinx. O FS(x) = 2 + 1+(-1)^ n-2 (n²+1) cos(nx) - sin x. 1+(-1)" cos(nx) + sinx. + En-2 (n²-1) T 1-(-1)" Zn-2 (n²-1) -sin(nx) — sin r. 1+(-1)^ -cos(nx) + sinx. O FS(x) = - +Σn=2 (n-1)π 2п
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![Find the trigonometric Fourier series for the function f(x): [-T, π] → R given by the expression:
J sinc if x = [-T, 0]
0 if x = (0, π]
f(x) =
(-1)"
O FS(x) = -²/+n=2 (n²-1) π
O FS(x) =
+-2 1+(-1)^ cos(nx) - sinx.
n=2 (²+1)
-cos(nx) - sinx.
1+(-1)" cos(nx) + sinx.
FS(x) = - +En-2 (n²-1) π
1-(-1)"
FS(x) = ² + n-2 (n²-1) π
п
FS(x) = - +-2
2π
-sin(nữ) — sin 2.
1+(-1)^
(n-1) T
-cos(nx) + sinx.
W](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F12c62ea9-2423-4a35-a6cd-74646c6bbd41%2Fb41059f2-af49-4c0c-910d-73c276ad0a38%2Fgez8qyi_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Find the trigonometric Fourier series for the function f(x): [-T, π] → R given by the expression:
J sinc if x = [-T, 0]
0 if x = (0, π]
f(x) =
(-1)"
O FS(x) = -²/+n=2 (n²-1) π
O FS(x) =
+-2 1+(-1)^ cos(nx) - sinx.
n=2 (²+1)
-cos(nx) - sinx.
1+(-1)" cos(nx) + sinx.
FS(x) = - +En-2 (n²-1) π
1-(-1)"
FS(x) = ² + n-2 (n²-1) π
п
FS(x) = - +-2
2π
-sin(nữ) — sin 2.
1+(-1)^
(n-1) T
-cos(nx) + sinx.
W
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