Find the trigonometric Fourier series for the function f(x): [-1, 1] → R given by the expression: f(x) = O [0 if x = [-1,0] 1+xifre (0, 1] 8 FS(x) = ³ + -1 FS(x) = ² + 1 FS(x) = ³ + Σ=1 FS(x) = ³ + Σ=1 -cos(nπx) sin(nTx)). (-1)"+1 n²π² (−1)”—¹ cos(nπx) nn (-1)"-1 n²77² - -сos(nπx) + 1+2(-1)" nn -cos(nπx) + 1+2(-1)" nn 1–2(−1) sin(nπx) 7²π² 1-2(-1)" NT ›) sin(nTx)). Tx)). (-1)"-1 sin(nax) 7² 7²
Find the trigonometric Fourier series for the function f(x): [-1, 1] → R given by the expression: f(x) = O [0 if x = [-1,0] 1+xifre (0, 1] 8 FS(x) = ³ + -1 FS(x) = ² + 1 FS(x) = ³ + Σ=1 FS(x) = ³ + Σ=1 -cos(nπx) sin(nTx)). (-1)"+1 n²π² (−1)”—¹ cos(nπx) nn (-1)"-1 n²77² - -сos(nπx) + 1+2(-1)" nn -cos(nπx) + 1+2(-1)" nn 1–2(−1) sin(nπx) 7²π² 1-2(-1)" NT ›) sin(nTx)). Tx)). (-1)"-1 sin(nax) 7² 7²
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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Question
![Find the trigonometric Fourier series for the function f(x) : [−1, 1] → R given by the
expression:
f(x) =
O
O
[0 if x = [-1,0]
11+xifre (0, 1]
FS(x) = ³ + x
f +Σ, (
n=1
FS(r) = ² + x1 (
n=1
8
FS(x) = ² + 1
FS (x) = ²/1 + Σ1
//
n=1
(-1)"+1
n²π²
(-1)^-1
NT
(-1)"-1
n² π²
cos(nлx) -
-
cos(nлx) +
1+2(-1)"
na
1+2(-1)"
nn
1-2(-1)"
cos(nπx) + ¹-2-¹) sin(nπx)
sin(nTr)).
COS
sin(nπx))
a)).
1-2(-1)"
NT
sin(nπx)
-cos(nπx) + -¹ sin(nra)).
(-1)" —1
7² 7²](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7fe9d10e-89b5-480b-b9fb-b8733688f212%2Fecd7eb17-8183-40c9-adca-978e89450318%2Fvk89ctg_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Find the trigonometric Fourier series for the function f(x) : [−1, 1] → R given by the
expression:
f(x) =
O
O
[0 if x = [-1,0]
11+xifre (0, 1]
FS(x) = ³ + x
f +Σ, (
n=1
FS(r) = ² + x1 (
n=1
8
FS(x) = ² + 1
FS (x) = ²/1 + Σ1
//
n=1
(-1)"+1
n²π²
(-1)^-1
NT
(-1)"-1
n² π²
cos(nлx) -
-
cos(nлx) +
1+2(-1)"
na
1+2(-1)"
nn
1-2(-1)"
cos(nπx) + ¹-2-¹) sin(nπx)
sin(nTr)).
COS
sin(nπx))
a)).
1-2(-1)"
NT
sin(nπx)
-cos(nπx) + -¹ sin(nra)).
(-1)" —1
7² 7²
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