Find the trigonometric Fourier series for the function f(a): -1, 1] →→R given by the expression: f(x) = O (0 if a € (-1,0] [1 + x if a € (0, 1] FS(x) = +Σ-1 1+2(-1)" 1 11.7 -cos(nπx) + (-1)"-1 1²7² sin(nee)).
Find the trigonometric Fourier series for the function f(a): -1, 1] →→R given by the expression: f(x) = O (0 if a € (-1,0] [1 + x if a € (0, 1] FS(x) = +Σ-1 1+2(-1)" 1 11.7 -cos(nπx) + (-1)"-1 1²7² sin(nee)).
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(a): [-1, 1] → R given by the
expression:
f(x) =
f0ifa E [-1,0]
1 + x if x € (0, 1]
FS(x) = =+=1
FS(x) = ³ + Σ=1
FS(x) = ³ + -1
FS(x) = ³ + Σ=1
1+2(-1)"
THAT
(-1)"-1
7² 7²
(-1)"-1
TUTT
-cos(nTX) +
(-1)" +1
n²7²
cos(nar) +
-сos (nπx)
(-1)"-1
n²π²
-cos(na) + 1-2(1) sin(n=x)
71272
-
-sin(nπx)
1-2(-1) sin(x)
72.75
1+2(-1)"
VZ7T
sin(nTx)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F52d2dd6f-6ff9-45b4-bc92-9c80648934a4%2F9983ae36-4ade-4acc-bbc0-921bd8e58f40%2Fne18ymc_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Find the trigonometric Fourier series for the function f(a): [-1, 1] → R given by the
expression:
f(x) =
f0ifa E [-1,0]
1 + x if x € (0, 1]
FS(x) = =+=1
FS(x) = ³ + Σ=1
FS(x) = ³ + -1
FS(x) = ³ + Σ=1
1+2(-1)"
THAT
(-1)"-1
7² 7²
(-1)"-1
TUTT
-cos(nTX) +
(-1)" +1
n²7²
cos(nar) +
-сos (nπx)
(-1)"-1
n²π²
-cos(na) + 1-2(1) sin(n=x)
71272
-
-sin(nπx)
1-2(-1) sin(x)
72.75
1+2(-1)"
VZ7T
sin(nTx)
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