c) Use the Fourier series to calculate the sum of the series ř (-1)" 4n² – 1°
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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handwritten solution for part c
![A= 1 B = 1 C = 5
f (x) = cos (Tx) for -1/2 < x < 1/2.
Let the function be defined by
(a) Sketch f (x) on the interval [-2,2], given that f (x + 1) = f (x)
(b) Show that the Fourier series of f (x) is
(-1)"
(2n)² – 1
2
4
cos (2ntx)
-
To solve this, you can use the following similarity
2 cos A cos B = cos (A + B) + cos (A – B).
c) Use the Fourier series to calculate the sum of the series
–1)"
Š(-1)"
4n² – 1'](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff51bec3a-2485-4f5d-9267-17a2270308c8%2Fd574446d-0025-439d-8ef5-867a9c722490%2F7uk9hi_processed.png&w=3840&q=75)
Transcribed Image Text:A= 1 B = 1 C = 5
f (x) = cos (Tx) for -1/2 < x < 1/2.
Let the function be defined by
(a) Sketch f (x) on the interval [-2,2], given that f (x + 1) = f (x)
(b) Show that the Fourier series of f (x) is
(-1)"
(2n)² – 1
2
4
cos (2ntx)
-
To solve this, you can use the following similarity
2 cos A cos B = cos (A + B) + cos (A – B).
c) Use the Fourier series to calculate the sum of the series
–1)"
Š(-1)"
4n² – 1'
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