f(x) = x² si xe[- n; ¤] The Fourier series of the function (f) is as follows: n=+00 f(x) = ao + > a, cos(nx). n=1 Deduct the sum Sn=t0 (-1)" . n2 1. 2. Using Parseval's formula n=+00 1 [f(x)]² dx = a¿ + 2 ai + bå , n=1 To show that : Sn=+∞ 1 Ln=i n4 90 ||
f(x) = x² si xe[- n; ¤] The Fourier series of the function (f) is as follows: n=+00 f(x) = ao + > a, cos(nx). n=1 Deduct the sum Sn=t0 (-1)" . n2 1. 2. Using Parseval's formula n=+00 1 [f(x)]² dx = a¿ + 2 ai + bå , n=1 To show that : Sn=+∞ 1 Ln=i n4 90 ||
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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![Duration: 12 hours
Exercise 1 :
The function (f), periodic, is defined by:
f(x) 3 х? si xе[-п; т]
The Fourier series of the function (f) is as follows:
n=+00
f(x) — а, +
an cos(nx).
n=1
Deduct the sum: Sn=+∞(-1)"
n2
En=1
1.
2.
Using Parseval's formula
1
n=+00
1
[f(x)]? dx
a +
> ai + bỉ ,
n=1
To show that: n=1
n=+0
n4
90](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F40324ad2-76ec-40f8-9ce6-bd770ddaf3da%2F35ed8b97-c14f-4ec7-a853-c3394a2fa7c5%2Friwm3s_processed.png&w=3840&q=75)
Transcribed Image Text:Duration: 12 hours
Exercise 1 :
The function (f), periodic, is defined by:
f(x) 3 х? si xе[-п; т]
The Fourier series of the function (f) is as follows:
n=+00
f(x) — а, +
an cos(nx).
n=1
Deduct the sum: Sn=+∞(-1)"
n2
En=1
1.
2.
Using Parseval's formula
1
n=+00
1
[f(x)]? dx
a +
> ai + bỉ ,
n=1
To show that: n=1
n=+0
n4
90
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