Fourier series

  • Thread starter kieranl
  • Start date
  • #1
24
0

Homework Statement



Compute the Fourier series for the given function f on the specified interval
f(x) = x^2 on the interval − 1 < x < 1

The Attempt at a Solution




Just wondering if anyone can verify my answer?

f(x)=1/3+[tex]\sum[/tex](4/(n^2*pi^2)*(-1)^n*cos(n*pi*x))

Homework Statement





Homework Equations





The Attempt at a Solution

 

Answers and Replies

  • #2
Cyosis
Homework Helper
1,495
0
Yep that is correct.
 
  • #3
24
0
cheers
 
  • #4
24
0
the next part of the question says to determine if the function to which the fourier series for f(x) converges?? does this make sense to anyone?
 
  • #5
Cyosis
Homework Helper
1,495
0
Is that exactly how the question is asked in your text? The "if" confuses me. I guess what they are asking you is if the Fourier series you just derived converges. Which is pretty easy to show.
 
  • #6
24
0
how do you show that it converges?? just pick example numbers??
 
  • #7
Cyosis
Homework Helper
1,495
0
That would mean you would have to pick an infinite amount of numbers though. To show that it converges compare it to a series you know to be convergent. For example, [itex]\sum_{n=1}^\infty \frac{1}{n^2}[/itex]. You could also try the root test and or ratio test.
 
  • #8
jbunniii
Science Advisor
Homework Helper
Insights Author
Gold Member
3,446
224
That would mean you would have to pick an infinite amount of numbers though. To show that it converges compare it to a series you know to be convergent. For example, [itex]\sum_{n=1}^\infty \frac{1}{n^2}[/itex]. You could also try the root test and or ratio test.
You should even be able to show uniform convergence if you use the right test.
 
  • #9
txy
15
0
there are theorems that state that when the function satisfies certain conditions, the Fourier series of the function converges to some expression. if you have learned these theorems, then it's quite easy to show that the Fourier series converges to the function itself.
 

Related Threads on Fourier series

Replies
5
Views
9K
  • Last Post
Replies
21
Views
1K
  • Last Post
Replies
1
Views
1K
  • Last Post
Replies
7
Views
658
  • Last Post
Replies
2
Views
2K
  • Last Post
Replies
7
Views
1K
  • Last Post
Replies
6
Views
3K
  • Last Post
Replies
1
Views
1K
  • Last Post
Replies
8
Views
1K
  • Last Post
Replies
3
Views
674
Top