# Fourier series

1. Apr 25, 2004

### nizama

Hi there!!

Find the Fourier Sine series of f(x)=sin(x/2) for interval (0,pi)

thanx a lot :)

2. Apr 25, 2004

well, sin(x/2) is already a periodical function with period pi, so even if you construct a furier series of this one you would get the same: sin(x/2)

3. Apr 26, 2004

### Xishan

get the standard Fourier series for sin(X) and replace X=x/2, and thats it!

4. Apr 26, 2004

### Muzza

Wouldn't it have a period of 4pi?

5. Apr 26, 2004

### nizama

Well hmm...not really

I did get almoust correct answer BUT...
you see b_n is zero but a_n is not...and this is where i stuck ...i cant get correct a_n
by the way...can you tell me is this true?

cos(npi) + cos(0pi) = (-1)^(n+1)

thanx again

6. Apr 26, 2004

### Muzza

(Assuming n is an integer). It's not true. cos(npi) is either 1 or -1, and cos(0pi) = cos(0) = 1, so the LHS is either 1 + 1 = 2 or -1 + 1 = 0, while the RHS is either 1 or -1... So you can never get equality.

7. Apr 26, 2004

### nizama

aha

Yes i just got it..
it is when you use integr. in series
so then it would be ((-1)^n +1)

thanx

8. Apr 26, 2004

### Ebolamonk3y

couldn't you just use the regular Taylor series?

9. Apr 27, 2004

### nizama

hm

Not really
the task...as so on my exam..they strictly want it with fourier ...
bcs we do also taylor..and in task they mention which one they want..

10. Apr 27, 2004

### matt grime

THe answers would be different for a start as well.