# Frouier series problem

[SOLVED] Frouier series problem

Lately I took Frouier series...
1. Homework Statement

Find the Fourier series of the function below which is assumed to have the period 2 $$\pi$$, and find the first three partial sums.

http://www.imagehosting.com/out.php/i1650739_untitled.JPG

2. Homework Equations

3. The Attempt at a Solution

I used office 2007 to write my solution....and here they are hosted as a picture..
http://www.imagehosting.com/out.php/i1650792_untitled1.JPG

I see my answer not correct, I hope someone helps me..Thanks

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G01
Homework Helper
Gold Member
You are correct to integrate from -pi to pi in the integral, but your function is non-zero over that entire interval, so I do not know why you have the function value as 0 in $$[-\pi , -\pi/2]$$ and $$[\pi/2 , \pi]$$.

Also I believe your constant in front of your integral for a_n is incorrect. The constant in front of that integral should be:

$$\frac{2}{Period}=\frac{2}{2\pi}=\frac{1}{\pi}$$

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sorry, there is a wrong in the picture of the function...the correction is
-2Pi becomes -Pi; -Pi becomes -Pi/2; Pi becomes P/2; and 2Pi becomes Pi.

so 'GO' the 0's in the integrals you specified becomes right with me..and you are correct about a_n, it should be 1/Pi and the same in the denominator of the cosine in that line..

G01
Homework Helper
Gold Member
sorry, there is a wrong in the picture of the function...the correction is
-2Pi becomes -Pi; -Pi becomes -Pi/2; Pi becomes P/2; and 2Pi becomes Pi.

so 'GO' the 0's in the integrals you specified becomes right with me..and you are correct about a_n, it should be 1/Pi and the same in the denominator of the cosine in that line..
OK your integration makes sense then.

BTW. I usually imagine my PF name being pronounces "G Zero One." So, was the constant your problem or do are you still having trouble?

yes it was the constant..it's now solved..thanks

G01
Homework Helper
Gold Member
Glad to be of help. 