# Homework Help: Help With Fourier Series Expansion of a Periodic Function

1. Dec 3, 2011

### ediggity

1. The problem statement, all variables and given/known data

f(t) defined by f(t) = |t| for (-pi,pi) and f(t+2pi)=f(t)

the graph is just ^^^

where w=2pi/T = 1

2. Relevant equations

Periodic function using Trigonometric from

Even Function f(t) = (1/2)anot + (the sum from n=1 to inf) (an)*COS(nwt), where an = 4/T Integrated from 0 to T/2 f(t)*COS(nwt)dt, where T= 2pi

3. The attempt at a solution

My answer: I used integration by parts and calculated pi/2 +(the sum from n=1 to inf) (4/(pi)n^2)*COS(nt),

where anot/2 = 1/T integrated from -T/2 to T/2 f(t)dt, anot=pi

The book answer has pi/2- [4/pi *the sum from n=1 to inf (1/(2n-1)^2*COS(2n-1)t

Can anyone tell me if I basically have the same thing?

Thanks.

2. Dec 4, 2011

### HallsofIvy

No, they are not at all the same thing. Your sum has cos(nt) for all n. The second sum only odd integers times t.