Fourier Series Question

**craig** · November 23rd 2010, 10:31 AM

Think this is a pretty simple question, just getting stuck on the last section, here's what I've got:

Let $f$ be a periodic function with period 6, such that $f(x) = x \: \text{for} \: -3 < x \leq 3$ . Calculate the Fourier series of $f$ .

Odd function, so we know $a_0 = a_n = 0$ .

$b_n = \frac{2}{3} \int_0^3 x \cos{\frac{\pi n}{3} x} \: dx$

...

$= \frac{6}{\pi^2n^2}(\cos{\pi n} - \cos{0})$

$= \frac{6}{\pi^2n^2}((-1)^n - 1)$ .

However in the answer they've got:

$\frac{6}{\pi} \displaystyle\sum\limits_{n=1}^{\infty} \frac{(-1)^{n+1}}{n}\sin{\frac{\pi n}{3} x}$ .

Just wondering how they get to the $\frac{6}{\pi} \frac{(-1)^{n+1}}{n}$ , as far as I can see my integration's correct?

Thanks in advance for the help

**tonio** · November 23rd 2010, 01:29 PM

Originally Posted by craig

Think this is a pretty simple question, just getting stuck on the last section, here's what I've got:

Let $f$ be a periodic function with period 6, such that $f(x) = x \: \text{for} \: -3 < x \leq 3$ . Calculate the Fourier series of $f$ .

Odd function, so we know $a_0 = a_n = 0$ .

$b_n = \frac{2}{3} \int_0^3 x \cos{\frac{\pi n}{3} x} \: dx$

...

$= \frac{6}{\pi^2n^2}(\cos{\pi n} - \cos{0})$

$= \frac{6}{\pi^2n^2}((-1)^n - 1)$ .

However in the answer they've got:

$\frac{6}{\pi} \displaystyle\sum\limits_{n=1}^{\infty} \frac{(-1)^{n+1}}{n}\sin{\frac{\pi n}{3} x}$ .

Just wondering how they get to the $\frac{6}{\pi} \frac{(-1)^{n+1}}{n}$ , as far as I can see my integration's correct?

Thanks in advance for the help

As far as I can see your answer's correct, and I wonder what happened to the squared pi and n in the denominator, not to mention

the numerator.

Is this from some book? Perhaps you misread the number of the question...?

Tonio

**craig** · November 24th 2010, 12:23 AM

I don't think so. I'll try find the questions and post them here.

**craig** · November 24th 2010, 12:30 AM

Here's the question:

And here's the answer. Sorry about the quality, this is how I received it. There's no indication as to how they've come by the answer as far as I can tell.

It's solution number 2 by the way.

Thanks for the relpy

Thread: Fourier Series Question

LinkBack

Thread Tools

Display

Fourier Series Question

Similar Math Help Forum Discussions

Fourier series question

question about sum of fourier series

Question about Fourier Series

Fourier Series Question

A question on Fourier series

Search Tags