Quick question regarding the def. of this function.

[Je m'appelle]

I have to find the Fourier Series of the following function

$$f(x) = \begin{cases} 1, & \mbox{if } 0 \leq x \leq \pi, \\ -1, & \mbox{if } 0 \leq x < 0. \end{cases}$$

My question is, is the above definition for the function f(x) correct? How can the function have two values at x = 0? Could it be a typo?

 

[hgfalling]

It's probably supposed to be -pi <= x < 0 in the second line.

 

[vela]

The way it appears now (second line reads 0≤x<0), no, it's not correct, but I'm guessing that's your typo, not the problem's. I assume that was supposed to be -π≤x<0.

 

[Je m'appelle]

It's probably supposed to be -pi <= x < 0 in the second line.

That's precisely what I was thinking about, I just wasn't so sure if there was some special condition or anything like that. Then it really is a typo. Thanks hgfalling.

 

[Je m'appelle]

The way it appears now (second line reads 0≤x<0), no, it's not correct, but I'm guessing that's your typo, not the problem's. I assume that was supposed to be -π≤x<0.

It has been posted exactly as it is in the problem, that was the whole point of this thread. But I can see it now that it really is a typo, I just needed a confirmation. Thanks vela.

 

[vela]

Oh, OK. It's just that your question about two values at x=0 didn't really make sense to me as there are no values of x such that 0≤x<0 (so the second line would never matter).