Interval in Fourier Series

Question

I'm new in Fourier Series, and I'm not understanding the following exercise:

Let $f$ be a odd function given by $f(x)=\pi+x$, with period $2\pi$, in $[-\pi,0[ $.

Calculate Fourier Serie.

Since $f$ is odd we have $a_n=0$ and have $b_n=\frac{2}{L} \int_{0}^{L} f(x)sen(\frac{n\pi x}{L})dx$.

However we don't have $f$ in interval $[-L,L]$. What value of $L$ should I work with in the integral?

Answer 1

Since your function is $2\pi$ periodic, any interval with length $2\pi$ will work. I suggest you use the interval $[-\pi,\pi]$.