# Finding the Fourier series for a function on a defined interval

Consider the function $$\phi(x) = \begin{cases} 0 \ \ &-4\leq x < -2,\\ 4 - x^2 \ \ &-2\leq x \leq 2, \\ 0 \ \ &2 < x \leq 4 \end{cases}$$

Defined on the interval $[-4,4]$. Find the Fourier series of $\phi$.

Is this the equation I need to use? $$\phi(x) = \frac{1}{2}A_0 + \sum_{n=1}^{\infty}A_n\cos\frac{n\pi x}{l} + \sum_{n=1}^{\infty} B_n \sin\frac{n\pi x}{l}$$

• You forgot the summation sign before $B_n$. – Mark Fischler May 2 '18 at 22:39
• And you need to think about what $\ell$ would be in that equation... – Mark Fischler May 2 '18 at 22:40
• The definition of the ranges for $\phi (x)$ is incorrect. I think you meant $2\le x\le 4$ for the third interval. – herb steinberg May 3 '18 at 0:19
• @herbsteinberg Ah, yes I did, thank you. – KBG May 3 '18 at 2:28
• @MarkFischler would $l$ be 4? – KBG May 3 '18 at 2:39