題組內容

4. Let \( f(x) = x^2 \) for \( -2 \leq x \leq 2 \), the Fourier series of \( f(x) \) on \( [-2, 2] \) is \[ f(x) = a_0 + \frac{16}{\pi^2} \sum_{n=1}^{\infty} \frac{(-1)^n}{n^2} \cos\left(\frac{n\pi x}{2}\right) \]


(a) Find the Fourier coefficient a0 = ? (10%)