[UPSC CSE 1986] Waves (Q115, 20M)

Out of the following three functions only one can be Fourier analysed in the range -\pi \leqslant x \leqslant \pi. Choose the correct function and obtain its Fourier series expansion: (i) f(x) = x^{2} \text{ for } 0 < x < \pi (ii) f(x) = 0 \text{ for } -\pi < x < 0 = \pi \text{ for } 0 < x < \pi (iii) f(x) = 1/x^{2} \text{ for } -\pi < x < \pi