Question: Find the Fourier series of the following functions on \([-\pi, \pi].\) and use Corollary 5.7 to deduce the stated formulae.

1. \(f(x)=x\) \(\sum_{n=1}^{\infty} \frac{1}{n^{2}}=\frac{\pi^{2}}{6}\)
2. \(f(x)=x^{2} ; \quad \sum_{n=1}^{\infty} \frac{1}{n^{4}}=\frac{\pi^{4}}{90}\).
3. \(f(x)=\mathrm{e}^{s x} ; \quad \sum_{n=-\infty}^{\infty} \frac{1}{n^{2}+s^{2}}=\frac{\pi}{s}\) \(\coth \left( \pi s \right)\) .

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