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. \(f(x)={{\text{e}}^{sx}};\quad \sum\limits_{n=-\infty }^{\infty }{\frac{1}{{{n}^{2}}+{{s}^{2}}}}=\frac{\pi }{s}\coth \left( \pi s \right)\).

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