$$\frac{1}{2}x\frac{{{e^x} + 1}}{{{e^x} - 1}} = \sum\limits_{k = 0}^{ + \infty } {\frac{{\operatorname{bernoulli} \left( {2k} \right)}}{{\left( {2k} \right)!}}{x^{2k}}} ,{\text{ }}\left| x \right| < 2\pi $$