Infinite series involving hyperbolic cotangent

In this article we want to prove the following three infinte series:


\begin{align*} & \sum_{n=1}^\infty \frac{\coth(n \pi )}{n^{3} } =\frac{7\pi^3}{180}\\ & \sum_{n=1}^\infty \frac{\coth(n \pi )}{n^{7} } =\frac{19\pi^7}{56700}\\ & \sum_{n=1}^\infty \frac{\coth(n \pi )}{n^{11} } =\frac{1453\pi^{11}}{425,675,250}\\ \end{align*}



click here for the proof.


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