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The Bernoulli constants
\beta_n are defined for n \ge 0 as
\begin{equation} { \beta_n \, = \, 2\pi \! \int\limits_{- \infty }^{+\infty }{\frac { \log\! \left( \frac{1}{2} + iz \right) ^n } {\left( {{\exp}^{- \pi \,z}}+{{\exp}^{\pi \,z }} \right) ^{2}}}\,{dz} . } \end{equation}

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