\[\begin{array}{l} {\text{Докажите по индукции:}} \hfill \\ \sum\limits_{k = 1}^n {\frac{1}{k}} = \Psi \left( {n + 1} \right) + \gamma . \hfill \\ \Psi \left( n \right){\text{ - дигамма - функция}}{\text{, }}\Psi \left( {n + 1} \right) = \Psi \left( n \right) + \frac{1}{n}. \hfill \\ \end{array}\]

\[\begin{array}{l} \int\limits_0^1 {\frac{{\ln {{\left( x \right)}^m}}}{{1 - {x^s}}}dx} = - \frac{1}{{{s^{m + 1}}}}\Psi \left( {m,\frac{1}{s}} \right), \hfill \\ s > 0,{\text{ }}m \in \mathbb{N} \hfill \\ \end{array} \]