\begin{definition}[Definition:Harmonic Numbers/General Definition]
Let $r \in \R_{>0}$.
For $n \in \N_{> 0}$ the '''Harmonic numbers order $r$''' are defined as follows:
:$\ds H_n^{\paren r} = \sum_{k \mathop = 1}^n \frac 1 {k^r}$
\end{definition}