Definition:Harmonic Numbers/General Definition

Definition
Let $r \in \R_{>0}$.

For $n \in \N_{> 0}$ the Harmonic numbers order $r$ are defined as follows:
 * $\displaystyle H_n^{\paren r} = \sum_{k \mathop = 1}^n \frac 1 {k^r}$

Notation
There is no standard notation for this series.

The notation given here is as advocated by.

Also see

 * Definition:Riemann Zeta Function: $\displaystyle H_\infty^{\paren r} = \lim_{n \mathop \to \infty} H_n^{\paren r}$


 * Definition:P-Series