# 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 Donald E. Knuth.

## Also see

• Results about general harmonic numbers can be found here.