Definition:Harmonic Numbers/General Definition

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This page is about General Harmonic Numbers. For other uses, see Harmonic.


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

For $n \in \N_{> 0}$ the Harmonic numbers order $r$ are defined as follows:

$\ds H_n^{\paren r} = \sum_{k \mathop = 1}^n \frac 1 {k^r}$


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.