# Category:General Harmonic Numbers

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This category contains results about **General Harmonic Numbers**.

Definitions specific to this category can be found in Definitions/General Harmonic Numbers.

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

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

- $\ds \map {H^{\paren r} } n = \sum_{k \mathop = 1}^n \frac 1 {k^r}$

## Subcategories

This category has the following 5 subcategories, out of 5 total.

## Pages in category "General Harmonic Numbers"

The following 16 pages are in this category, out of 16 total.

### G

### S

- Sequence of General Harmonic Numbers Converges for Index Greater than 1
- Sum of General Harmonic Numbers in terms of Riemann Zeta Function
- Sum of General Harmonic Numbers in terms of Riemann Zeta Function/Corollary
- Summation over k to n of Harmonic Number k by Harmonic Number n-k
- Summation over k to n of Harmonic Numbers over n+1-k
- Summation to n of kth Harmonic Number over k
- Summation to n of kth Harmonic Number over k+1