**real harmonic series**with respect to $p \in \mathbb{R}$ is the D4685: Real sequence \begin{equation} \{ 1, 2, 3, \ldots \} \to \mathbb{R}, \quad N \mapsto \sum_{n = 1}^N \frac{1}{n^p} \end{equation}

Definition D4930

Real harmonic series

Formulation 0

The **real harmonic series** with respect to $p \in \mathbb{R}$ is the D4685: Real sequence
\begin{equation}
\{ 1, 2, 3, \ldots \} \to \mathbb{R}, \quad
N \mapsto \sum_{n = 1}^N \frac{1}{n^p}
\end{equation}

Children

▶ | Apéry's constant |

▶ | Standard real harmonic series |