**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}

▾ Set of symbols

▾ Alphabet

▾ Deduction system

▾ Theory

▾ Zermelo-Fraenkel set theory

▾ Set

▾ Binary cartesian set product

▾ Binary relation

▾ Map

▾ Operation

▾ N-operation

▾ Binary operation

▾ Enclosed binary operation

▾ Groupoid

▾ Semigroup

▾ Standard N-operation

▾ Indexed sum

▾ Series

▾ Harmonic complex series

▾ Alphabet

▾ Deduction system

▾ Theory

▾ Zermelo-Fraenkel set theory

▾ Set

▾ Binary cartesian set product

▾ Binary relation

▾ Map

▾ Operation

▾ N-operation

▾ Binary operation

▾ Enclosed binary operation

▾ Groupoid

▾ Semigroup

▾ Standard N-operation

▾ Indexed sum

▾ Series

▾ Harmonic complex 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}

Also known as

P-series

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