▾ 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
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}
Also known as
P-series
Child definitions
» D6074: Apéry's constant
» D4691: Standard real harmonic series
Results
» R3414: Necessary and sufficient condition for convergence of real harmonic series