Definition:P-Series

Theorem
Let $p \in \C$ be a complex number.

The series defined as:
 * $\displaystyle \sum_{n \mathop = 1}^\infty \frac 1 {n^p} = 1 + \frac 1 {2^p} + \frac 1 {3^p} + \frac 1 {4^p} + \dotsb$

is known as a $p$-series.

Also defined as
Authors whose focus is on real analysis define a $p$-series for real $p$ only.

Also known as
Some sources dispose of the hyphen: $p$ series.

Also see

 * Definition:Riemann Zeta Function


 * Convergence of P-Series


 * Definition:General Harmonic Numbers: where the index remains finite