# Definition:Replicative Function

## Definition

A replicative function is a real function $f$ such that:

$\displaystyle \forall n \in \Z_{\ge 0}: \sum_{k \mathop = 0}^{n - 1} f \left({x + \frac k n}\right) = f \left({n x}\right)$

where $\sum$ denotes indexed summation.

## Also see

• Results about replicative functions can be found here.