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.