Definition:Replicative Function

Definition

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

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

Sources

• Donald E. Knuth: The Art of Computer Programming: Volume 1: Fundamental Algorithms (1968): $\S 1.2.4$: Exercises $39$