Definition:Replicative Function
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Definition
A replicative function is a real function $f$ such that:
- $\ds \forall n \in \Z_{\ge 0}: \sum_{k \mathop = 0}^{n - 1} \map f {x + \frac k n} = \map f {n x}$
where $\sum$ denotes indexed summation.
Also see
- Results about replicative functions can be found here.
Sources
- 1997: Donald E. Knuth: The Art of Computer Programming: Volume 1: Fundamental Algorithms (3rd ed.) ... (previous) ... (next): $\S 1.2.4$: Integer Functions and Elementary Number Theory: Exercise $39$