Definition:Summatory Function

Definition
Let $a: \N \to \C$ be an arithmetic function.

Its summatory function is the mapping:
 * $A \left({x}\right) = \displaystyle\sum_{n \mathop \le x} a \left({n}\right)$

defined for $x \in \Z_{\ge 0}$.

Also see

 * Definition:Asymptotic Mean Value
 * Abel's Summation Formula