Definition:Ordinary Mean Value

Definition

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

The (ordinary) mean value of $f$ is the limit:

$\map M f = \ds \lim_{x \mathop \to \infty} \frac 1 x \sum_{n \mathop \le x} \map f n$

if it exists.

Also known as

The ordinary mean value is also known as asymptotic mean value, or simply mean value.

Also see

• Definition:Logarithmic Mean Value