Definition:O Notation/Big-O Notation/Also known as

Also denoted as
The big-$\OO$ notation, along with little-$\mathcal o$ notation, are also referred to as Landau's symbols or the Landau symbols, for.

In analytic number theory, sometimes Vinogradov's notations $f \ll g$ or $g \gg f$ are used to mean $f = \map \OO g$.

This can often be clearer for estimates leading to typographically complex error terms.

Some sources use an ordinary $O$:
 * $f = \map O g$