# Definition:Schwarz Function

## Definition

Let $f: \R \to \C$ be a function.

$f$ is a Schwarz function if and only if:

$\forall c \in \R, n \in \N_0: \left\vert{f^{\left({n}\right)} \left({x}\right)}\right\vert = o \left({\left\vert{x}\right\vert^c}\right)$

where:

$f^{\left({n}\right)}$ denotes the $n$th derivative
$o$ is the little-o notation.

## Source of Name

This entry was named for Karl Hermann Amandus Schwarz.