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The principal part of the [[Schwarz symmetric derivative|Schwarz symmetric derivative]] of order  $  n $. 
More precisely, if for a function  $  f $
of a real variable,

$$ 
\Delta  ^ {n} f ( x, \Delta x)  =  \sum _ { k= } 0 ^ { n }  \left (
\begin{array}{c}
n \\
 k 
\end{array}
 \right ) (- 1)  ^ {k}
f \left ( x + n- 
\frac{2k}{2}
 \Delta x \right ) =
$$

$$ 
= \ 
A \cdot ( \Delta x)  ^ {n} + o(( \Delta x)  ^ {n} ),
$$

then the expression  $  A \cdot ( \Delta x)  ^ {n} $
is called the Schwarz differential of order  $  n $. 
When a Schwarz differential is mentioned without specifying the order, it is usually assumed that  $  n= 2 $.