The forward difference operator, , on some function , is defined as .

 

Similarly, the backward difference operator, , on the same function , is defined as .

 

The central difference operator, , on the same function , is defined as .

 

 

From the definition of the derivate of at , we know that , or equivalently . Hence we say that for small , .

 

The difference operators are linear so that applying the difference operator on a previous difference operation leads to

 

or or .