Definition of Divided Differences
The zeroth divided difference of the function with respect to is simply the function evaluation at : .
The first divided difference of the function with respect to and is given by .
Given the ( )-th divided differences and are known, one can calculate the -th divided difference as .
This formula can be used to calculate all divided differences from -st till -th . Notice that we only use forward differences, i.e. the later value minus the earlier value, as in
, or , .