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 , .