Newton's forward divided difference formula

In Worksheet 3, we have seen how the interpolating polynomial can be written in terms of divided differences, as [Maple Math]

This is called Newton's (forward) divided difference formula. The values of the coefficients can easily be calculated in table form:

[Maple Math]

............ [Maple Math]

[Maple Math] ................... [Maple Math]

............ [Maple Math] ......................... [Maple Math]

[Maple Math] ................... [Maple Math]

............ [Maple Math]

[Maple Math]

Only a simple calculation is necessary to obtain each value.