Newton’s second interpolation formula

Newton’s first interpolation formula is practically inconvenient for interpolation of functions near to end of the table. In this case usually Newton’s second interpolation formula is applied:

(4)

The detailed conclusion of the formula (4) is resulted in [1].

Let's note, that if and х it is close to it is meaningful to apply Newton’s first interpolation formula, if and х it is close to , in this case is more convenient for using Newton’s second interpolation formula. In other words, Newton’s first interpolation formula is used usually for interpolation forward , and Newton’s second interpolation formula – for interpolation back .