Reciprocal difference - Alchetron, The Free Social Encyclopedia

In mathematics, the reciprocal difference of a finite sequence of numbers ( x 0 , x 1 , . . . , x n ) on a function f ( x ) is defined inductively by the following formulas:

ρ 1 ( x 0 , x 1 ) = x 0 − x 1 f ( x 0 ) − f ( x 1 ) ρ 2 ( x 0 , x 1 , x 2 ) = x 0 − x 2 ρ 1 ( x 0 , x 1 ) − ρ 1 ( x 1 , x 2 ) + f ( x 1 ) ρ n ( x 0 , x 1 , … , x n ) = x 0 − x n ρ n − 1 ( x 0 , x 1 , … , x n − 1 ) − ρ n − 1 ( x 1 , x 2 , … , x n ) + ρ n − 2 ( x 1 , … , x n − 1 )

References

Reciprocal difference Wikipedia

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