Reciprocal difference

In mathematics, the reciprocal difference of a finite sequence of numbers (x0,x1,...,xn) on a function f(x) is defined inductively by the following formulas:

ρ1(x1,x2)=x1−x2f(x1)−f(x2)

ρ2(x1,x2,x3)=x1−x3ρ1(x1,x2)−ρ1(x2,x3)+f(x2)

ρn(x1,x2,…,xn+1)=x1−xn+1ρn−1(x1,x2,…,xn)−ρn−1(x2,x3,…,xn+1)+ρn−2(x2,…,xn)

## See also

* Divided differences

## References

* Weisstein, Eric W.. "Reciprocal Difference". http://mathworld.wolfram.com/ReciprocalDifference.html.
* Abramowitz, Milton; Irene A. Stegun (1972) [1964]. Handbook of Mathematical Functions (ninth Dover printing, tenth GPO printing ed.). Dover. p. 878. ISBN 0-486-61272-4.

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