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Reciprocal Difference

The reciprocal differences are closely related to the divided difference. The first few are explicitly given by

rho(x_0,x_1)=(x_0-x_1)/(f_0-f_1)
(1)
rho_2(x_0,x_1,x_2)=(x_0-x_2)/(rho(x_0,x_1)-rho(x_1,x_2))+f_1
(2)
rho_3(x_0,x_1,x_2,x_3)=(x_0-x_3)/(rho_2(x_0,x_1,x_2)-rho_2(x_1,x_2,x_3))+rho(x_1,x_2)
(3)
rho_n(x_0,x_1,...,x_n) =(x_0-x_n)/(rho_(n-1)(x_0,...,x_(n-1))-rho_(n-1)(x_1,...,x_n))+rho_(n-2)(x_1,...,x_(n-1)).
(4)

See also

Backward Difference, Central Difference, Divided Difference, Finite Difference, Forward Difference

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References

Abramowitz, M. and Stegun, I. A. (Eds.). Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, 9th printing. New York: Dover, p. 878, 1972.Beyer, W. H. (Ed.). CRC Standard Mathematical Tables, 28th ed. Boca Raton, FL: CRC Press, p. 443, 1987.

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Reciprocal Difference

Cite this as:

Weisstein, Eric W. "Reciprocal Difference." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/ReciprocalDifference.html

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