Reciprocal Difference
The reciprocal differences are closely related to the divided difference. The first few are explicitly given by
| 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 DifferenceExplore with Wolfram|Alpha
WolframAlpha
More things to try:
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.Referenced on Wolfram|Alpha
Reciprocal DifferenceCite this as:
Weisstein, Eric W. "Reciprocal Difference." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/ReciprocalDifference.html