Markoff's Formulas
Formulas obtained from differentiating Newton's forward difference formula,
| f^'(a_0+ph)=1/h[Delta_0+1/2(2p-1)Delta_0^2+1/6(3p^2-6p+2)Delta_0^3+...+d/(dp)(p; n)Delta_0^n]+R_n^', |
where
(n; k) is a binomial coefficient, and a_0<xi<a_n. Abramowitz and Stegun (1972) and Beyer (1987) give derivatives h^nf_0^((n)) in terms of Delta^k and derivatives in terms of delta^k and del ^k.
See also
Finite DifferenceExplore with Wolfram|Alpha
WolframAlpha
References
Abramowitz, M. and Stegun, I. A. (Eds.). Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, 9th printing. New York: Dover, p. 883, 1972.Beyer, W. H. CRC Standard Mathematical Tables, 28th ed. Boca Raton, FL: CRC Press, pp. 449-450, 1987.Referenced on Wolfram|Alpha
Markoff's FormulasCite this as:
Weisstein, Eric W. "Markoff's Formulas." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/MarkoffsFormulas.html