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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

R_n^'=h^nf^((n+1))(xi)d/(dp)(p; n+1)+h^(n+1)(p; n+1)d/(dx)f^((n+1))(xi),

(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 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. 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 Formulas

Cite this as:

Weisstein, Eric W. "Markoff's Formulas." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/MarkoffsFormulas.html

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