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Gauss's Forward Formula

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Gauss's forward formula is

f_p=f_0+pdelta_(1/2)+G_2delta_0^2+G_3delta_(1/2)^3+G_4delta_0^4+G_5delta_(1/2)^5+...,
(1)

for p in [0,1], where delta is the central difference and

G_(2n)=(p+n-1; 2n)
(2)
G_(2n+1)=(p+n; 2n+1),
(3)

where (n; k) is a binomial coefficient.

See also

Central Difference, Gauss's Backward Formula

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References

Beyer, W. H. CRC Standard Mathematical Tables, 28th ed. Boca Raton, FL: CRC Press, p. 433, 1987.Whittaker, E. T. and Robinson, G. "The Newton-Gauss Formula for Interpolation." §21 in The Calculus of Observations: A Treatise on Numerical Mathematics, 4th ed. New York: Dover, pp. 36-37, 1967.

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Gauss's Forward Formula

Cite this as:

Weisstein, Eric W. "Gauss's Forward Formula." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/GausssForwardFormula.html

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