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Stirling's Finite Difference Formula

f_p=f_0+1/2p(delta_(1/2)+delta_(-1/2))+1/2p^2delta_0^2+S_3(delta_(1/2)^2+delta_(-1/2)^2)+S_4delta_0^4+...,
(1)

for p in [-1/2,1/2], where delta is the central difference and

S_(2n+1)=1/2(p+n; 2n+1)
(2)
S_(2n+2)=p/(2n+2)(p+n; 2n+1),
(3)

with (n; k) a binomial coefficient.

See also

Central Difference, Steffenson's 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-Stirling Formula." §23 in The Calculus of Observations: A Treatise on Numerical Mathematics, 4th ed. New York: Dover, pp. 38-39, 1967.

Referenced on Wolfram|Alpha

Stirling's Finite Difference Formula

Cite this as:

Weisstein, Eric W. "Stirling's Finite Difference Formula." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/StirlingsFiniteDifferenceFormula.html

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