Gauss's interpolation formula is given by
 |
where 
is a trigonometric polynomial of degree 
such that 
for 
, ..., 
, and
![zeta_k(x)=(sin[1/2(x-x_0)]...sin[1/2(x-x_(k-1))])/(sin[1/2(x_k-x_0)]...sin[1/2(x_k-x_(k-1))])
(sin[1/2(x-x_(k+1))]...sin[1/2(x-x_(2n))])/(sin[1/2(x_k-x_(k+1))]...sin[1/2(x_k-x_(2n))]).](/images/equations/GausssInterpolationFormula/NumberedEquation2.svg) |
Gauss's Interpolation Formula
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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. 881, 1972.Beyer, W. H. (Ed.). CRC Standard Mathematical Tables, 28th ed. Boca Raton, FL: CRC Press, pp. 442-443, 1987.Referenced on Wolfram|Alpha
Gauss's Interpolation FormulaCite this as:
Weisstein, Eric W. "Gauss's Interpolation Formula." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/GausssInterpolationFormula.html