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Gauss's Interpolation Formula

f(x) approx t_n(x)=sum_(k=0)^(2n)f_kzeta_k(x),

where t_n(x) is a trigonometric polynomial of degree n such that t_n(x_k)=f_k for k=0, ..., 2n, 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))]).

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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.

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Gauss's Interpolation Formula

Cite this as:

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

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