Gauss-Jacobi Mechanical Quadrature

If x_1<x_2<...<x_n denote the zeros of p_n(x), there exist real numbers lambda_1,lambda_2,...,lambda_n such that


for an arbitrary polynomial of order 2n-1 and the lambda_n^'s are called Christoffel numbers. The distribution dalpha(x) and the integer n uniquely determine these numbers lambda_nu.

See also

Gaussian Quadrature

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Szegö, G. Orthogonal Polynomials, 4th ed. Providence, RI: Amer. Math. Soc., p. 47, 1975.Yakimiw, E. "Accurate Computation of Weights in Classical Gauss-Christoffel Quadrature." J. Comput. Phys. 129, 406-430, 1996.

Referenced on Wolfram|Alpha

Gauss-Jacobi Mechanical Quadrature

Cite this as:

Weisstein, Eric W. "Gauss-Jacobi Mechanical Quadrature." From MathWorld--A Wolfram Web Resource.

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