If 
denote the zeros of 
, there exist real numbers 
such that
 |
for an arbitrary polynomial of order 
and the 
are called Christoffel
numbers. The distribution 
and the integer 
uniquely determine these numbers 
.
Gauss-Jacobi Mechanical Quadrature
See also
Gaussian QuadratureExplore with Wolfram|Alpha
References
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 QuadratureCite this as:
Weisstein, Eric W. "Gauss-Jacobi Mechanical Quadrature." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Gauss-JacobiMechanicalQuadrature.html