Gauss-Jacobi Mechanical Quadrature

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 .

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.