Jacobi-Gauss Quadrature

Jacobi-Gauss quadrature, also called Jacobi quadrature or Mehler quadrature, is a Gaussian quadrature over the interval with weighting function

(1)

The abscissas for quadrature order are given by the roots of the Jacobi polynomials . The weights are

			(2)
			(3)

where is the coefficient of in . For Jacobi polynomials,

(4)

where is a gamma function. Additionally,

(5)

so

			(6)
			(7)

where

(8)

The error term is

(9)

(Hildebrand 1956).