Also called Jacobi Quadrature or Mehler Quadrature. A Gaussian Quadrature over the interval with Weighting Function . The Abscissas for quadrature order are given by the roots of the Jacobi Polynomials . The weights are

 (1)

where is the Coefficient of in . For Jacobi Polynomials,
 (2)

where is a Gamma Function. Additionally,

 (3)

so

 (4) (5)

where
 (6)

The error term is

 (7)

(Hildebrand 1959).

References

Hildebrand, F. B. Introduction to Numerical Analysis. New York: McGraw-Hill, pp. 331-334, 1956.